Application of the Mechanics of Tropical Soils in Geotechnical Engineering

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Ongoing Global Energy Conservation R&D within Geotechnical/Civil Engineering and general science by Dr. John N Mukabi and Team
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  Application of the Mechanics of Tropical Soils in Geotechnical Engineering;Some Recent Advances and Introduction of Futuristic Concepts on GeoscientificGECS John MUKABI Kensetsu Kaihatsu Consultants Ltd. dr.mukabi@kensetsu.co.ke Abstract : Sound knowledge of Soil Mechanics is a fundamental requirement for aGeotechnical Engineer. Increased application of theories and principles related to soilmechanics as a basis for fostering enhanced geotechnical engineering practice isindeed imperative for industrial and infrastructure development.It is also common knowledge that the stability of any structure depends on thesuitability of soil as the load bearing capacity primarily depends on the soilcharacteristics.The various ways in which soil is used in structures are; as load bearing strata directlyunder the structure, transferring load through piers, cassions or piles, as a constructionmaterial for earthen dams and as embankment material for highways, railways andrunways.Consequently, taking this into account, the importance of advancing the knowledge of research based soil mechanics cannot be over-emphasized. It is important toemphasize the fact that this research is still it its infant stage.1. INTRODUCTIONIt is indeed appreciated that the Special Theory of Relativity constitutes one of themost beautiful chapters of the twentieth century physics. Its srcin provides a particularlyinteresting example of the overthrow of the notion of measure connected with space,time and motion, hitherto regarded as fundamental. The departure from classicalconcepts was forced by the discovery of new facts which were not in accordance withthe earlier theories.The postulation of the Special Theory of Relativity in 1905 and the General theory in1916, led to a radical revision of the accepted concepts of space and time. It denied theneed and possibility of the mechanistic view of nature that one can constructmechanical models for all physical phenomena. It gave a great fillip to further development of contemporary physics, in particular atomic and nuclear physics. Thisrole consisted not only of the use of important relations of the theory of relativity but alsoshowing that classical concepts obtained from everyday life turn out to be inadequate indealing with new fields.To that extent, The Theory of Relativity envisaged the beginning of the developmentof a new, non-classical physics.In this Paper, new concepts of soil mechanics are introduced by relating soil structure,strength and deformation characteristics, Several Systematic Scientific ApproachConcepts (SSACs) are presented and various theories introduced. Application of newlyproposed Theory of Suspended Particles (TSP) and the String Dispersion Theory (SDT)in geo-scientifically and mathematically analyzing the intricate interaction of three phasestate of geomaterials by applying Lorentz transformations and their relativisticconsequences, is also discussed. Derivation of these equations in deducing thekinematical geophysics is also presented and extended to the implications of SpecialRelativity to Dynamics. 1  One such approach proposed is the formulation of the dynamic equation of motion inaccordance with the postulates of The Special Theory of Relativity through the adoptionof the concepts of four-vectors and relativistic invariance in a four-dimensional space-time coordinate system.The foregoing theories and principles are then to be consistently broadened toestablish hypothetical theories that can support the future development of the proposedGlobal Energy Conservation Systems (GECS).The fundamental idea behind this theory is to scientifically develop energyconservation systems that can harness potentially destructive and disastrous energiesthat emanate from as earthquakes, volcanic eruptions, tsunamis etc and transform theminto constructive and useful energy sources. One of the proposed theories is the EDF 2 .Under this theory, relative motion, ballistics-collisions, dynamic stresses, tensors,viscous and damping effects, particle movement and orientation, stress-strain energy,variation in voids ratios, and hydrostatic/hydrodynamic stresses/forces are analyzed inrelation to an advanced multi-phase geosciences phenomenon.Applying SSACs advanced theoretical analysis of canvassing systematic, organized,entropic and complex interference, time-space dynamics, localized inter-particlegravitational forces, constitutive solutions and redundancy theories defined in terms of energy dissipation, conserved potential and kinetic energy, advanced laws of motion,the Theory of Relativity and the Big Bang Theory are to be developed as a primaryattempt to the realization of the GECS. 2. BRIEF INTRODUCTION OF SOME FUNDAMENTAL THEORIES AND CONCEPTS As mentioned in the introduction, the new theories introduced are based onSystematic Scientific Approach Concepts (SSAC). The SSACs are merely controlconcepts that ensure that the theories are systematic and not entropic in terms of logicalapproach, definitive terms and development of events with a given space-time frame of reference. 2.1 Theory of Suspended Particles (TSP) Fundamentally, the TSP assumes that a particle is initially suspended in vacuum as aresult of the equilibrium between a gravitational force () initiated field and a fieldresulting from the force of gravity as schematically depicted Fig. 2.1Fig. 2.1 Schematic depiction of the Theory of Suspended Particles 2  2.2 String Dispersion Theory This theory is intended to quantitatively define the dispersion of particles under dampedcollision conditions both in dynamic and static fields depending on the rate, level andintensity of damping.The particle motions are mainly translational in the major principal axis experiencingreversible influxes of dispersion, suspension and flocculation.An attempt will be made, during this research, to modify the Lorentz transformationequations expressed in Eqs. (2.1) and (2.2) and application of kinematicalconsequences of the same to characterize and quantify the lengths of the deformedwater strings and the relative motion of the particles.The hypothetical postulates of the modified Lorentz transformations are:(2.1)(2.2)Where and are the modifiers respectively.The above equations would then be further modified to quantitatively define thekinematical consequences.On the other hand, the force transformations defining the action and reaction of the particles relative to the water and air medium would be developed and modifiedbased on the following equations.(2.3)(2.4)Thus,(2.5)(2.6)The transformation of relativistic momentum and energy is then derived from modifiedequations expressed as(2.7)and(2.8)respectively. and are the respective modifiersFurther modification to incorporate the four-vector concepts and their transformationswould then be undertaken. 3. INTRODUCTION OF SOME RELEVANT THEORIES AND CONCEPTS3.1 Homogenization Theory of Elastic Problems and Particle Micro-damage3.1.1Concept of Estimation of micro-damage initiation and propagation Considering that most grains are in contact with each other as set out in the Hertzianloading arrangement in Fig. 3.1.1 interpretation is based on the micro-crack initiationand propagation at the contact portion of the grains incorporating a special formation of the stress field of Hertzian loading [Wilshaw (1971) 3  Fig.3.1.1 Hertzian loading Arrangement showing a schematic Array of Graincontact.The radius a, as shown in Fig.3.1.1. of the circle of contact between the two spheresQ and F is derived from the Hertzian analysis as: ( ) ( ) −+−= − 1223 1143  E v E v Pf  a (3.1)Where,P: Normal land Applied on the Grain’E’, E: Young’s Moduli for Quartz and Feldspar Grains RespectivelyV’, V: Corresponding values of the poisson RatioThe primary stress – induced intracrystalline micro-crack is initiated from the contactportion of the two grains while the crack in small and normal to the contact surface, themaximum tensile stress Qm σ   and  F m σ   in the Quartz and Feldspar grains are uniformlydistributed along the micro-crack and the microcracking criterion is assumed equivalentto that for a single edge microcrack in tension.The stress intensity factors Q I   K  and  F  I   K  which are the function of the stress andmicrocrack length Q C  and 1  F  C  are given by: ( ) 5.0 QQmQ I  C  A K  π σ  = (3.2)and ( ) 5.011 F  F m F  I  C  A K  π σ  = (3.3)Where, = C  I   A 1.12 Predetermined Material Constant, ( ) 21 221 a P v QQm π  σ   −= (3.4) 4
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