Morgenstern & Price

Home

Introduction
Theoretical_Background
   Method of Slices
   Bishop
   Spencer
   Morgenstern & Price
Use of Limit Equilibrium
   Choice of Geometry
   Strengths & Pressures
   Long Term Problems
   Short Term Problems
   Summary
References
Input Instructions
   Geometry
   Boundary Forces
   Pore Pressures
   Strength Parameters
   Earthquake Loading
   Iteration Control
   M-P Method
   Convergence
Examples
   Example 1
   Example 2
   Example 3i
   Example 3ii
   Example 4

Products Calculators | Product Pricing | Order Corporate Info | Discussion Bookstore | News

Morgenstern and Price's Method Morgenstern and Price's Method as originally formulated took a somewhat different approach to the solution of complete slice equilibrium (Morgenstern and Price, 1965). While Spencer considered overall moment equilibrium, Morgenstern and Price have considered only the moment equations of individual slices. Each method satisfies all conditions of equilibrium but Spencer's Method requires about half the computer time. For this reason TSLOPE's version of the Morgenstern and Price Method is actually just an extension of Spencer's Method to allow side forces that are not necessarily parallel (Spencer, 1973). Morgenstern and Price assume that the ratio of the side forces is given by:

(15)

where f(x) represents a user-defined variational relationship between X and E. The parameter

is an unknown scaling factor determined by the program to yield complete equilibrium.

Spencer's Method assumes that the side forces are inclined at angle with respect to horizontal:

(16)

The angle

is determined in the calculation process. To extend Spencer's Method to allow non-parallel side forces we let:

(17)

where f(x) is as defined previously. Note that f(x) = 1 is equivalent to Spencer's method. The angle of each side force becomes:

(18)

The forces on a typical slice and the force polygon are shown in Figure 5. The side forces are calculated using:

(19)

where Q is calculated using Equation 10 in which

is replaced by

. The horizontal force and moment imbalance are calculated and F and

are varied until the imbalances are within acceptable limits.

Figure 5 Force polygon for Morgenstern and Price Method.

Top of Page

Privacy

Acknowledgements