Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Analytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one- and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions. Copyright (C) 2004 John Wiley Sons, Ltd.

Study on small-strain behaviours of methane hydrate sandy sediments using discrete element method

Methane hydrate bearing soil has attracted increasing interest as a potential energy resource where methane gas can be extracted from dissociating hydrate-bearing sediments. Seismic testing techniques have been applied extensively and in various ways, to detect the presence of hydrates, due to the fact that hydrates increase the stiffness of hydrate-bearing sediments. With the recognition of the limitations of laboratory and field tests, wave propagation modelling using Discrete Element Method (DEM) was conducted in this study in order to provide some particle-scale insights on the hydrate-bearing sandy sediment models with pore-filling and cementation hydrate distributions. The relationship between shear wave velocity and hydrate saturation was established by both DEM simulations and analytical solutions. Obvious differences were observed in the dependence of wave velocity on hydrate saturation for these two cases. From the shear wave velocity measurement and particle-scale analysis, it was found that the small-strain mechanical properties of hydrate-bearing sandy sediments are governed by both the hydrate distribution patterns and hydrate saturation. © 2013 AIP Publishing LLC.

Fatigue behavior of laser-welded NiTi wires in small-strain cyclic bending

NiTi wires and their weldments are commonly used in micro-electro-mechanical systems (MEMS), and in such applications, cyclic loading are commonly encountered. In this paper, the bending-rotation fatigue (BRF) test was used to study the bending fatigue behavior of NiTi wire laser weldment in the small-strain regime. The fracture mechanism, which includes crack initiation, crack growth and propagation of the weldment in the BRF test, was investigated with the aid of SEM fractography and discussed in terms of the microstructure. It was found that crack initiation was primarily surface-condition dependent. The cracks were found to initiate at the surface defects at the weld zone (WZ) surface, and the crack propagation was assisted by the gas inclusions in the WZ. The weldment was finally fractured in a ductile manner. The fatigue life was found to decrease with increasing surface strain and also with increasing bending frequency (controlled by the rotational speed in the BRF test). In comparison, the fatigue life of the unwelded NiTi wires was higher than their welded counterparts at all strain levels and bending frequencies. The decrease in fatigue resistance of the weldment could be attributed to the surface and microstructural defects introduced during laser welding.

Estimation of the small strain stiffness of glacial till using geophysical methods and barometric loading response

Stiffness values in geotechnical structures can range over many orders of magnitude for relatively small operational strains. The typical strain levels where soil stiffness changes most dramatically is in the range 0.01-0.1%, however soils do not exhibit linear stress-strain behaviour at small strains. Knowledge of the in situ stiffness at small strain is important in geotechnical numerical modelling and design. The stress-strain regime of cut slopes is complex, as we have different principle stress directions at different positions along the potential failure plane. For example, loading may be primarily in extension near the toe of the slope, while compressive loading is predominant at the crest of a slope. Cuttings in heavily overconsolidated clays are known to be susceptible to progressive failure and subsequent strain softening, in which progressive yielding propagates from the toe towards the crest of the slope over time. In order to gain a better understanding of the rate of softening it would be advantageous to measure changes in small strain stiffness in the field.

Small strain elastic behaviour of unsaturated soil investigated by bender/extender element testing

The aim of this project was to investigate very small strain elastic behaviour of soils under unsaturated conditions, using bender/extender element (BEE) testing. The behaviour of soils at very small strains has been widely studied under saturated conditions, whereas much less work has been performed on very small strain behaviour under unsaturated conditions. A suction-controlled double wall triaxial apparatus for unsaturated soil testing was modified to incorporate three pairs of BEEs transmitting both shear and compression waves with vertical and horizontal directions of wave transmission and wave polarisation. Various different techniques for measuring wave travel time were investigated in both the time domain and the frequency domain and it was concluded that, at least for the current experimental testing programme, peak-to-first-peak in the time domain was the most reliable technique for determining wave travel time. An experimental test programme was performed on samples of compacted speswhite kaolin clay. Two different forms of compaction were employed (i.e. isotropic and anisotropic). Compacted kaolin soil samples were subjected to constant suction loading and unloading stages at three different values of suction, covering both unsaturated conditions (s= 50kPa and s= 300kPa) and saturated conditions (s=0). Loading and unloading stages were performed at three different values of stress ratio (η=0, η=1 and η=-1 ). In some tests a wetting-drying cycle was performed before or within the loading stage, with the wetting-drying cycles including both wetting-induced swelling and wetting-induced collapse compression. BEE tests were performed at regular intervals throughout all test stages, to measure shear wave velocity Vs and compression wave velocity Vp and hence to determine values of shear modulus G and constrained modulus M. The experimental test programme was designed to investigate how very small strain shear modulus G and constrained modulus M varied with unsaturated state variables, including how anisotropy of these parameters developed either with stress state (stress-induced anisotropy) or with previous straining (strain-induced anisotropy). A new expression has been proposed for the very small strain shear modulus G of an isotropic soil under saturated and unsaturated conditions. This expression relates the variation of G to only mean Bishop’s stress p* and specific volume v, and it converges to a well-established expression for saturated soils as degree of saturation approaches 1. The proposed expression for G is able to predict the variation of G under saturated and unsaturated conditions at least as well as existing expressions from the literature and it is considerably simpler (employing fewer state variables and fewer soil constants). In addition, unlike existing expressions from the literature, the values of soil constants in the proposed new expression can be determined from a saturated test. It appeared that, in the current project at least, any strain-induced anisotropy of very small strain elastic behaviour was relatively modest, with the possible exception of loading in triaxial extension. It was therefore difficult to draw any firm conclusion about evolution of strain-induced anisotropy and whether it depended upon the same aspects of soil fabric as evolution of anisotropy of large strain plastic behaviour. Stress-induced anisotropy of very small strain elastic behaviour was apparent in the experimental test programme. An attempt was made to extend the proposed expression for G to include the effect of stress-induced anisotropy. Interpretation of the experimental results indicated that the value of shear modulus was affected by the values of all three principal Bishop’s stresses (in the direction of wave transmission, the direction of wave polarisation and the third mutually perpendicular direction). However, prediction of stress-induced anisotropy was only partially successful, and it was concluded that the effect of Lode angle was also significant.

A method for predicting the consolidated undrained bearing capacity of shallow foundations

The effect of consolidation on the undrained bearing capacity of both rough and smooth strip and circular surface foundations is investigated, examining the influence of the magnitude and duration of an applied preload and the initial over-consolidation ratio of the deposit. The investigation comprised small strain finite-element analysis, with the soil response represented by Modified Cam Clay. The results are distilled into dimensionless and generalised forms, from which simple trends emerge. Based on these results, a simple method for predicting the consolidated undrained bearing capacity is proposed.

Seismic response of submarine slopes

The geological profile of submerged slopes on the continental shelf typically includes soft cohesive soils with thicknesses ranging from a few meters to tens or hundreds of meters. The response of these soils in simple shear tests is largely influenced by the presence of an initial consolidation shear stress, inducing anisotropic stress-strain-strength properties which depend also on the direction of shear. In this paper, a new simplified effective-stress-based model describing the behavior of normally to lightly overconsolidated cohesive soils is used in conjunction with a one-dimensional seismic site response analysis computer code to illustrate the importance of accounting for anisotropy and small strain nonlinearity. In particular, a simple example is carried out to compare results for different slope inclinations. Depth profiling of the maximum shear strains and permanent deformations provide insight into the mechanisms of deformation during a seismic event, and the effects of sloping ground conditions.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.