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Reliability Assessment of soil parameters affecting the stability of earth dams using various slope analysis methods
Abstract
Dams due to their advantages such as the use of
natural materials and relatively simple procedure, and
lower cost, have always been considered. One of the
important issues in the design and construction of earth
dams is stability analysis of slopes that use in earth dams.
There are various methods to slope stability analysis that
one of the most important methods is Limit Equilibrium
Method (LEM). By consideration that soil is a
heterogeneous material; the analysis must be conducted
in a manner that all of the plausible values be considered.
By using statistical methods, we can evaluate the
influence of soil parameters uncertainty in stability
analysis of earth dam’s slopes. One of the most applicable
and important statistical method in engineering is
MonteCalro simulation (MCs). In this paper we tried to
evaluate the Influence of soil parameters uncertainty in
earth dams slope stability by using limit equilibrium
method of slices
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The majority of slope stability analyses performed in practice still use traditional limit equilibrium approaches involving methods of slices that have remained essentially unchanged for decades, This was not the outcome envisaged when Whitman & Bailey (1967) set criteria for the then emerging methods to become readily accessible to all engineers, The finite element method represents a powerful alternative approach for slope stability analysis which is accurate, versatile and requires fewer a priori assumptions, especially, regarding the failure mechanism, Slope failure in the finite element model occurs 'naturally' through the zones in which the shear strength of the soil is insufficient to resist the shear stresses. The paper describes several examples of finite element slope stability analysis with comparison against other solution methods, including the influence of a free surface on slope and dam stability. Graphical output is included to illustrate deformations and mechanisms of failure. It is argued that the finite element method of slope stability analysis is a more powerful alternative to traditional limit equilibrium methods and its widespread use should now be standard in geotechnical practice.
An approach using strength reduction factor (SRF) for finite element analysis, with the provision of a failure criterion, and incorporation of graphical output, to examine the failure zone developed, was used in order to determine slope failure and the corresponding safety factor. The state of the effective stresses in a slope is calcu-lated by the finite element method using eight-node quadrilateral elements of elastic-plastic soil with the Drucker-Prager nonlinear stress-strain relationship and a nonassociated flow rule. Slope failure occurs when the yield zone spreads over the entire slip surface and the corresponding SRF is the safety factor of the soil slope. The slope failure could be clearly defined and progressive failure was also observed. It should be kept in mind that the critical slip surface is not unique. A narrow yield-ing zone was developed when the slope started to fail and any slip surface passing through the yield zone could be the failure surface. The factor of safety obtained by the proposed procedure is in good agreement with that determined by Bishop's method.
Synopsis
A method of analysis is described for determining the factor of safety of an embankment against failure on a cylindrical slip surface. The analysis is in terms of effectivce stress and leads to two equa-tions of equilibrium, the first in respect of forces and the second in respect of moments.
Using this method of analysis, the factors affecting the accuracy of Bishop's simplified method have been investigated. Charts have been obtained for three different values of the pore pressure coefficient (r u ) which identify the position of the critical slip circle. A set of stability charts is also given.
On décrit une méthode d'analyse pour déterminer le facteur de sécurité d'un remblai contre la rupture sur une surface de glissement cylindrique. L'analyse est faite d'après la contrainte effective ett amène à deux équations d'équilibre, la première se rapportant aux forces et la deuxième aux moments.
En utilisant cette méthod d'analyse, on a étudié les facteurs qui affectent la précision de la méthode simplifiée de Bishop. On est arrivé à des diagram-mes pour les trois valeurs différentes de coefficient de pression interstitielle (r u ) quiidentifient la position du cercle de glissement critique. On donne aussi un groupe de diagrammes de stabilité.
Synopsis
Within the framework of limit equilibrium methods of stability analysis, no restriction need be placed at the outset upon the shape of the possible slip surface. In many cases, the critical surface may deviate significantly from a circle or a plane and therefore a method that facilitates the analysis of surfaces of arbitrary shape is of interest. A method for doing this is presented. The assumptions necessary to make the problem statically determinate are discussed. The solution of the governing equations ensures that all equilibrium and boundary conditions are satisfied. The method has been programmed for a digital computer and some examples of its application are given. Comparisons are also made with other methods of analysis.
