Global convergence in systems of differential equations arising from chemical reaction networks

It is shown that certain classes of differential equations arising from the modelling of chemical reaction networks have the following property: the state space is foliated by invariant subspaces each of which contains a unique equilibrium which, in turn, attracts all initial conditions on the associated subspace

Pore-Pressure Generation and Liquefaction of Granular Soil Tested in Triaxial Conditions

The paper deals with modelling of pore-pressure generation in saturated sand subjected to triaxial cyclic loading in undrained conditions. The model proposed links the pore-pressure generation with the cyclic loading induced compaction of the same sand, but tested in fully drained conditions. The governing equation for the pore-pressure changes is derived from the assumption that no volumetric strain develops in saturated sand in undrained conditions. The numerical solutions are compared with experimental data, for a large number of loading cycles

Instability line as a basic characteristic of non-cohesive soils

In the paper, the experimental results of undrained response of non-cohesive soil subjected to either monotonic or cyclic loading, are analysed and discussed. The analysis was based on the results of comprehensive testing programme made of "Skarpa" sand investigated in the triaxial compression. Two main undrained behaviours such as liquefaction and cyclic mobility were experimentally identified and studied. In the analysis of undrained behaviour, the concept of steady state of deformation has been adopted. It was shown that the undrained response of non-cohesive soils is governed by different failure mechanisms than in the case of drained samples. In undrained failure mechanism, an important role is played by an instability line, which may be identified with the initiation of potential liquefaction

On the measurement of strains in the triaxial test

In the paper, various methods of measuring a sample strains in a triaxial test are analysed. Accurate determination of the deformation of a specimen in a triaxial compression test is of great importance for correct evaluation of soil strain-stress characteristics, particularly in the pre-failure stress state in the range of small strains. In the paper, three different methods of measuring axial strains are analysed and discussed. Two consider the measurement of relative movement between top cap and base pedestal of the triaxial cell, the third being based on the direct measurement of local axial deformation of the sample tested. The measurement of radial strains is also discussed in respect of the corrections introduced for the specimen's bulging. To analyse various methods of strains measurements tests on diverse materials such as sand, steel and rubber were carried out, enabling the evaluation of the efficiency and accuracy of the measurement methods applied

Wave-induced stresses and liquefaction in seabed according to the biot-type approach

The problem of wave-induced stresses and liquefaction in the seabed according to the Biot-type approach is discussed. The first part of the paper deals with critical analysis of approaches presented in recent literature. It is shown that such approaches do not lead to proper description of the process of wave-induced pore-pressure generation and subsequent liquefaction of seabeds. The second part of this paper deals with the generalisation of the Biot-type approach to the case of shear modulus depending on mean effective stress

Some effects of intrinsic cyclic loading in saturated sands

This paper presents original results of triaxial experiments performed at a cyclically changed pore pressure (intrinsic cyclic loading). The results display unusual behaviour of saturated sand subjected to such atypical loading. Some features of this behaviour are shown, including the following effects: static liquefaction of initially contractive sand, apparent creep of initially dilative sand, initial anisotropy, etc. Some differences between the classical geotechnical understanding of the effects of external cyclic loadings (such as earthquakes) and those caused by intrinsic cyclic loadings (such as wave-induced pressures) are discussed

SOME EFFECTS OF INTRINSIC CYCLIC LOADING IN SATURATED SANDS

This paper presents original results of triaxial experiments performed at a cyclically changed pore pressure (intrinsic cyclic loading). The results display unusual behaviour of saturated sand subjected to such atypical loading. Some features of this behaviour are shown, including the following effects: static liquefaction of initially contractive sand, apparent creep of initially dilative sand, initial anisotropy, etc. Some differences between the classical geotechnical understanding of the effects of external cyclic loadings (such as earthquakes) and those caused by intrinsic cyclic loadings (such as wave-induced pressures) are discussed