A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd.     

Three-Dimensional Numerical Investigations of the Failure Mechanism of a Rock Disc with a Central or Eccentric Hole

The diametrical compression of a circular disc (Brazilian test) or cylinder with a small eccentric hole is a simple but important test to determine the tensile strength of rocks. This paper studies the failure mechanism of circular disc with an eccentric hole by a 3D numerical model (RFPA3D). A feature of the code RFPA3D is that it can numerically simulate the evolution of cracks in three-dimensional space, as well as the heterogeneity of the rock mass. First, numerically simulated Brazilian tests are compared with experimental results. Special attention is given to the effect of the thickness to radius ratio on the failure modes and the peak stress of specimens. The effects of the compressive strength to tensile strength ratio (C/T), the loading arc angle (2α), and the homogeneity index (m) are also studied in the numerical simulations. Secondly, the failure process of a rock disc with a central hole is studied. The effects of the ratio of the internal hole radius (r) to the radius of the rock disc (R) on the failure mode and the peak stress are investigated. Thirdly, the influence of the vertical and horizontal eccentricity of an internal hole on the initiation and propagation of cracks inside a specimen are simulated. The effect of the radius of the eccentric hole and the homogeneity index (m) are also investigated.     

Upper bound limit analysis using linear finite elements and non‐linear programming

A new method for computing rigorous upper bounds on the limit loads for one‐, two‐ and three‐dimensional continua is described. The formulation is based on linear finite elements, permits kinematically admissible velocity discontinuities at all interelement boundaries, and furnishes a kinematically admissible velocity field by solving a non‐linear programming problem. In the latter, the objective function corresponds to the dissipated power (which is minimized) and the unknowns are subject to linear equality constraints as well as linear and non‐linear inequality constraints. Provided the yield surface is convex, the optimization problem generated by the upper bound method is also convex and can be solved efficiently by applying a two‐stage, quasi‐Newton scheme to the corresponding Kuhn–Tucker optimality conditions. A key advantage of this strategy is that its iteration count is largely independent of the mesh size. Since the formulation permits non‐linear constraints on the unknowns, no linearization of the yield surface is necessary and the modelling of three‐dimensional geometries presents no special difficulties. The utility of the proposed upper bound method is illustrated by applying it to a number of two‐ and three‐dimensional boundary value problems. For a variety of two‐dimensional cases, the new scheme is up to two orders of magnitude faster than an equivalent linear programming scheme which uses yield surface linearization. Copyright © 2001 John Wiley & Sons, Ltd.     

Probabilistic estimates of future changes in California temperature and precipitation using statistical and dynamical downscaling

Sixteen global general circulation models were used to develop probabilistic projections of temperature (T) and precipitation (P) changes over California by the 2060s. The global models were downscaled with two statistical techniques and three nested dynamical regional climate models, although not all global models were downscaled with all techniques. Both monthly and daily timescale changes in T and P are addressed, the latter being important for a range of applications in energy use, water management, and agriculture. The T changes tend to agree more across downscaling techniques than the P changes. Year-to-year natural internal climate variability is roughly of similar magnitude to the projected T changes. In the monthly average, July temperatures shift enough that that the hottest July found in any simulation over the historical period becomes a modestly cool July in the future period. Januarys as cold as any found in the historical period are still found in the 2060s, but the median and maximum monthly average temperatures increase notably. Annual and seasonal P changes are small compared to interannual or intermodel variability. However, the annual change is composed of seasonally varying changes that are themselves much larger, but tend to cancel in the annual mean. Winters show modestly wetter conditions in the North of the state, while spring and autumn show less precipitation. The dynamical downscaling techniques project increasing precipitation in the Southeastern part of the state, which is influenced by the North American monsoon, a feature that is not captured by the statistical downscaling.     

Climate change projections of the North American Regional Climate Change Assessment Program (NARCCAP)

We investigate major results of the NARCCAP multiple regional climate model (RCM) experiments driven by multiple global climate models (GCMs) regarding climate change for seasonal temperature and precipitation over North America. We focus on two major questions: How do the RCM simulated climate changes differ from those of the parent GCMs and thus affect our perception of climate change over North America, and how important are the relative contributions of RCMs and GCMs to the uncertainty (variance explained) for different seasons and variables? The RCMs tend to produce stronger climate changes for precipitation: larger increases in the northern part of the domain in winter and greater decreases across a swath of the central part in summer, compared to the four GCMs driving the regional models as well as to the full set of CMIP3 GCM results. We pose some possible process-level mechanisms for the difference in intensity of change, particularly for summer. Detailed process-level studies will be necessary to establish mechanisms and credibility of these results. The GCMs explain more variance for winter temperature and the RCMs for summer temperature. The same is true for precipitation patterns. Thus, we recommend that future RCM-GCM experiments over this region include a balanced number of GCMs and RCMs.     

A review of the relevance of the ‘CLOUD’ results and other recent observations to the possible effect of cosmic rays on the terrestrial climate

The problem of the contribution of cosmic rays to climate change is a continuing one and one of importance. In principle, at least, the recent results from the CLOUD project at CERN provide information about the role of ionizing particles in ’sensitizing’ atmospheric aerosols which might, later, give rise to cloud droplets. Our analysis shows that, although important in cloud physics the results do not lead to the conclusion that cosmic rays affect atmospheric clouds significantly, at least if H₂SO₄ is the dominant source of aerosols in the atmosphere. An analysis of the very recent studies of stratospheric aerosol changes following a giant solar energetic particles event shows a similar negligible effect. Recent measurements of the cosmic ray intensity show that a former decrease with time has been reversed. Thus, even if cosmic rays enhanced cloud production, there would be a small global cooling, not warming.     

Finite element formulation and algorithms for unsaturated soils. Part I: Theory

This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd.     

Upper bound limit analysis using finite elements and linear programming

This paper describes a technique for computing rigorous upper bounds on limit loads under conditions of plane strain. The method assumes a perfectly plastic soil model, which is either purely cohesive or cohesive-frictional, and employs finite elements in conjunction with the upper bound theorem of classical plasticity theory. The computational procedure uses three-noded triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the grid. The finite element formulation of the upper bound theorem leads to a classical linear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power and is expressed in terms of the velocities and plastic multiplier rates. The unknowns are subject to a set of linear constraints arising from the imposition of the flow rulé and velocity boundary conditions. It is shown that the upper bound optimization problem may be solved efficiently by applying an active set algorithm to the dual linear programming problem. Since the computed velocity field satisfies all the conditions of the upper bound theorem, the corresponding limit load is a strict upper bound on the true limit load. Other advantages include the ability to deal with complicated loading, complex geometry and a variety of boundary conditions. Several examples are given to illustrate the effectiveness of the procedure.