# On the stability of geotechnical systems and its fractal progressive loss

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## Abstract

Geotechnical systems, consisting of soil and embedded solid structures, are practically stable if inevitable actions cause at most harmless redistributions. This kind of robustness can often be achieved with limit state design, i.e. by assuming representative snapshots of worst cases. Changes in configuration and state due to changing boundary conditions can be better judged with quasi-static numerical simulations using validated constitutive relations. The ever-present fractality of the ground may be neglected as long as the system is stable, whereas it gets dominant during a progressive loss of stability with jerky critical phenomena which elude mathematical treatment until present. In this sense geotechnical systems can be or get sensitive, i.e. further actions can trigger detrimental chain reactions with seismogeneous collapse of the soil fabric, pore pressure increase up to liquefaction, erosion, cracking of ground and structural parts and/or tilting. The geotechnical risk can be better mitigated by taking into account chain reactions with wild randomness. It can be further reduced by monitoring the seismic emission in addition to mass flows, structural deformations and pore pressures. The paper is to clarify notions and concepts.

## Keywords

Fractal Geotechnical system Limit state design Stability Sensitivity## Notes

### Acknowledgements

We owe Prof. W. Förster (Freiberg), Dr. M. Külzer (Stuttgart), Dr. A. Niemunis (Karlsruhe), Dr. K. Nübel (Stuttgart) and Prof. P. v. Wolffersdorff (Dresden) for valuable hints.

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