Dunja Perić

On the analytical solutions for the three-invariant Cam clay model

Abstract The analytical solutions are presented for a generalized shear strain, based on the three-invariant Cam clay model. The solutions are derived for an undrained loading by adopting the assumption of incompressibility, which is valid for any fully saturated soil. Two loading histories are considered: the so-called proportional and circular loading. They correspond to the situations where Lodes angle θ is either constant or changing during loading, respectively. The maximum possible change in Lodes angle for any circular loading is equal to π ⧸3 due to plastic isotropy. Failure occurs within this segment only for the cases which are loaded from higher initial values of the overconsolidation ratio. The solutions presented here complete the picture of the undrained stress–strain-strength behavior for the soft clays by defining the analytical relationship between a shear strain and a stress ratio.

Influence of Lode’s angle on the pore pressure generation in soils

Abstract The equation which describes generation of a pore pressure during undrained loading is derived, on the basis of a general three-invariant plasticity model. A new pore pressure parameter c , is identified. This parameter describes coupling between the mean effective stress and Lode′s angle. The pore pressure equation is applied to the three-invariant Cam clay model. Two sets of loading histories are presented: proportional and circular stress paths. Analytical solutions for tangent and secant values of the pore pressure parameters a and c are obtained. In addition, analytical solutions for the specific volume and volumetric strain during any drained stress controlled loading are derived. Furthermore, the solution for the effective stress path during undrained loading is then obtained as a special case of a drained loading, for which the rate of volume change is equal to zero. It is shown that the effective stress path for an undrained loading depends on the total stress path. Moreover, it is found that the limiting initial overconsolidation ratio below which an isotropically plastic soil does not fail when subjected to a circular stress path, depends on the compressibility and ellipticity parameters of the soil.

Assessment of sand stabilization potential of a plant-derived biomass

Abstract Lignin is a coproduct of biofuel and paper industries, which exhibits binding qualities when mixed with water. Lignin is an ideal candidate for a sustainable stabilization of unpaved roads. To this end, an experimental program was devised and carried out to quantify effects of lignin on compaction and early age shear strength behaviors of sand. Samples were prepared by mixing a particular type of coproduct called calcium lignosulfonate (CaL) with sand and water. Based on the extensive analyses of six series of strength tests, it was found that a normalized cohesion increased with an increasing normalized areas ratio. Normalizations were carried out by dividing the cohesion and area ratio by gravimetric CaL content whereby the area ratio was obtained by dividing the portion of the cross-sectional area occupied with lignosulfonate-water (CaL-W) paste by the total cross-sectional area. While the increase in the normalized cohesion eventually leveled out, the cohesion peaked at 6% of CaL. Thus, sand-CaL-water (S-CaL-W) mixes sustained larger shear stresses than dry sand for a range of normal stresses below the limiting normal stress. Consequently, the early age behavior indicates that adding CaL-W to sand is clearly beneficial in the near-surface applications in dry sand.

Assessment of wheat fibre reinforced cementitious matrix

The technology of using synthetic fibres in reinforced concrete structures continues to mature. This research is intended to address the use of natural fibres derived from wheat straws for reinforcing cementitious matrix specimens. In order to study the properties of the cementitious matrix reinforced with wheat fibres, 156 specimens were tested in uniaxial compression and flexure. The compression tests were conducted on 2 in (50.8 mm) cubes, while the flexural tests were conducted on 1.58 × 1.58 × 6.30 in (40 × 40 × 160 mm) prisms. Several lengths of fibres and percentages in the range of 0.5% to 5% by volume of the specimens were tested in order to determine which would yield the highest load and stiffness. Specimens reinforced with polypropylene fibres were tested in order to benchmark the results. The average uniaxial compression load of the specimens reinforced with 0.5% long wheat fibres exceeded that of their counterparts reinforced with 0.5% polypropylene fibres by 15%.

Onset of Strain Localization in Fiber Reinforced Composites Subjected to Plane Stress Loading

The main objective of this study was to find analytical solutions for the onset of strain localization in fiber reinforced composites subjected to plane stress loading. In particular, elastic multidirectional fibers are embedded into an elastic-plastic matrix. A macroscopic tangent stiffness tensor of the fiber-reinforced composite is obtained by consistently homogenizing the contribution of fibers in a cylindrical representative volume element. Upon deriving analytical solutions their properties are further illustrated on the example of Drucker–Prager model. Results show that fibers decrease the critical hardening modulus, thus inhibiting the onset of strain localization. The main fiber parameters that control the stress level at the inception of strain localization are their volumetric content and their stiffness modulus.

