The Theoretical Research on the Stress Relaxation of Clay

Abstract

Recently, with development of soil engineering, when we stand on a view-point that the soil is also one of the engineering materials such as the high polymer or metal, and wish to explain unificatively the complicated mechanical behaviour of soils, it is methodologically necessary that we must consider an introduction of thermo-dynamics and statistical mechanics based on the molecular theoretical investigation.In this case, however, we cannot avoid facing a difficulty which is due to that the deformations of soils are irreversible in general, because the thermo-dynamical analysis is confined to considerations of reversible process of deformation only.Then, in order to overcome the above difficulty, the authors have established several assumptions as follows:(1) The authors have adopted a network structure of“card-house”presented by T. K. TAN1) for the skeletal structure of clay. However, we cannot mathematically express a formal distribution of the skeletal structure merely by this network structure. Therefore, a pattern showed in Fig. 2(a) was presented by the authors anew, which was a cross section of the clay network structure. In Fig. 2(b), a broken line turned at random was called“imaginary chain”of the clay network by the authors, further the mutual contact between the clay particles (i.e., the turning point of the imaginary chain) was denominated“unit mechanism of deformation”. The bonding force at this contact point, of course may be due to Coulomb attraction force between the positively charged edges and negatively charged flat sides of the clay particles, van der Waals forces, bonding by cations, and dipole hydrogen bridges.(2) For the deformation process, we have assumed that a micro elastic deformation may occur at the instant of loading, and a retarded deformation that is due to slipping of the clay particles follows on the instantaneous elastic deformation. The macro plastic deformation consists of these two deformations. The micro irreversible deformation at the contact point occurs only when the stress component acted to the unit mechanism of deformation becomes greater than the bonding energy of the contact point.(3) For a thermo-dynamical expression of the micro reversible deformation process of the clay, we have assumed that the external force is composed of the energy elasticity and the entropy elasticity, and the former is proportional to the latter.By the above hypotheses, the authors have accomplished the introduction of thermo-dynamics and statistical mechanics to soil mechanics. As a result of the theoretical investigation, the authors have obtained a unificative equation (12) that is of the same type as Maxwell's equation. However, by the simple Maxwell's equation, it is not yet enough to explain the complicated rheological properties of clay, and so the authors introduce the structural viscosity of clay by applying Eyring's viscosity theory to the double water layer of clay particles. Consequently we have been able to explain molecular theoretically the rheological behaviour of clay.