Tectonic upliftTectonic uplift is the geologic uplift of Earth's surface that is attributed to plate tectonics. While isostatic response is important, an increase in the mean elevation of a region can only occur in response to tectonic processes of crustal thickening (such as mountain building events), changes in the density distribution of the crust and underlying mantle, and flexural support due to the bending of rigid lithosphere. Tectonic uplift results in denudation (processes that wear away the earth's surface) by raising buried rocks closer to the surface.
OrogenyOrogeny is a mountain building process that takes place at a convergent plate margin when plate motion compresses the margin. An orogenic belt or orogen develops as the compressed plate crumples and is uplifted to form one or more mountain ranges. This involves a series of geological processes collectively called orogenesis. These include both structural deformation of existing continental crust and the creation of new continental crust through volcanism.
DamA dam is a barrier that stops or restricts the flow of surface water or underground streams. Reservoirs created by dams not only suppress floods but also provide water for activities such as irrigation, human consumption, industrial use, aquaculture, and navigability. Hydropower is often used in conjunction with dams to generate electricity. A dam can also be used to collect or store water which can be evenly distributed between locations.
ReservoirA reservoir (ˈrɛzərvwɑːr; from French réservoir ʁezɛʁvwaʁ) is an enlarged lake behind a dam. Such a dam may be either artificial, usually built to store fresh water, or it may be a natural formation. Reservoirs can be created in a number of ways, including controlling a watercourse that drains an existing body of water, interrupting a watercourse to form an embayment within it, excavating, or building any number of retaining walls or levees.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Soil mechanicsSoil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually clay, silt, sand, and gravel) but soil may also contain organic solids and other matter. Along with rock mechanics, soil mechanics provides the theoretical basis for analysis in geotechnical engineering, a subdiscipline of civil engineering, and engineering geology, a subdiscipline of geology.
Creep (deformation)In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increase as they near their melting point. The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load.
HydrogeologyHydrogeology (hydro- meaning water, and -geology meaning the study of the Earth) is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust (commonly in aquifers). The terms groundwater hydrology, geohydrology, and hydrogeology are often used interchangeably. Hydrogeology is the study of the laws governing the movement of subterranean water, the mechanical, chemical, and thermal interaction of this water with the porous solid, and the transport of energy, chemical constituents, and particulate matter by flow (Domenico and Schwartz, 1998).
Deformation (engineering)In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve.
Hoover DamHoover Dam is a concrete arch-gravity dam in the Black Canyon of the Colorado River, on the border between the U.S. states of Nevada and Arizona. It was constructed between 1931 and 1936 during the Great Depression and was dedicated on September 30, 1935, by President Franklin D. Roosevelt. Its construction was the result of a massive effort involving thousands of workers, and cost over 100 lives. It was referred to as the Hoover Dam after President Herbert Hoover in bills passed by Congress during its construction; it was named the Boulder Dam by the Roosevelt administration.
St. Francis DamThe St. Francis Dam was a concrete gravity dam located in San Francisquito Canyon in northern Los Angeles County, California that was built between 1924 and 1926 to serve the city of Los Angeles's growing water needs. It failed catastrophically in 1928 due to a defective soil foundation and design flaws, unleashing a flood that claimed the lives of at least 431 people.
Rock mechanicsRock mechanics is a theoretical and applied science of the mechanical behavior of rocks and rock masses. Compared to geology, it is the branch of mechanics concerned with the response of rock and rock masses to the force fields of their physical environment. Rock mechanics is part of a much broader subject of geomechanics, which is concerned with the mechanical responses of all geological materials, including soils. Rock mechanics is concerned with the application of the principles of engineering mechanics to the design of structures built in or on rock.
Plasticity (physics)In physics and materials science, plasticity (also known as plastic deformation) is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding. Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams.
GeologyGeology () is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth sciences, including hydrology. It is integrated with Earth system science and planetary science. Geology describes the structure of the Earth on and beneath its surface and the processes that have shaped that structure.
Effective stressThe effective stress can be defined as the stress, depending on the applied tension and pore pressure , which controls the strain or strength behaviour of soil and rock (or a generic porous body) for whatever pore pressure value or, in other terms, the stress which applied over a dry porous body (i.e. at ) provides the same strain or strength behaviour which is observed at ≠ 0. In the case of granular media it can be viewed as a force that keeps a collection of particles rigid.
