scholarly journals A new procedure for computing the factor of safety using the Morgenstern-Price method

2001 ◽  
Vol 38 (4) ◽  
pp. 882-888 ◽  
Author(s):  
D Y Zhu ◽  
C F Lee ◽  
Q H Qian ◽  
Z S Zou ◽  
F Sun
Keyword(s):  
Factor Of Safety ◽  
Recurrence Relations ◽  
Limit Equilibrium ◽  
Solution Process ◽  
Stability Factor ◽  
Equilibrium Conditions ◽  
Scaling Parameter ◽  
Newton Raphson ◽  
Safety Limit ◽  
Raphson Method

By employing the same assumption regarding interslice forces as that used in the Morgenstern-Price method, two concise recurrence relations between interslice forces and interslice moments are derived which satisfy both force and moment equilibrium conditions. The Newton-Raphson method is used for determining the factor of safety and the associated scaling parameter of the interslice force function. Algebraic derivatives required in the solution process are evolved in a recursive manner which can be easily implemented in a computer program. The choices of initial values of safety factor and scaling parameter are suggested. The procedure proposed in this paper proves to be efficient and solutions converge rapidly.Key words: slope, stability, factor of safety, limit equilibrium method.

scholarly journals A concise algorithm for computing the factor of safety using the Morgenstern–Price method

2005 ◽  
Vol 42 (1) ◽  
pp. 272-278 ◽  
Author(s):  
D Y Zhu ◽  
C F Lee ◽  
Q H Qian ◽  
G R Chen
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
High Efficiency ◽  
Limit Equilibrium ◽  
Limit Equilibrium Method ◽  
Scaling Factor ◽  
Stability Factor ◽  
Equilibrium Method ◽  
Safety Limit ◽  
Present Algorithm

A concise algorithm is proposed in this paper for the calculation of the factor of safety of a slope using the Morgenstern–Price 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.

Convergence aspect of limit equilibrium methods for slopes

1990 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. N. Chowdhury ◽  
S. Zhang
Keyword(s):  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Solution Process ◽  
Iterative Solution ◽  
Friction Angle ◽  
Equilibrium Analysis ◽  
Negative Slope ◽  
Slip Surfaces ◽  
Geological Discontinuity

This note is concerned with the multiplicity of solutions for the factor of safety that may be obtained on the basis of the method of slices. Discontinuities in the function for the factor of safety are discussed and the reasons for false convergence in any iterative solution process are explored, with particular reference to the well-known Bishop simplified method (circular slip surfaces) and Janbu simplified or generalized method (slip surfaces of arbitrary shape). The note emphasizes that both the solution method and the method of searching for the critical slip surface must be considered in assessing the potential for numerical difficulties and false convergence. Direct search methods for optimization (e.g., the simplex reflection method) appear to be superior to the grid search or repeated trial methods in this respect. To avoid false convergence, the initially assumed value of factor of safety F0 should be greater than β1(=−tan α1 tan [Formula: see text]) where α1 and [Formula: see text] are respectively the base inclination and internal friction angle of the first slice near the toe of a slope, the slice with the largest negative reverse inclination. A value of F0 = 1 + β1, is recommended on the basis of experience. If there is no slice with a negative slope for any of the slip surfaces generated in the automatic, search process, then any positive value of F0 will lead to true convergence for F. It is necessary to emphasize that no slip surface needs to be rejected for computational reasons except for Sarma's methods and similarly no artificial changes need to be made to the value of [Formula: see text] except for Sarma's methods. Key words: slope stability, convergence, limit equilibrium, analysis, optimization, slip surfaces, geological discontinuity, simplex reflection technique.

The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses

2003 ◽  
Vol 40 (3) ◽  
pp. 643-660 ◽  
Author(s):  
John Krahn
Keyword(s):  
Finite Element ◽  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Geotechnical Engineering ◽  
Software Tools ◽  
Great Promise ◽  
Engineering Practice ◽  
Stability Factor ◽  
Limit Equilibrium Methods

Limit equilibrium types of analysis have been in use in geotechnical engineering for a long time and are now used routinely in geotechnical engineering practice. Modern graphical software tools have made it possible to gain a much better understanding of the inner numerical details of the method. A closer look at the details reveals that the limit equilibrium method of slices has some serious limitations. The fundamental shortcoming of limit equilibrium methods, which only satisfy equations of statics, is that they do not consider strain and displacement compatibility. This limitation can be overcome by using finite element computed stresses inside a conventional limit equilibrium framework. From the finite element stresses both the total shear resistance and the total mobilized shear stress on a slip surface can be computed and used to determine the factor of safety. Software tools that make this feasible and practical are now available, and they hold great promise for advancing the technology of analyzing the stability of earth structures.Key words: limit equilibrium, stability, factor of safety, finite element, ground stresses, slip surface.

