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Terzaghi's Principle
Terzaghi's Principle states that when stress is applied to a porous material, it is opposed by the fluid pressure filling the pores in the material. Karl von Terzaghi introduced the idea in a series of papers in the 1920s based on his examination of building Soil consolidation, consolidation on soil. The principle states that all quantifiable changes in Stress (physics), stress to a porous medium are a direct result of a change in effective stress. The ''effective stress,'' \boldsymbol_, is related to ''total stress,'' \boldsymbol , and the ''pore pressure,'' P, by :\boldsymbol_ = \boldsymbol - P\mathbb , where \mathbb I is the Identity Matrix, identity matrix. The negative sign is there because the pore pressure serves to lessen the volume-changing stress; physically this is because there is fluid in the pores which bears a part of the total stress, so partially unloading the solid matrix from normal stresses. Terzaghi's principle applies well to porous materials whose solid con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Von Terzaghi
Karl von Terzaghi (October 2, 1883 – October 25, 1963) was an Austrians, Austrian Mechanical Engineer, mechanical engineer, geotechnical engineer, and geologist known as the "father of soil mechanics and geotechnical engineering". Early life In 1883, he was born the first child of Army Lieutenant-Colonel Anton von Terzaghi, of Italian origin, and Amalia Eberle in Prague, in what is now the Czech Republic. Upon his father's retirement from the army, the family moved to Graz, Austria. At 10, Terzaghi was sent to a military boarding school, where he developed an interest in astronomy and geography. At age fourteen, Terzaghi entered a different military school, in Hranice (Přerov District), Hranice, the Crown of Bohemia. He was an excellent student, especially in geometry and mathematics, and graduated with honors at 17. In 1900, Terzaghi entered the Technical University Graz, Technical University in Graz to study mechanical engineering, where he also developed an interest in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soil Consolidation
Soil consolidation refers to the soil mechanics, mechanical process by which soil changes volume gradually in response to a change in pressure. This happens because soil is a three-phase material. The first phase consists of soil grains, and a combination of void (air) or other fluid (typically groundwater) comprise the second and third phases. When soil soil saturation, saturated with water is subjected to an increase in pressure, the high bulk modulus, volumetric stiffness of water compared to the soil matrix means that the water initially absorbs all the change in pressure without changing volume, creating excess pore water pressure. As water diffuses away from regions of high pressure due to seepage, the soil matrix gradually takes up the pressure change and shrinks in volume. The theoretical framework of consolidation is therefore closely related to the concept of effective stress, and hydraulic conductivity. The early theoretical modern models were proposed one century ago, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (physics)
In continuum mechanics, stress is a physical quantity that describes Force, forces present during Deformation (physics), deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to Tension (physics), ''tensile'' stress and may undergo Elongation (materials science), elongation. An object being pushed together, such as a crumpled sponge, is subject to Compression (physics), ''compressive'' stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has Dimension (physics), dimension of force per area, with SI Units, SI units of newtons per square meter (N/m2) or Pascal (unit), pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while Strain (mechanics), ''strain'' is the measure of the relative deformation (mechanics), deformation of the material. For example, when a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Porous Medium
In materials science, a porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media. A porous medium is most often characterised by its porosity. Other properties of the medium (e.g. permeability, tensile strength, electrical conductivity, tortuosity) can sometimes be derived from the respective properties of its constituents (solid matrix and fluid) and the media porosity and pores structure, but such a derivation is usually complex. Even the concept of porosity is only straightforward for a poroelastic medium. Often both the solid matrix and the pore network (also known as the pore space) are continuous, so as to form two interpenetrating continua such as in a sponge. However, there is also a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Stress
Effective stress is a fundamental concept in soil mechanics and geotechnical engineering that describes the portion of total stress in a soil mass that is carried by the solid soil skeleton, rather than the pore water. It is crucial for understanding the mechanical behaviour of soils, as effective stress governs both the strength and volume change (deformation) of soil. More formally, effective stress is defined as the stress that, for any given pore pressure p, produces the same strain or strength response in a porous material (such as soil or rock) as would be observed in a dry sample where p = 0. In other words, it is the stress that controls the mechanical behaviour of a porous body regardless of pore pressure present. This concept applies broadly to granular media like sand, silt, and clay, as well as to porous materials such as rock, concrete, metal powders and biological tissues. History Karl von Terzaghi first proposed the relationship for effective stress in 1925. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context. I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \dots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end. The term unit matrix has also been widely used, but the term ''identity matrix'' is now standard. The term ''unit matrix'' is ambiguous, because it is also used for a matrix of on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maurice Anthony Biot
