Victor N. Nikolaevskiy – författare

Geomechanics is the basic science for many engineering fields, including oil and gas recovery, mining, civil engineering, water supply, etc., as well as for many environmental sciences, including earthquake prediction, ecology, landscape dynamics, and explosion works. Historically, the major concepts of geomechanics were founded on the methods of the elasticity theory and the static equilibrium of joints with solid friction. Underground hydrodynamics was developed quite separately and included only simple, conventional ideas of elastic pore-space deformation. Today, the situation is drastically different. Tremendous achievements in numerical computer technique have eliminated many of the routine difficulties of problem solution with respect to selected mathematical models. As the result, major efforts now are applied to sophisticated experimental studies and to new applications of generalized continuum theories. Of course, traditional rheological schemes have been adjusted to be into account the real properties of such geomaterials as soils, rocks and ice. The main changes have been connected with the kinematics of the internal structure of geomaterials that influences their strength and that can play unusual roles in dynamic processes. The theoretical considerations are in good agreement with experimental observations in situ because of precise measuring devices, impact of modern physics concepts and large-scale monitoring.

Turbulence theory is one of the most intriguing parts of fluid mechanics and many outstanding scientists have tried to apply their knowledge to the development of the theory and to offer useful recommendations for solution of some practical problems. In this monograph the author attempts to integrate many specific approaches into the unified theory. The basic premise is the simple idea that a small eddy, that is an element of turbulent meso-structure, possesses its own dynamics as an object rotating with its own spin velocity and obeying the Newton dynamics of a finite body. A number of such eddies fills a coordinate cell, and the angular momentum balance has to be formulated for this spatial cell. If the cell coincides with a finite­ difference element at a numerical calculation and if the external length scale is large, this elementary volume can be considered as a differential one and a continuum parameterization has to be used. Nontrivial angular balance is a consequence of the asymmetrical Reynolds stress action at the oriented sides of an elementary volume. At first glance, the averaged dyad of velocity components is symmetrical, == However, if averaging is performed over the plane with normal nj, the principle of commutation is lost. As a result, the stress tensor asymmetry j is determined by other factors that participate in the angular momentum balance. This is the only possibility to determine a stress in engineering.

Geomechanics is the basic science for many engineering fields, including oil and gas recovery, mining, civil engineering, water supply, etc., as well as for many environmental sciences, including earthquake prediction, ecology, landscape dynamics, and explosion works. Historically, the major concepts of geomechanics were founded on the methods of the elasticity theory and the static equilibrium of joints with solid friction. Underground hydrodynamics was developed quite separately and included only simple, conventional ideas of elastic pore-space deformation. Today, the situation is drastically different. Tremendous achievements in numerical computer technique have eliminated many of the routine difficulties of problem solution with respect to selected mathematical models. As the result, major efforts now are applied to sophisticated experimental studies and to new applications of generalized continuum theories. Of course, traditional rheological schemes have been adjusted to be into account the real properties of such geomaterials as soils, rocks and ice. The main changes have been connected with the kinematics of the internal structure of geomaterials that influences their strength and that can play unusual roles in dynamic processes. The theoretical considerations are in good agreement with experimental observations in situ because of precise measuring devices, impact of modern physics concepts and large-scale monitoring.

Turbulence theory is one of the most intriguing parts of fluid mechanics and many outstanding scientists have tried to apply their knowledge to the development of the theory and to offer useful recommendations for solution of some practical problems. In this monograph the author attempts to integrate many specific approaches into the unified theory. The basic premise is the simple idea that a small eddy, that is an element of turbulent meso-structure, possesses its own dynamics as an object rotating with its own spin velocity and obeying the Newton dynamics of a finite body. A number of such eddies fills a coordinate cell, and the angular momentum balance has to be formulated for this spatial cell. If the cell coincides with a finite­ difference element at a numerical calculation and if the external length scale is large, this elementary volume can be considered as a differential one and a continuum parameterization has to be used. Nontrivial angular balance is a consequence of the asymmetrical Reynolds stress action at the oriented sides of an elementary volume. At first glance, the averaged dyad of velocity components is symmetrical, == However, if averaging is performed over the plane with normal nj, the principle of commutation is lost. As a result, the stress tensor asymmetry j is determined by other factors that participate in the angular momentum balance. This is the only possibility to determine a stress in engineering.

Geomechanics is the basic science for many engineering fields, including oil and gas recovery, mining, civil engineering, water supply, etc., as well as for many environmental sciences, including earthquake prediction, ecology, landscape dynamics, and explosion works. Historically, the major concepts of geomechanics were founded on the methods of the elasticity theory and the static equilibrium of joints with solid friction. Underground hydrodynamics was developed quite separately and included only simple, conventional ideas of elastic pore-space deformation. Today, the situation is drastically different. Tremendous achievements in numerical computer technique have eliminated many of the routine difficulties of problem solution with respect to selected mathematical models. As the result, major efforts now are applied to sophisticated experimental studies and to new applications of generalized continuum theories. Of course, traditional rheological schemes have been adjusted to be into account the real properties of such geomaterials as soils, rocks and ice. The main changes have been connected with the kinematics of the internal structure of geomaterials that influences their strength and that can play unusual roles in dynamic processes. The theoretical considerations are in good agreement with experimental observations in situ because of precise measuring devices, impact of modern physics concepts and large-scale monitoring.