SUMMARYThe paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The in#uence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a "nite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FEcalculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar e!ects manifested by the appearance of grain rotations and couple stresses are only signi"cant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement.

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After an introductory presentation of design approaches the risks involved are investigated. Considered are different ground improvement methods, like soil mixing, vibro compaction and vibro stone columns, as well as pile-like supporting elements, including vibro concrete columns and full displacement columns named rigid inclusions. The difference in stiffness of the inserted material and the soil determines the design and the risks involved. Three categories with increasing risk are proposed. Ground improvement methods, ductile in compliance with EN 1997-1 and DIN 1054, proved to be extraordinary robust and present only a small risk with regard to a possible variation of soil and material parameters and loads. The design is usually determined by the serviceability limit state. Risks increase with the application of non-ductile methods with small column diameter, like rigid inclusions, because the ultimate limit state is controlling the behaviour. Namely, in order to mobilize high skin friction, the lower and upper end of the column have to fail during punching in the soil below and the load transfer platform above. Even a small variation in material parameters, system geometry or loads may lead to a complete loss of bearing capacity and progressive failure, resulting in expensive damages of civil engineering structures and time consuming repair works.

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