Maurice Anthony Biot (May 25, 1905 – September 12, 1985) was a Belgian-American applied physicist. He made contributions in thermodynamics, aeronautics, geophysics, earthquake engineering, and electromagnetism. Particularly, he was accredited as the founder of the theory of poroelasticity. Born in Antwerp, Belgium, Biot studied at Catholic University of Leuven in Belgium where he received a bachelor's degrees in philosophy (1927), mining engineering (1929) and electrical engineering (1930), and Doctor of Science in 1931. He obtained his Ph.D. in Aeronautical Science from the California Institute of Technology in 1932 under Theodore von Kármán. In 1930s and 1940s Biot worked at Harvard University, the Catholic University of Leuven, Columbia University and Brown University, and later for a number of companies and government agencies, including NASA during the Space Program in the 1960s. After 1969 Biot became a private consultant for various companies and agencies, and part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poroelasticity
Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow, pressure and bulk solid deformation within a linear porous medium and it is an extension of elasticity and porous medium flow (diffusion equation). The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot (1935, 1941) as a theoretical extension of soil consolidation models developed to calculate the settlement of structures placed on fluid-saturated porous soils. The theory of poroelasticity has been widely applied in geomechanics, hydrology, biomechanics, tissue mechanics, cell mechanics, and micromechanics. An intuitive sense of the response of a saturated elastic porous medium to mechanical loading can be developed by thinking about, or experimenting with, a fluid-saturated sponge. If a fluid-saturated sponge is compressed, fluid will flow from the sponge. If the sponge is in a fluid reservoir and compre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poromechanics
Poromechanics is a branch of physics and specifically continuum mechanics that studies the behavior of fluid-saturated porous media. A porous medium or a porous material is a solid (referred to as matrix) permeated by an interconnected network of pores or voids filled with a fluid. In general, the fluid may be composed of liquid or gas phases or both. In the simplest case, both the solid matrix and the pore space occupy two separate, continuously connected domains, such as in a kitchen sponge. Some porous media has a more complex microstructure in which, for example, the pore space is disconnected. Pore space that is unable to exchange fluid with the exterior is termed occluded pore space. Alternatively, in the case of granular porous media, the solid phase may constitute disconnected domains, termed the "grains", which are load-bearing under compression, though can flow when sheared. Natural substances including rocks, soils, biological tissues including plants, heart, and canc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain (physics)
In mechanics, strain is defined as relative deformation, compared to a position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. Strain has dimension of a length ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage. Parts-per notation is also used, e.g., parts per million or parts per billion (sometimes called "microstrains" and "nanostrains", respectively), corresponding to μm/m and nm/m. Strain can be formulated as the spatial derivative of displacement: \boldsymbol \doteq \cfrac\left(\mathbf - \mathbf\right) = \boldsymbol'- \boldsymbol, where is the identity tensor. The displacement of a body may be expressed in the form , where is the reference position of material po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permeability (earth Sciences)
In fluid mechanics, materials science and Earth sciences, the permeability of porous media (often, a rock or soil) is a measure of the ability for fluids (gas or liquid) to flow through the media; it is commonly symbolized as ''k''. Fluids can more easily flow through a material with high permeability than one with low permeability. The permeability of a medium is related to the '' porosity'', but also to the shapes of the pores in the medium and their level of connectedness. Fluid flows can also be influenced in different lithological settings by brittle deformation of rocks in fault zones; the mechanisms by which this occurs are the subject of fault zone hydrogeology. Permeability is also affected by the pressure inside a material. The SI unit for permeability is the square metre (m2). A practical unit for permeability is the '' darcy'' (d), or more commonly the ''millidarcy'' (md) The name honors the French Engineer Henry Darcy who first described the flow of wat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
