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For free, without analysis restrictions. The software won't run on mobile devices. We can however send you a download link to your email. The first ones are equilibrium equations, the second ones describe the behavior of the soil. These equations are particularly complex since the soil is made of multiphase systems, which can be traced to single-phase systems only in dry soil conditions, or analysis in drained conditions.
For preliminary analysis and design, however, the use of manual methods of slope stability analysis may be justified. A landfill is composed of different materials. Slope Stability | TerrainWorks Slope stability analysis has urban 1s Slope Stability and Protection (Engineering SoundBites) (English.
In most cases we have to deal with a material that if is saturated is at least two-phase, which makes the treatment of the equilibrium equations considerably complicated. Furthermore, it is practically impossible to define a constitutive law of general validity, because the soils have a non-linear behavior already at small strains, are anisotropic, and also their behavior depends not only on the deviatoric stress but also on the normal stress. Because of the above difficulties are introduced simplifying assumptions:.
Limit equilibrium method LEM The limit equilibrium method consists of the study of the equilibrium between a rigid body, such as the slope, and of a slip surface of any shape straight line, arc of a circle, logarithmic spiral, etc. From this comparison derives the first indication of stability as the Factor of Safety:. Among the various equilibrium methods some consider the global equilibrium of the rigid body Culman , while others divide the rigid body into slices to cater for its non homogeneity and consider the equilibrium of each of these Fellenius, Bishop, Janbu, etc.
S lice method The volume affected by slide is subdivided into a convenient number of slices. If the number of the slices is n the problem presents the following unknowns:. The degree of indetermination is further reduced to n-2 as it is assumed that N i is applied at a mid point of the slice, which is equivalent to assume the hypothesis that total normal stresses are distributed uniformly. The various methods that are based on limit equilibrium theory differ in the way in which the n-2 degrees of indetermination are eliminated. This equation is easy to solve, but it was found that provides conservative results low safety factors especially for deep surfaces or at the increase in the value of the pore pressure.
Bishop method None of the contributing forces acting on slices is ignored using this method that was the first to describe the problems of conventional methods.
The equations used to resolve the problem are:. When freeform generic form sliding surfaces are treated, the arm of the forces changes in case of circular surfaces it is constant and equal to the radius of the arc and therefore it is more convenient to evaluate the moment equation at the angle of each slice. Janbu also proposed a method for the correction of the safety factor obtained by the ordinary method according to the following:. This correction is very reliable for slightly inclined slopes. The total normal stress can include an excess of the pore pressure u that must be specified with the introduction of the parameters of effective force.
In practice, this method can be considered as an extension of the method of the circle of friction for homogeneous sections previously described by Taylor.
In accordance with Mohr-Coulomb theory in terms of effective stress, the shear stress acting on the base of the i-th slice is given by:. The equilibrium is obtained by equating to zero the sum of the horizontal forces, the sum of the vertical forces and the sum of the moments compared to the origin. It is adopted the following assumption on the variation of the normal stress acting on the potential sliding surface:. A sensitive part of weight reduction associated with a vertical acceleration of the ground K y g g can be transmitted directly to the base and this is included in the factor 1 — K y.
The total normal stress at the base of a slice is given by:.
Any pair of values of the safety factor in the close to a physically reasonable estimate can be used to initiate an iterative solution. The required number of iterations depends on the initial estimate and the desired accuracy of the solution, normally, the process converges rapidly.
It is a method based on the principle of limit equilibrium of the slices, therefore, is considered the equilibrium of a potential sliding soil mass divided into n vertical slices of a thickness sufficiently small to be considered eligible the assumption that the normal stress N i acts in the midpoint of the base of the slice. The equilibrium equation of moments is written choosing as a reference point the center of gravity of the entire mass; so that, after performing a series of trigonometric and algebraic positions and transformations, the solution of the problem in Sarma method passes through the resolution of two equations:.
Imposing the equilibrium of moments from the center of the arc described by the sliding surface:. The method proposes to calculate two safety factors: the first F sm obtainable from 1 , related to the equilibrium of moments, the second F sf dalla 2 obtainable from 2 related to the equilibrium of forces. The function f x is arbitrarily chosen constant, sine, half-sine, trapezoidal, etc.
The particularity of the method is that the mass is divided into infinitesimal strips to which are imposed the equations of equilibrium to the horizontal and vertical translation and failure on the basis of the strips themselves. This leads to a first differential equation that binds interslice unknown forces E, X, the factor of safety F s ,the weight of the infinitesimal strip dW and the resultant of the pore pressure at the base dU.
The calculation method satisfies all equilibrium equations and is applicable to surfaces of any shape, but not necessarily imply the use of a computer. Method of Zeng e Liang Zeng and Liang carried out a series of parametric analyzes of a two-dimensional model developed by finite element code, which reproduces the case of drilled shafts piles immersed in a moving soil.
The two-dimensional model reproduces a slice of soil of unit thickness and assumes that the phenomenon occurs in plane strain conditions in the direction parallel to the axis of the piles. The model was used to investigate the influence on the formation of an arch effect of some parameters such as the distance between the piles, the diameter and the shape of the piles, and the mechanical properties of the soil. The problem appears to be statically indeterminate, with degree of indeterminacy equal to 8n-4 , but in spite of this it is possible to obtain a solution by reducing the number of unknowns and thus taking simplifying assumptions, in order to make determined the problem..
The assumptions that make the problem determined are:. The total number of unknowns is then reduced to 3n , to be calculated using the factor of load transfer. Furthermore it should be noted that the stabilization force transmitted on the soil downhill of the piles is reduced by an amount R, called reduction factor, calculated as:. The factor R therefore depends on the ratio between the distance present between the piles and the diameter of the piles and by the factor R p which takes into account the arch effect.
Evaluation of the seismic action The slope stability against seismic action is checked with the pseudo-static method.
For soils that under the action of a cyclic loading can develop high pore-water pressure is considered an increase in percent of pore-water pressures that takes account of this factor of loss of resistance. For the assessment of the seismic forces are considered the following:. Search of the critical sliding surface In the presence of homogeneous mediums there are no available methods for detecting the critical sliding surface and must examine a large number of potential surfaces. Stabilization of slopes using piles The realization of a row of piles on a slope serves to make increase the shear strength of certain sliding surfaces.
The intervention may be consequent to a stability already ascertained, for which you know the sliding surface or, acting preventively, is designed in relation to hypothetical sliding surfaces which responsibly can be assumed as the most probable ones.