Study On Finite Characteristic Ratio Theory For Analyzing Mechanical Responses Of Soils

Soil mechanics have been developed for over 200 years since Charles Augustin de Coulomb published his paper "Essay on the application of the rules of the maxima and minima to certain statics problems relavant to architecture" in Paris, France. However, the key problem, i.e. the problem with non-linear constitutive equations, faced by scientists and engineers in the field of soil mechanics and engineering is still difficult to deal with. Countless scholars have been groping for the new path to break through in the research of non-linear constitutive equations.It is the fact from vast and long time tests, monitors, and engineering practices that the mechanical responses of geomaterials mainly depend on the meso-scale (granule scale) mechanism, even macro-scale mechanism; in other word, characteristic ratio L of a material point (internal) characteristic measurement to the material or engineering structure external measurement is not small enough. Then, a object discussed might not include enough material points (volume elements) which could represent the mechanical nature of the whole object. It means that the consideration of the "mathematical point" on the volume element might not be right in geotechnical engineering. It is originally presented by author that â‘ the material point which represents statistic mechanical properties of a geomaterial is a finite geometry point but is not a mathematical point, â‘¡the finite characteristic ratio L defined as above is a basic phenomenological variable which is connected with the irrecoverable deformation and energy dissipation, and â‘¢the L can be expressed as a function of stress or strain, temperature, and internal variable. With the above concepts, the new constitutive relations are derived within the general frame of the thermodynamics with internal variable; and consequently, the relevant soil model is proposed. The finite element analysis method on the model is put forward, and the accurate determination method of the only four non-elastic material parameters in the model is also presented based on the deformation feature of sand. The tests on two sands with different grain size are carried through, and the result compare between the tests is put up. Furthermore, the result compares between the model and the tests are also gone alone. It shows that the various compare results are well-pleasing. Besides above, the mechanical responses of sands with different packing arrangements are analyzed quantificationally at meso-scale. The innovations here are: (1) The finite characteristic ratio constitutive theory system (including the presentation of some basic concepts, the constitution of basic theory and its model, the determination of the model parameters, the test method, and finite element method) is originally proposed. (2) That the material point (volume element) to be able to represent statistic mechanical properties of a geomaterial should be a "finite geometry point" but not a "mathematical point" is presented according to facts. (3) The quantificational analysis, taking the lead by the author, on the sand show that there are different responses between stress ratio and volume strain for different packs even though the granule in sands is same. (4) It is posted that under same external condition the mechanical response curves of sands with different granule are similar, but not stress value when the corresponding strain is certain.The essential mechanical properties of soils and typical constitutive relations for soils are also discussed for the sake of above study need.