The DAN method for calculation of vapour-liquid equilibria using an equation of state; Flash calculation

1985 ◽  
Vol 50 (1) ◽  
pp. 23-32 ◽  
Author(s):  
Josef P. Novák ◽  
Vlastimil Růžička ◽  
Anatol Malijevský ◽  
Jaroslav Matouš ◽  
Jan Linek
Keyword(s):  
Equation Of State ◽  
Computational Technique ◽  
Equilibrium Conditions ◽  
Newton Raphson ◽  
Flash Calculation ◽  
Raphson Method ◽  
Number Of Iterations

A modification of the computational technique for flash calculations using an equation of state has been developed. The procedure consists in the double application of the Newton-Raphson method (DAN) to the set of equilibrium conditions. The algorithm is designed to minimize the number of iterations. It is, therefore, especially useful in successive calculations, where a family of solutions at slightly changing conditions is desired.

scholarly journals A Computer Model for the Hydraulic Analysis of Open Channel Cross Sections

1996 ◽  
Vol 1 ◽  
pp. 57
Author(s):  
W. H. Shayya ◽  
R. H. Mohtar ◽  
M. S Baasiri
Keyword(s):  
Computer Model ◽  
Cross Sections ◽  
Solution Process ◽  
Initial Guess ◽  
Hydraulic Design ◽  
Implicit Equations ◽  
Actual Solution ◽  
Newton Raphson ◽  
Geometric Elements ◽  
Raphson Method

Irrigation and hydraulic engineers are often faced with the difficulty of tedious trial solutions of the Manning equation to determine the various geometric elements of open channels. This paper addresses the development of a computer model for the design of the most commonly used channel-sections. The developed model is intended as an educational tool. It may be applied to the hydraulic design of trapezoidal , rectangular, triangular, parabolic, round-concered rectangular, and circular cross sections. Two procedures were utilized for the solution of the encountered implicit equations; the Newton-Raphson and the Regula-Falsi methods.  In order to initiate the solution process , these methods require one and two initial guesses, respectively. Tge result revealed that the Regula-Flasi method required more iterations to coverage to the solution compared to the Newton-Raphson method, irrespective of the nearness of the initial guess to the actual solution. The average number of iterations for the Regula-Falsi method was approximately three times that of the Newton-Raphson method.

The DAN method for calculation of vapour-liquid equilibria using an equation of state; Bubble and dew point calculations

1985 ◽  
Vol 50 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Josef P. Novák ◽  
Vlastimil Růžička ◽  
Anatol Malijevský ◽  
Jaroslav Matouš ◽  
Jan Linek
Keyword(s):  
Equation Of State ◽  
Equilibrium Point ◽  
Critical Point ◽  
Dew Point ◽  
Computational Technique ◽  
Equilibrium Conditions ◽  
Close Vicinity ◽  
Newton Raphson ◽  
Raphson Method ◽  
Phase Envelope

A modification of the computational technique for calculating bubble and dew points using an equation of state has been proposed. The procedure consists in the Double Application of the Newton-Raphson method (DAN) to the set of equilibrium conditions. The algorithm is very effective as it provides both values of equilibrium variables and a very qualified first estimate of the next equilibrium point. This enables to proceed along the phase envelope rather quickly and to achieve convergence within a few iterations except in the close vicinity of the critical point.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

A Generalized Compositional Approach for Reservoir Simulation

1983 ◽  
Vol 23 (05) ◽  
pp. 727-742 ◽  
Author(s):  
Larry C. Young ◽  
Robert E. Stephenson
Keyword(s):  
Enhanced Recovery ◽  
Gas Condensate ◽  
Reservoir Modeling ◽  
Pressure Equation ◽  
Compositional Modeling ◽  
Fluid Property ◽  
Black Oil ◽  
Fluid Properties ◽  
Newton Raphson ◽  
Raphson Method

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered area conventional waterflood problem,displacement of oil by CO, andthe displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727

scholarly journals Correction to: Efficient analysis of welding thermal conduction using the Newton–Raphson method, implicit method, and their combination

2020 ◽  
Author(s):  
Zhongyuan Feng ◽  
Ninshu Ma ◽  
Wangnan Li ◽  
Kunio Narasaki ◽  
Fenggui Lu
Keyword(s):  
Thermal Conduction ◽  
Implicit Method ◽  
Newton Raphson ◽  
Raphson Method

A Correction to this paper has been published: https://doi.org/10.1007/s00170-020-06437-w

Sign in / Sign up

Export Citation Format

Share Document