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Computational modelling of large deformations and the failure of geomaterials

ICSMGE Plenary session B

For the last two decades, studies on constitutive modelling and numerical analysis methods have been well developed. Today, numerical and analytical methods play a very important role in geotechnical engineering and in the related area of computational geotechnics.

Due to large deformations and failures, however, several issues have arisen in computational geotechnics.

They include constitutive modelling and its calibration, mechanical instabilities (strain localisation and progressive failure); the modelling of chemo-thermo-hydro-mechanical coupled behaviour; and the verification and validation of mathematical modelling.

The lead lecture from this plenary session will deal with the recent progress made to solve these problems, in particular, the constitutive modelling of soil for rate-dependent models with structural degradation, strain localisation, liquefaction of soil and their applications in the context of large deformations and the failure of geomaterials. Other problems are presented in the state-ofthe-art report by TC34 of ISSMGE (2005).

The lecture will cover:

Constitutive modelling of geomaterials and its calibration

Mechanical instabilities, namely, strain localisation and progressive failure

Coupled effects of internal porefluid flow and the large deformations of geomaterials: chemo-thermohydro-mechanically coupled analysis

Reconsideration of conventional analyses and design methods

Application and advanced computational methods Constitutive modelling Various constitutive models for soil have been developed over the last four decades. In particular, many elasto-plastic models have been proposed since Cam-clay models were established by Roscoe et al (1963, 1968).

A constitutive model for soil should be able to describe all types of soil behaviour. The behaviour of soil is complex, however, due to its nature, ie, its granularity, its multiphase structure and its inhomogeneity. The typical characteristics of soil can be listed as follows:

Multi-phase mixture of soil particles, pore water and pore air, saturated and unsaturated soil and effective stress l Elasticity and hypo-elasticity

Plasticity, hypo-plasticity and dilatancy characteristics

Pate sensitivity, viscoelasticity and viscoplasticity

Density dependency and confining pressure dependency

Strain-hardening and strain-softening characteristics

Cyclic deformation characteristics

Structural and induced aniso tropy

Non-coaxiality

Deformation localisation, bifurcation, and instability

Discontinuity

Degradation and the growth of microstructures

Inhomogeneity and non-locality

Temperature dependency

Electric characteristics, the dieletric constant and conductivity

Some of the characteristics have been included in the formulation of the constitutive models. In particular, elasto-plasticity and dilatancy are now included in almost all models. However, some of them are not incorporated very well.

Part of the lecture will discuss the characteristics of soil, such as rate dependency, structural degradation and cyclic plasticity with regard to constitutive modelling and its use in numerical analyses.

(a) Rate dependency: The timedependent behaviour of soil, manifested as creep, relaxation and rate sensitivity, comprises indispensable factors for predicting the long-term settlement behaviour of soft clay deposits, slope stability and landslides. Rate-dependent models, such as viscoplasticity models, have been examined and it has been shown that elasto-viscoplastic models are applicable to soil.

(b) Degradation of soil microstructures: Strain-softening behaviour is due not only to localised strain but also to material degradation. The lecture examines typical degradation of geomaterials for soft rock and cemented soil.

To accurately simulate deformation behaviour, in particular localised shear and compressive strain, it is necessary to account for soil degradation, namely, the failure of microstructures.

Strain softening during shearing is a well known type of behaviour that is brought about by both material degradation and geometrical instability. A drop in stress is observed after the stress has reached its peak during the displacement control shearing of the geomaterials.

Due to the strain-softening, localisation manifests as 'shear bands'.

Additionally, volumetric strain localisation is observed - forming 'compaction bands' - which arises from the volumetric softening in porous rock and cemented soil.

Additionally, a diffuse mode of deformation is also taken into account. Elasto-viscoplastic models with structural degradation are presented and validated.

(c) Cyclic plasticity: Cyclic constitutive models for sand consider dynamic phenomena such as liquefaction and vibrational problems.

For a dynamic analysis of sand deposits, models have to be well calibrated against the behaviour of loose to dense sands.

Strain localisation and progressive failure It is recognised that strain localisation such as shear banding is of great importance, because it is a precursor to the failure of geomaterials.

Numerical modelling methods have been developed for the analysis of post failure behaviour. In the analysis of strain localisation, the prediction of the onset direction and the size of the localisation zone are very important.

If the usual approach is taken, such as applying elasto-plastic models with strain softening, we encounter ill-posedness of the boundary value problems at hand.

Results of numerical analysis strongly depend on mesh size; they do not converge with mesh refinement. These defects derive from the violation of mathematical well-posedness, which requires a uniqueness of the solution and a continuous dependency of the solution on the boundary data.

To rectify these shortcomings, several methods have been developed and used in analysis, such as:

(a) Non-local constitutive models, strain-gradient dependent models, Cosserat models, and integral type models (b) Elasto-viscoplastic formulations and generalized elasto-viscoplastic formulations (c) Discontinuous numerical methods, such as discontinuous FEM, DEM, DDA, etc (d) Introduction of pore-water pressure migration which leads to the weak removal of ill-posedness (e) Dynamic formulation and the introduction of acceleration For the presentation of these methods, numerical examples and comparisons with experimental or fi eld data are shown to discuss the advantages and the accuracy of these approaches. Strain localisation is not only observed in shear, but also under compression and/or compaction.

When porous sandstone compaction bands are observed, compaction strain is localised for cemented soil and soft porous rock. Compaction bands are the result of unstable volumetric behaviour.

Coupled analysis

Thermo-hydro-mechanical coupling is very important for predicting the behaviour of the fluid contained in soil and for assessing the stability of geomaterials, ie slope stability, landslides, and liquefaction.

Contractive soil, such as loose sand, may easily lead to liquefaction. If the problem of soil-structure interaction is considered, a more complex coupled behaviour may be encountered. If the soil has dilatant characteristics, the strength of the soil will increase due to a rise in the effective stress. Thus, the existence of pore water may delay strain localisation and failure.

A more interesting point regarding time-dependent behaviour is the comparison between the effects of the inherent rate dependency of geomaterials and pore water migration.

For thermal effects, the fluidisation of soil is affected by the thermal coupling in rapid flow problems such as landslides.

Reconsideration of conventional methods

Conventional analysis methods and design codes should be re-examined using recent developments in new prediction methods. For example, bearing capacity has been studied again, and has been compared with conventional criteria.

Additionally, conventional methods of consolidation behaviour need to be re-examined with respect to the unusual pore water pressure response etc.

Application and advanced computational methods

Slope stability, landslides, soil liquefaction problems, bearing capacity problems (Figure 1), excavation problems and large settlement problems are major examples of when computational methods may be applied. Advanced computational methods such as FDM, FEM, BEM, Mesh Free Method, and FVM are among those that have been used.

Fusao Oka is professor at the department of civil and earth resources engineering of Kyoto University in Japan. He has made outstanding contributions to the constitutive modelling of geomaterials and computational geotechnics over the past 25 years.

Oka has developed elastoviscoplastic models and cyclic elasto-plastic models for clays, sands and soft rocks. These have been successfully applied to various geotechnical problems such as consolidation analysis, progressive failure, strain localisation and liquefaction. He has developed computer codes to analyse the strain localisation problem, ie deformation bands, as shear bands of multi-phase soil and liquefaction (LIQCA) and has published more than 200 papers.

References Oka F (2005). Computational modelling of large deformations and the failure of geomaterials, Proc 16th ICSMGE, Osaka, Vol1 pp59-106.

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