Hypoplastic constitutive relations for cohesive soils

Hypoplasticity is a new mathematical framework for constitutive equations. To date, hypoplastic equations have been developed for cohesionless soils such as sand and gravel. These equations have an outstanding simplicity and can be easily calibrated and implemented in Finite Element programme codes. Thus, they form the basis for many research projects devoted to theoretical and practical questions (e.g. of Civil and Mining Engineering and Tunnelling). However, hypoplastic equations are not yet applicable to cohesive soils, such as clays. Cohesive soils are characterized by much more complicated interactions between the individual particles. The cohesion emanates from physicochemical effects residing on the surface of the particles and results in force transmission mechanisms characterized by rate-dependence (i.e. non-linear viscosity). In addition, the clay particles are not rounded like the sand grains. They look like platelets or rods. Thus, their mutual arrangement (configuration) imposes a pronounced anisotropy. This anisotropy can be decisive for the mechanical behaviour of clay and depends on the previous history of the considered soil (so-called consolidation). The proposed project aims to find a hypoplastic equation capable of describing these effects.

Constitutive laws are mathematical relations aiming to decsribe the mechanical behaviour of soils. They are needed not only for purposes of numerical simulation of geotechnical processes but also for interpretation of the soil behaviour as this is observed in laboratory tests and field measurements. The main mathematical difficulty underlying cosntitutive models is their pronounced memory. I.e., soils do not forget their loading history, the previous loading can be detected by means of their actual mechanical response. There is a very evident example for this. Humans beings and animals leave behind them traces when walking upon soft soil. These manifest the memory of soil to the loading by the weight of the walkers. The theory of hypoplasticity models the loading history using the actual stress as carier of the memory. This allowed torealistically model many aspects of memory in a very simple but also realistic way. This success was made possible by the theoretical results of theorems derived by a school of thinking in continuum mechanics called Rational Mechanics. There is, however, a class of soils, the so-called cohesive soils such as clay, which have such a pronounced capacity of memorizing previous loading that cannot be stored solely in the actual stress. As a consequence, there must be introduced an additional tensorial parameter to store the memory of previous loading. This was the aim of this reserach project. We succeeded in finding such a parameter by means of introducing the `intergranular strain`. We could show that intergranular strain is capable to describe those effects of material memory which were missed so far. We have shown how to calibrate and how to calculate with this new parameter in such a way that the underlying experiments can be described. A particular difficulty in describing the memory of soils constitutes the so-called cyclic (i.e. repeated) loading. This difficulty has the same roots as the aforementioned difficulty related with memory. All influences of loading history are accumulated and appera more pronounced whever loading is cyclic. Modelling of cyclic loading is the notorious Achilles heel of constitutive modelling. It is to be added that cyclic loading is for some problems (e.g. for pavements of railways) very important. Introducing a memory or structure tensor as an intergranular strain helps to overcome the related problems and allows a realistic modelisation of the pertinent effects, as tehy are known form laboratory testing of soils. Intergranular strain operates in the strain space. Its way of modelling hysteretic behaviour can be described in easy terms as follows: the actual strain caries with it the memory in the form of a region that moves within the strain space. Intoducing appropriate kinetics of the moved region makes possible to realitically describe hysteretic effects.