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Morgenstern & Price method (1965)

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Morgenstern & Price method (1965)

A relation is established between the components of the interslice forces of the type X= λ f(x) E, where λ is a scale factor and f(x), a function of the position of E and X, defining a relation between the variation of the force X and the force E inside the sliding mass. The function f(x) is arbitrarily chosen (constant, sine, half-sine, trapezoidal, etc.) and has little influence on the result, but it should be verified that the values ​​obtained for the unknowns are physically acceptable.

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 Fs, the weight of the infinitesimal strip dW and the resultant of the pore pressure at the base dU.

Actions on the i-th slice according to Morgenstern & Price add representation of the entire mass

The result is the so-called "equation of forces":

A second equation, called "equation of moments", is written by imposing the condition of equilibrium to rotation with respect to the middle of the base:

these two equations are extended by integration at the whole mass concerned from sliding.

The calculation method satisfies all equilibrium equations and is applicable to surfaces of any shape, but not necessarily imply the use of a computer.