Critical-state Mechanics Research Articles

Hydro-mechanical response of volcanic ash on removal of fines: Shear stiffness to critical state mechanics

Natural volcanic soils containing pumice particles are commonly found in Hokkaido, Japan, and this type of soil is prone to landslides, internal erosion, and liquefaction. Therefore, the purpose of this paper is to summarise the hydro-mechanical response of volcanic ash soil subjected to internal erosion using the modified erosion triaxial apparatus, based on the literature and additional investigations. The results of the study show that the rate of erosion and shear strain during the erosion process are influenced by initial density, stress state, and hydraulic gradient. Notably, anisotropic consolidation is experienced by specimens under seepage flow. Additionally, the removal of fines leads to a slight decrease in the grading state index. Moreover, suffosion increases the maximum shear modulus and Poisson’s ratio of the soil, while increasing seepage time stabilises the peak shear strength of eroded specimens. Furthermore, the critical state line does not change much with internal erosion. To sum up, this study offers valuable insights into the behaviour of volcanic ash soil subjected to internal erosion and provides an integrated interpretation of hydro-mechanical response of volcanic ash on removal of fines.

Constitutive Modelling of Temperature-Dependent Behaviour of Soft Rocks with Fractional-Order Flow Rule

This paper regards soft rock as a heavily overconsolidated clay and proposes a new fractional elastoplastic model to describe its temperature-dependent mechanical behaviour. Together with the critical state mechanics, the subloading surface concept is adopted to capture the irreversible plastic deformation developed inside the normal yield surface and provides a smooth transition between the elastic and plastic zones. In addition, the proposed model uses a fractional-order flow rule to account for the nonorthogonality between the plastic flow direction and the yield surface without introducing an extra plastic potential. The evolution law of the fractional-order is affected by the degree of overconsolidation and temperature. The proposed model is verified by the drained triaxial test data of Ohya rock under various confining pressures and temperatures with satisfactory performance. It can be found that an increase in the temperature will reduce the peak strength of soft rock and lead to a ductile failure pattern with a smaller tangent modulus.

Unified sand modeling using associated or non-associated flow rule

A constitutive model for unified modeling of sand behavior was formulated in this study. The model is based on generalized plasticity and critical state mechanics. It incorporates a unique flow rule and a unique hardening modulus. The flow rule is a function of the void ratio and its deviation from an associated flow rule reduces with an increase in sand density. The hardening modulus allows the model to simulate a wide range of sand behavior even with an associated flow rule. With 13 material constants, most of which have definite physical meanings and are straightforward to calibrate using conventional element tests, the model can simulate the drained and undrained responses of sand over a large range of initial void ratios and confining pressures. In addition, the model can be readily degenerated to follow an associated flow rule. The associated-flow-model, which requires 11 material constants, can also reproduce the responses of medium-loose to dense sands when the confining pressure is modest. Although the associated-flow model is not capable of describing the bifurcation of sand responses before the failure surface is reached, it may have advantage in the numerical simulation of well-compacted earth structures like earthdams, embankments and retaining walls.

New Pressuremeter Test Analysis Based on Critical State Mechanics

AbstractTo analyze the pressuremeter test results, the medium around the probe is modeled by a clay hollow cylinder subjected to external and internal uniform pressures. However, assuming that during the test the medium strains around the pressuremeter test cavity are homogeneous results in an oversimplification of the problem. A new analysis method is proposed based on an energy approach concept. The objectives are to determine the outer radius of the clay hollow cylinder that models a normally consolidated clay medium idealized in undrained conditions and to express the clay behavior by the effective stress path and the stress-strain relationship. At the position of three particles across such a cylinder, the developed excess pore water pressures were measured during testing. The analysis showed that the development of greater excess pore pressure than the circumferential stress in compression indicates the critical state and that the testing rate has a negligible influence on the deduced critical state...

Critical state finite element models of contractional fault-related folding: Part 2. Mechanical analysis

Finite element modeling of contractional fault-related folding with critical state mechanics concepts reveals fundamentally different behaviors at two levels, depending on (1) mechanical stratigraphy and (2) initial fault geometry. Deviatoric plastic strain rate and strain patterns show that ‘strong’ layers, like normally consolidated sandstone or overconsolidated shale, develop strain localization in form of narrow plastic shear bands. ‘Soft’ layers like normally consolidated shale fail to develop localizations and respond by diffuse, distributed plastic strain. Inter-layered overburdens display both deformation modes. Models with listric thrust fault seeds develop basement-cored anticlines in the hangingwall that are characterized by locally tensile stress regimes within overall compressive regional stress fields. The anticline crests of these models show evidence for strain softening. By contrast, anticlines emerging in detached fault-related fold models are subject to locally compressive stress regimes, consistent with the applied far-field shortening. These anticline crests strain-harden during deformation. Stresses resulting from the finite element models deviate from stress estimates based on integrated densities. The discrepancy is small for basement-involved models but significant for detached style models, suggesting that stress predictions based on integrated densities may be inaccurate for contractional systems. First-order predictions of plastic deformation suggest that footwall synclines in basement-involved fold styles may host reservoirs with relatively poor quality owing to horizontal and vertical compaction. Anticlines found in detached deformation styles are bounded by compactive domains whereas the crestal regions are less affected by volumetric plastic deformation thus producing relatively better reservoir quality.

