Critical State for Anisotropic Granular Materials: A Discrete Element Perspective

Summary A bounding surface model is formulated to simulate the behavior of clays that are subject to an anisotropic consolidation stress history. Conventional rotational hardening is revisited from the perspective of thermodynamics. As the free energy cannot be accumulated infinitely upon critical state failure, the deviatoric back stress must vanish. This requires the rotated yield surface to be turned back to eventually align on the hydrostatic axis in the stress plane. Noting that most of the previous propositions violate this restriction, an innovative rotational hardening rule is formulated that is thermodynamically admissible. The bounding surface framework that employs the modified yield surface is applied to simulate elastoplastic deformations for overconsolidated clays, with which the overprediction of strength on the “dry” side can be greatly improved with reasonable results. Other important features, including contractive or dilative response and hardening or softening behavior, can also be well‐captured. It has been shown that the model can simulate three types of reconstituted clays that are sheared with initial conditions over a wide range of anisotropic consolidation stress ratios and overconsolidation ratios under both triaxial undrained and drained conditions. Limitations and potential improvement of the model regarding the fabric anisotropy at critical state have been discussed.

Section: Discussionmentioning

confidence: 99%

A bounding surface model for anisotropically overconsolidated clay incorporating thermodynamics admissible rotational hardening rule

Chen

Yang

2019

“…It simply describes the state at which soils continuously deform in shear with constant stresses and volume . The condition for soils reaching the critical state can be analytically expressed as

\overset{p}{true} = 0, \overset{s}{true} = 0, {\dot{ε}}_{v} = 0 but {\dot{ε}}_{q} \neq 0,

where p is the mean effective stress, s is the deviatoric part of the stress tensor, ε v is the volumetric strain, ε q is the deviatoric strain, and a superposed dot signifies the rate. Therefore, on reaching the critical state, the following conditions should be satisfied:

η = η_{c} = {(q / p)}_{c} = M ((), θ),

e = e_{c} ((), p),

where η is the stress ratio and the subscript c denotes the critical state.…”

Section: Anisotropic Critical State Theorymentioning

confidence: 99%

“…The prominent debate is related to the fabric at the critical state. Ample evidence (both experimental and numerical) has indicated that soils are highly anisotropic when reaching the critical state, while no prerequisite related to the fabric at the critical state is prescribed. Recently, Li and Dafalias revisited critical state theory from the theoretical perspective.…”

Section: Anisotropic Critical State Theorymentioning

confidence: 99%

“…Although the performance of these models is acceptable, to some extent, as evidenced by the broad agreement between the model response and the experimental data, the associated fabric and its evolution are largely hypothesized without sound theoretical evidence. For example, abundant evidence from both numerical and experimental studies has shown that the fabric of the specimen, such as the contact normal and void orientation, undergoes dramatic changes during shearing, and becomes highly anisotropic on reaching the critical state . This clearly conflicts with the fixed fabric assumption employed in those models while; however, no sound theory available can guide the fabric evolution in other models, leading to the fabric arbitrarily evolving toward the critical state.…”

Section: Introductionmentioning

confidence: 99%

“…A unique critical state in the void ratio ( e ) and mean effective stress ( p ) plane becomes the natural consequence of ACST, accompanied by the fabric tensor evolving toward a properly defined critical state direction and a Lode‐angle‐dependent (or shear‐mode‐dependent) norm. Although the uniqueness of the critical state line (CSL) has been a subject of debate over many years, it tends to be corroborated by the increasing and consistent evidence from both experimental studies and discrete element method (DEM) simulations . Because of the paramount role of critical state theory in the development of constitutive models, the ACST framework has been adopted to develop various anisotropic models for granular soils …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hypoplastic model for granular soils incorporating anisotropic critical state theory

Yang

Liao

2020

Summary It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress‐strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus‐Bauer hypoplastic model, and a scalar‐valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.

Necessary and sufficient conditions for reaching and maintaining critical state

Theocharis

Vairaktaris

Dafalias

et al. 2019

Summary According to classical critical state theory (CST) of granular mechanics, two analytical conditions on the ratio of stress invariants and the void ratio are postulated to be necessary and sufficient for reaching and maintaining critical state (CS). The present work investigates the sufficiency of these two conditions based on the results of a virtual three‐dimensional discrete element method experiment, which imposes continuous rotation of the principal axes of stress with fixed stress principal values at CS. Even though the fixity of the stress principal values satisfies the two analytical CST conditions at the initiation of rotation, contraction and abandonment of CS occur, which proves that these conditions may be necessary but are not sufficient to maintain CS. But if fixity of stress and strain rate directions in regard to the sample is considered at CS, the two analytical conditions of CST remain both necessary and sufficient. The recently proposed anisotropic critical state theory (ACST) turned this qualitative requirement of fixity into an analytical condition related to the CS value of a fabric anisotropy variable A defined in terms of an evolving fabric tensor and the plastic strain rate direction, thus, enhancing the two CST conditions by a third. In this way, the three analytical conditions of ACST become both necessary and sufficient for reaching and maintaining CS. In addition, the use of A explains the observed results by relating the stress‐strain response, in particular the dilatancy, to the evolution of fabric by means of the relevant equations of ACST.