Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity

This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.     

Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd.     

A simple hypoplastic model for normally consolidated clay

The paper presents a simple constitutive model for normally consolidated clay. A mathematical formulation, using a single tensor-valued function to define the incrementally nonlinear stress–strain relation, is proposed based on the basic concept of hypoplasticity. The structure of the tensor-valued function is determined in the light of the response envelope. Particular attention is paid towards incorporating the critical state and to the capability for capturing undrained behaviour of clayey soils. With five material parameters that can be determined easily from isotropic consolidation and triaxial compression tests, the model is shown to provide good predictions for the response of normally consolidated clay along various stress paths, including drained true triaxial tests and undrained shear tests.     

Use of photo-based 3D photogrammetry in analysing the results of laboratory pressure grouting tests

This paper presents a non-destructive, low-cost, photo-based, 3D reconstruction technique for characterizing geo-materials with irregular shapes of a relatively large size. After being validated against two traditional volume measurement methods, namely the vernier caliper method and the fluid displacement method for regular and irregular shapes, respectively, 3D photogrammetry was used to analyse the grout bulbs formed in laboratory pressure grouting tests. The reconstructed 3D mesh model of the sample provides accurate and detailed 3D vertex data, which allowed the volume, densification efficiency and bleeding behaviour of the grout bulbs to be analysed. Comparing the bulb section views at different grouting pressures also offers an intuitive observation of the grout development and propagation process. Moreover, the 3D vertex data and surface area included in the model are of great importance in validating numerical predictions of the pressure grouting process and analysing the interface shear resistance of grouted soil nails or anchors. Compared to existing approaches, the new 3D photogrammetry method possesses several key advantages: (a) it does not require expensive, specialized equipment; (b) samples are not destroyed or modified during testing; (c) it allows to reconstruct objects of various scales and (d) the software is public domain. Therefore, the adoption of this 3D photogrammetry method will facilitate research in the pressure grouting process and can be extended to other problems in geotechnical engineering.     

How accurately may we project tropical forest-cover change? A validation of a forward-looking baseline for REDD

The Reduced Emissions from Deforestation and forest Degradation (REDD+) mechanism of a future post-2012 global climate-change treaty would aim to give incentive to tropical countries to reduce deforestation and thus forest-carbon emissions. It would do so by crediting tropical countries for reducing deforestation relative to a baseline scenario describing carbon emissions and removals from forest-cover change expected in the absence of REDD+. Defining a credible and accurate baseline is both critical and challenging. One approach considered promising is spatial modelling to project forest-cover change on the basis of historical trends; yet few such projections have been validated at a national scale. We develop and validate a novel GEOMOD projection of forest-cover change in Panama over 2000–2008, based on trends over 1990–2000 and 25 drivers of forest-cover change. Compared with the actual landscape of 2008, our projection is 85.2% accurate at a 100-m pixel resolution. More error is attributable to the location of projected forest (8.6%) than to its area (6.2%). Accuracy was least where forest regeneration predominated (80%), and greatest where deforestation predominated (90%). Despite the sophistication of our projection, it is slightly less accurate than if we had assumed no forest-cover change over 2000–2008. We identify factors limiting projection accuracy, including the complexity of forest-cover change, the spatial variability of forest-carbon density, and the relatively small area of change at the national scale. We conclude that, with the exception of contexts where forest-cover change is significant and straightforward and where forest-carbon density relatively uniform (e.g., agricultural frontiers), spatially projected baselines are of limited value for REDD+ – their accuracy is too limited given their relative lack of transparency. Simpler, relatively coarse scale, retrospective baselines are recommended instead.     

Validation of climate model output using Bayesian statistical methods

The growing interest in and emphasis on high spatial resolution estimates of future climate has demonstrated the need to apply regional climate models (RCMs) to that problem. As a consequence, the need for validation of these models, an assessment of how well an RCM reproduces a known climate, has also grown. Validation is often performed by comparing RCM output to gridded climate datasets and/or station data. The primary disadvantage of using gridded climate datasets is that the spatial resolution is almost always different and generally coarser than climate model output. We have used a Bayesian statistical model derived from observational data to validate RCM output. We used surface air temperature (SAT) data from 109 observational stations in California, all with records of approximately 50 years in length, and created a statistical model based on this data. The statistical model takes into account the elevation of the station, distance from coastline, and the NOAA climate region in which the station resides. Analysis indicates that the statistical model provides reliable estimates of the mean monthly SAT at any given station. In our method, the uncertainty in the estimates produced by the statistical model are directly determined by obtaining probability density functions for predicted SATs. This statistical model is then used to estimate average SATs corresponding to each of the climate model grid cells. These estimates are compared to the output of the RCM to assess how well the RCM matches the observed climate as defined by the statistical model. Overall, the match between the RCM output and the statistical model is good, with some deficiencies likely due in part to the representation of topography in the RCM.