Critical state finite element models of contractional fault-related folding: Part 1. Structural analysis

Fourteen Lagrangian finite element models with a critical state mechanics constitutive model illustrate some of the primary controls on the formation of fault propagation, fault bend, and diffuse folds. The models demonstrate how variable mechanical stratigraphy, initial fault dip and inter-layer detachments affect the way faults propagate and thus exert a significant control on resultant fold layer geometry. For example, models of uniform sandstone properties exhibit efficient strain localization and clear patterns of fault tip propagation. Uniform shale properties tend to inhibit fault propagation due to distributed plastic deformation. Models with mixed inter-layered sandstone and shale deform in a disharmonic manner, resembling lobate–cuspate arrangements that are common to many folds observed in outcrop. Detachments accommodate shortening by bed-parallel slip, resulting in fault-bend fold kinematics and poorly expressed fault propagation across layers. Structural analysis of the numerical model results reveals that contractional deformation is a composite of lateral compaction, pure shear shortening, fault propagation along narrowly localized zones of reverse shear, and flexure of layers. The relative proportions of these shortening components vary in time and with mechanical properties (shale vs. sandstone). Depth-to-detachment calculations performed on selected numerical models suggest that reasonably accurate predictions can be made for detachment fold-thrust belts and toe-of-slope contractional systems. However, our study suggests that applications to mid-crustal level detachments within the basement beneath a sedimentary cover may be inaccurate.

Volumetric matrix strain related to intraformational faulting in argillaceous sediments

Soft-sediment deformation involves complex interactions between discrete fracturing and diffuse bulk strain, described in terms of volume change and shear strain in a critical state mechanics framework. This study reports on a mesoscale normal fault zone, intraformational in Oligocene argillaceous sediments from the Boom Formation (Belgium), containing several metre-scale normal fault strands. They form either discrete fault planes or decimetre-wide shear zones with internal fabric. The faults have been subjected to microtectonic and petrophysical analysis. Small but significant changes occur in the porous network of the argillaceous matrix approaching a fault or shear zone, indicating compactional strain in both footwall and hanging wall. Internal compaction associated with faulting is put forward as a ductile–brittle feedback mechanism in the kinematics of intraformational fracture systems. Small differential stress induced by compaction and minor regional tectonic forces (differential uplift and tilt) and subsequent gravitational forces (downslope shear stress) induce small shear bands in nearly critically stressed weak mud. Shear banding is accompanied by layer-parallel shortening and bulk volume loss. This provides an additional extension of endogenous origin, accommodated by further deformation. This ductile–brittle feedback mechanism eventually leads to commonly observed intraformational collapse structures called polygonal fault systems.

A Strength Criterion Based on Critical State Mechanics for Intact Rocks

A Strength Criterion Based on Critical State Mechanics for Intact Rocks

Theoretical prediction of rutting in flexible pavement subgrades

The theoretical model for predicting the cyclic response of soils is extended to handle the generation and dissipation of pore-water pressures and to predict the rutting of the subgrade of a flexible pavement. The model utilizes multiyield surfaces and the concepts of critical state mechanics to predict the permanent deformation of the subgrade under vehicular loading. The theoretical solution also considers the effects of the drainage characteristics of the subgrade soil on the rate of development of the permanent deformation. Experimental verification of the model concepts are presented for a drained cyclic load test on Ottawa sand and for undrained cyclic loading on Newfield clay using published experimental data. An illustrative example is given for the prediction of rutting in a silty clay subgrade. The model parameters for the silty clay are obtained from triaxial and consolidation tests. These parameters are then put into a computer program that determines the rut depth, pore-water pressure, and the ratio of the vertical deformation and the rut depth as functions of the number of vehicular loads for a flexible pavement for various conditions of drainage ranging from undrained to fully drained. The role of the coefficient of consolidation of the subgrade in controlling the rate of development of the rut depth is highlighted. Key words : critical state soil mechanics, multiyield surfaces, rutting, silty clay subgrade, drainage, vehicular loading.