Dans la cadre des méthodes d'équilibre limite d'analyse de stabilité, il n'y a pas besoin d'imposer de restrictions au départ sur la forme de la surface de glissement éventuelle. Dans bien des cas, la surface critique peut dévier d'une manière significative d'un cercle ou d'un plan at par conséquent une méthode qui facilite l'analyse des surfaces de formes arbitraires présente un intérêt. On présente une méthode pour accomplir cela. On discute des hypothèses nécessaires pour que le problème soit déterminé au point de vue de la statique. La solution des équations dominantes garantit que toutes les conditions d'équilibre et de limite soient satisfaites. La méthode a été programmée pour une calculatrice digitale et on donne quelques examples de ses applications. D'autres méthodes d'analyse y son comparées.
Synopsis
Stability charts are presented to facilitate the computation of the factor of safety of earth slopes during rapid drawdown. As the reservoir level is lowered, the factor of safety decreases if it be assumed that no dissipation of pore pressure occurs during drawdown. Pore pressures during drawdown have been estimated by assuming that B is unity and stability calculation for the range of sections and soil parameters commonly encountered in earth dam practice have been carried out using an electronic computer in order to obtain the data given in the charts
Des cartes de stabilité sont présentées pour faciliter le calcul du facteur de sérité des pentes en terre pendant un affaissement rapide. A mesure que le niveau du réservoir baisse, le facteur de sécurité diminue s'il est supposé qu'aucune disparition de la pression interstitielle n'a lieu pendant l'affaissement. L'évaluation de la pression inter-stitielle pendant l'affaissement a ét´ effectu´ en supposant que B est l'unite et les calculs de la stabilité pour la gamme des sections et les parametres relatifs au sol dont l´usaee est habitue1 dans les travaux ayant trait aux barrages en terre ont été exécutés en utilisant une machine á calculer électronique afin d'obtenir les donnés apparaissant sur les cartes.
The paper compares six methods of slices commonly used for slope stability analysis. The factor of safety equations are written in the same form, recognizing whether moment and (or) force equilibrium is explicitly satisfied. The normal force equation is of the same form for all methods with the exception of the ordinary method. The method of handling the interslice forces differentiates the normal force equations.A new derivation for the Morgenstern–Price method is presented and is called the 'best-fit regression' solution. It involves the independent solution of the force and moment equilibrium factors of safety for various values of λ. The best-fit regression solution gives the same factor of safety as the 'Newton–Raphson' solution. The best-fit regression solution is readily comprehended, giving a complete understanding of the variation of the factor of safety with λ.
A concise algorithm is proposed in this paper for the calculation of the factor of safety of a slope using the MorgensternPrice method. Based on force and moment equilibrium considerations, two expressions are derived for the factor of safety Fs and the scaling factor λ, respectively, both in relatively simple forms. With this algorithm and assumed initial values of Fs and λ, the solutions for Fs and λ are found to converge within a few iterations. Compared to other procedures, the present algorithm possesses the advantages of simplicity and high efficiency in application. It is rather straightforward to implement this algorithm into a computer program.Key words: slope, stability, factor of safety, limit equilibrium method.
In this paper, reliability analysis of slope stability is presented using two methods of uncertainty first-order second-moment method (FOSM) and Monte Carlo simulation method (MCSM). The results of these methods are compared using four recognized methods of slope stability. These are Ordinary method of slices, simplified Bishop's method, simplified Janbu's method and Spencer's method. Two illustrative examples are presented in this paper: one is homogenous slope and the other is non-homogeneous layered slope. The study shows that the reliability index (β) is independent of the seed random number generator and a sample size of 700 or greater is a good choice for MCSM. In the case of homogeneous slope a good agreement is observed between the calculated (β) using FOSM and MCSM for both the Ordinary and the Bishop's method. However, slight difference in (β) is observed between the two uncertainty methods whether Janbu's method or Spencer's method is used. In the case of the layered slope good agreement is obtained between the two uncertainty methods for Ordinary, Bishop and Janbu methods. Similar to example 1, Spencer's method shows also slight difference in (β) between FOSM and MCSM methods. Model uncertainty is addressed by evaluating the relative performance of the three slope stability methods i.e. Ordinary, Bishop and Janbu methods as compared to Spencer's method.
A practical method of solving the equations of statical equilibrium to obtain the factor of safety of earth slopes, with slip surfaces of arbitrary shape, is described. The basic mathematical problem is the solution of a pair of simultaneous non-linear equations which arise from the boundary conditions on the solution of an ordinary differential equation.
Embankment Dam Engineering (Casagrande Memorial Volume)
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