Onset of Strain Localization in Unsaturated Soils Subjected to Constant Water Content Loading

Analytical solutions for the inception of strain localization in unsaturated soils were implemented into the constitutive driver for a bounding surface plasticity model. Effects of the initial net mean stress and initial suction on the inception of strain localization in a porous material subjected to constant water content plane strain compression (PSC) were investigated. It was found that decreases in both, the initial suction and the initial net mean stress decreased the axial strain at onset, thus effectively increasing the susceptibility to strain localization. The corresponding deformation bands were largely contractant shear bands. Dilatant shear bands occurred only for the initial over consolidation ratios (OCR) larger than 3.25.

Meso-Scale Evolution of Shear Localization Observed in Plane Strain Experiment on Kaolin Clay

Undrained plane strain compression experiments were conducted on slurry consolidated kaolin clay samples to elucidate the mechanism of shear localization in clays. The biaxial device was heavily internally instrumented, thus enabling the multiple boundary displacement measurements. These measurements were combined with boundary digital imaging to compute and verify displacements of the shear band. The orientation of shear band was determined from photographs thus enabling the computation of its dilatancy angle. Finally, the volumetric and shear strains of the shear band were computed for two limiting initial thicknesses of the shear band corresponding to 1 mm and 1.5 mm. The computed meso scale strains are several times larger than those reported in sand

Propagation and Evolution of Strain Localization in Clay

This research focuses on propagation and evolution of strain localization in clay. To this end, an undrained plane strain compression test program was performed to investigate the effects of the past stress history and strain rates on the strain localization response of kaolin clay. Results of a single test (T3) are presented herein. They include the overall global stress/pore pressure versus axial strain response, as well as indicators of propagation and evolution of strain localization. The results indicate that the response consisted of the three distinct phases: (1) a homogenous deformation, (2) an inception and propagation of strain localization, and (3) an evolution of strain localization within the shear band. The Lagrange strain tensor was used to obtain local volumetric and shear strains developed within the shear band during the evolution stage. It was found that local volumetric and shear strains reached 80% and 200% respectively, which corresponds to a global axial strain increment of only 1.7%. Furthermore, the shear band exhibited a decreasing tendency to compress, thus resulting in its incremental dilatancy angle varying from initially −24° to a final value of −6°.

Strain Localization in High Performance Fiber Reinforced Cementitious Composites

High Performance Fiber Reinforced Cementitious Composite (HPFRCC) is a cementitious composite, which consists of a specifically tailored cementitious matrix reinforced with short discrete fibers that have a proper geometry and enhanced bond properties in order to improve tensile properties of the overall composite. Despite all of its beneficial properties HPFRCC has not yet found its way into the engineering practice largely due to the lack of adequate numerical models. To this end, the main objective of this research was to develop and implement a combined analytical-numerical algorithm that can capture a stress-strain response and inception of strain localization in elastic-plastic HPFRCC. Multi-directional fibers are embedded into a matrix and modeled as a linear elastic material, while the resulting composite is described by a two-invariant non-associated non-linear Drucker-Prager hardening plasticity model. A diagnostic strain localization analysis was conducted for several uniaxial tension and uniaxial compression tests on a non-reinforced cementitious composite as well as on the HPFRCC. It was found that the presence of fibers delayed the inception of strain localization in all tests on the HPFRCC. Furthermore, it appears that the onset of strain localization in uniaxial tension on HPFRCC detects the inception of distributed cracking, while the onset of strain localization in uniaxial compression detects the onset of more localized cracking.

Strain Localization Analysis of an Elastic-Plastic Model for High Performance Fiber Reinforced Cementitious Composites

The main goal of this study was to develop and implement a combined analyticalnumerical algorithm that can capture a stress-strain response and onset of strain localization in elastic-plastic fiber-reinforced cementitious composites. Multi-directional fibers are embedded into a matrix and the resulting composite is described by different non-linear, non-associated DruckerPrager hardening plasticity models. The corresponding macroscopic tangent stiffness moduli tensor of the fiber reinforced composite is derived by consistently homogenizing the contribution of fibers in a representative volume element (RVE). Several actual uniaxial tension tests on non-reinforced cementitious composite as well as on the High Performance Fiber Reinforced Cementitious Composites (HPFRCC) were modelled. It was found that the presence of fibers delayed the inception of strain localization in all uniaxial tension tests on the HPFRCC as compared to the plain mortar. However, the onset of strain localization always coincided with yielding, thus indicating a slight fiber induced increase in the yield stress. More importantly, the results indicate that a significant increase in the peak load that is exhibited by HPFRCC is due to a distributed cracking that causes a global level hardening culminating in the significantly increased peak loads. Furthermore, the results also indicate that presence of fibers did not have any effect on the orientation and mode of accompanying deformation bands.