Stiffness of clays and silts: Normalizing shear modulus and shear strain

An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p9 (i.e., G=p9 versus log g) or undrained shear strength cu (i.e., G=cu versus log g) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus,Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions forGmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value Gmax, and shear strain g is normalized with respect to a reference strain gref at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gref is approximated as a function of the plasticity index.Aunique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/Gmax ±30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. © 2013 American Society of Civil Engineers.

The Influence of Strain Gradient on the shear Band in a Saturated Soil

The dynamic localization of saturated soil is investigated by considering the influence of higher strain gradient. It is shown that the strain gradient has a significant influence on the evolution of shear band in saturated soil and that the width of shear band is proportional to the square root of the strain gradient softening coefficient. The numerical simulation is processed to investigate the influences of shear strain gradient and other factors on the evolution of shear band.

On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

Liquefaction And Pore Water Pressure Generation In Sand - A Cyclic Strain Approach

This paper presents the results of laboratory investigation carried out on Ahmedabad sand on the liquefaction and pore water pressure generation during strain controled cyclic loading. Laboratory experiments were carried out on representative natural sand samples (base sand) collected from earthquake-affected area of Ahmedabad City of Gujarat State in India. A series of strain controled cyclic triaxial tests were carried out on isotropically compressed samples to study the influence of different parameters such as shear strain amplitude, initial effective confining pressure, relative density and percentage of non-plastic fines on the behavior of liquefaction and pore water pressure generation. It has been observed from the laboratory investigation that the potential for liquefaction of the sandy soils depends on the shear strain amplitude, initial relative density, initial effective confining pressure and non-plastic fines. In addition, an empirical relationship between pore pressure ratio and cycle ratio independent of the number of cycles of loading, relative density, confining pressure, amplitude of shear strain and non-plastic fines has been proposed.

A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element

We present a biquadratic Lagrangian plate bending element with consistent fields for the constrained transverse shear strain functions. A technique involving expansion of the strain interpolations in terms of Legendre polynomials is used to redistribute the kinematically derived shear strain fields so that the field-consistent forms (i.e. avoiding locking) are also variationally correct (i.e. do not violate the variational norms). Also, a rational method of isoparametric Jacobian transformation is incorporated so that the constrained covariant shear strain fields are always consistent in whatever general quadrilateral form the element may take. Finally the element is compared with another formulation which was recently published. The element is subjected to several robust bench mark tests and is found to pass all the tests efficiently.

On the Evolution of Simple Shear in Saturated Soils

Development of shear bands in saturated soils is a multi-stage process based on the theoretical and numerical investigations in this paper. The soil is initially in homogenous shear strain state, and the instability can be characterized by a dimensionless number D. The inhomogenous distribution of shear strains appears when D>1, and the shear band will initiate and develop gradually. Numerical solutions show that only single shear band that is finally formed in the central region of the specimen even several disturbances (distributed along the specimen) appear in the beginning.

On post-instability processes in adiabatic shear in hot rolled steel

EXPERIMENTS carried out using a split Hopkinson torsional bar have shown that only one shear band develops in specimens of hot rolled steel which break during testing. We observed, however, that in specimens which were not deformed to failure, several fine shear bands appeared. We believe that these formed during the loading cycle before the appearance of the final shear band and were not due to the effect of unloading. So we developed a numerical model to study the evolution of shear banding from several finite amplitude disturbances (FADs) in both temperature and strain rate. This numerical model reveals the detailed processes by which the FADs evolve into a fully developed shear band and suggests that beyond instability, the so-called shear banding process consists of two stages: inhomogeneous shearing and true shear-banding. The latter is characterized by the collapse of the stress and an abrupt increase of the local shear strain rate.

