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Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement; the opposite condition is called slope instability or slope failure. The stability condition of slopes is a subject of study and research in soil mechanics , geotechnical engineering , and engineering geology .
Wind throw is the toppling of a tree due to the force of the wind, this exposes the root plate and adjacent soil beneath the tree and influences slope stability. Wind throw is a factor when considering one tree on a slope; however, it is of lesser importance when considering general slope stability for a body of trees as the wind forces involved represent a smaller percentage of the potential ...
The DEM is based on solution of dynamic equation of equilibrium for each block repeatedly until the boundary conditions and laws of contact and motion are satisfied. Discontinuum modelling belongs to the most commonly applied numerical approach to rock slope analysis and following variations of the DEM exist: [39] distinct-element method
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
Unless indicated to the contrary, the above limiter functions are second order TVD. This means that they are designed such that they pass through a certain region of the solution, known as the TVD region, in order to guarantee stability of the scheme. Second-order, TVD limiters satisfy at least the following criteria:
Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function = at any = based on the value and slope of the function at =, given that () is differentiable on [,] (or [,]) and that is close to .
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
Slope: = = This gives an exact value for the slope of a straight line. If the function is not linear, however, then the change in divided by the change in varies. The difference quotient give an exact meaning to the notion of change in output with respect to change in input.