Modeling cyclic behavior of lightly overconsolidated clays in simple shear

Assessment of seismic performance and estimation of permanent displacements for submerged slopes require the accurate description of the soil's stress-strain-strength relationship under irregular cyclic loading. The geological profile of submerged slopes on the continental shelf typically consists of normally to lightly overconsolidated clays with depths ranging from a few meters to a few hundred meters and very low slope angles. This paper describes the formulation of a simplified effective-stress-based model, which is able to capture the key aspects of the cyclic behavior of normally consolidated clays. The proposed constitutive law incorporates anisotropic hardening and bounding surface principles to allow the user to simulate different shear strain and stress reversal histories as well as provide realistic descriptions of the accumulation of plastic shear strains and excess pore pressure during successive loading cycles. (C) 2000 Published by Elsevier Science Ltd. | Assessment of seismic performance and estimation of permanent displacements for submerged slopes require the accurate description of the soil's stress-strain-strength relationship under irregular cyclic loading. The geological profile of submerged slopes on the continental shelf typically consists of normally to lightly overconsolidated clays with depths ranging from a few meters to a few hundred meters and very low slope angles. This paper describes the formulation of a simplified effective-stress-based model, which is able to capture the key aspects of the cyclic behavior of normally consolidated clays. The proposed constitutive law incorporates anisotropic hardening and bounding surface principles to allow the user to simulate different shear strain and stress reversal histories as well as provide realistic descriptions of the accumulation of plastic shear strains and excess pore pressures during successive loading cycles.

Fault development and interaction in distributed strike-slip shear zones: an experimental approach

Analogue model experiments using both brittle and viscous materials were performed to investigate the development and interaction of strike-slip faults in zones of distributed shear deformation. At low strain, bulk dextral shear deformation of an initial rectangular model is dominantly accommodated by left-stepping, en echelon strike-slip faults (Riedel shears, R) that form in response to the regional (bulk) stress field. Push-up zones form in the area of interaction between adjacent left-stepping Riedel shears. In cross sections, faults bounding push-up zones have an arcuate shape or merge at depth. Adjacent left-stepping R shears merge by sideways propagation or link by short synthetic shears that strike subparallel to the bulk shear direction. Coalescence of en echelon R shears results in major, through-going faults zones (master faults). Several parallel master faults develop due to the distributed nature of deformation. Spacing between master faults is related to the thickness of the brittle layers overlying the basal viscous layer. Master faults control to a large extent the subsequent fault pattern. With increasing strain, relatively short antithetic and synthetic faults develop mostly between old, but still active master faults. The orientation and evolution of the new faults indicate local modifications of the stress field. In experiments lacking lateral borders, closely spaced parallel antithetic faults (cross faults) define blocks that undergo clockwise rotation about a vertical axis with continuing deformation. Fault development and fault interaction at different stages of shear strain in our models show similarities with natural examples that have undergone distributed shear.

The behaviour of granular material in pure shear, direct shear and simple shear

In biaxial compression tests, the stress calculations based on boundary information underestimate the principal stresses leading to a significant overestimation of the shear strength. In direct shear tests, the shear strain becomes highly concentrated in the mid-plane of the sample during the test. Although the stress distribution within the specimen is heterogeneous, the evolution of the stress ratio inside the shear band is similar to that inferred from the boundary force calculations. It is also demonstrated that the dilatancy in the shear band significantly exceeds that implied from the boundary displacements. In simple shear tests, the stresses acting on the wall boundaries do not reflect the internal state of stress but merely provide information about the average mobilised wall friction. It is demonstrated that the results are sensitive to the initial stress state defined by K0 = sh/sv. For all cases, non-coaxiality of the principal stress and strain-rate directions is examined and the corresponding flow rule is identified. Periodic cell simulations have been used to examine biaxial compression for a wide range of initial packing densities. Both constant volume and constant mean stress tests have been simulated. The characteristic behaviour at both the macroscopic and microscopic scales is determined by whether or not the system percolates (enduring connectivity is established in all directions). The transition from non-percolating to percolating systems is characterised by transitional behaviour of internal variables and corresponds to an elastic percolation threshold, which correlates well with the establishment of a mechanical coordination number of ca. 3.0. Strong correlations are found between macroscopic and internal variables at the critical state.

Evaluation of One-Dimensional Seismic Site Response Analyses at Small to Large Strain Levels

Thesis (Master's)--University of Washington, 2016-08