General Considerations and Assumptions in the Soil Stability Analysis

1. Test samples to determine the cohesion and internal friction angle.
If the analysis is for a natural slope, it is essential that the sample is not disturbed. In aspects as important as the cutting application rate and the initial consolidation state, the condition of the test should represent as close as possible to the most unfavorable conditions that may occur in the real slope.

2. The study of the elements that are known to enter but that can not be explained in the calculations.
The most important element of these elements is the progressive cracking that will begin at the top of the slope where the ground is in tension and, aided by the pressure of the water, can progress to a considerable depth. In addition, there are the effects of the inhomogeneous nature of the typical soil and other variations of the ideal conditions that must be assumed.

3. Computing
If a slope is going to fail along a surface, all the shear strength must be overcome along that surface, which then becomes a rupture surface. Anyone like ABC in Fig. 2 (b) represents one of an infinite number of possible traces in which a failure could occur.

It is assumed that the problem is two-dimensional, which theoretically requires a long length of slope normal to the section.
It is assumed that the shear strength of the soil follows Mohr Coulomb’s law

Τ or s = c̕+ σ’ tan φ̕

Where, c’ ‐ effective unit cohesion
σ’= effective normal stress on the surface of rupture = (σ ‐ u)
σ ‐ total normal stress on the surface of rupture
u ‐ pore water pressure on the surface of rupture
φ̕= effective angle of internal friction.
The element of great importance is the loss of resistance to the cut that many clays show when they are subjected to a high cutting tension. The stress-strain curves for said clay show that the voltage increases when the voltage increases to a maximum value, after which it decreases and approaches a final value that can be much less than the maximum. 
Since a rupture surface tends to develop progressively instead of all points in the same state of tension, it is usually the final value that must be used for the shear strength instead of the maximum value.

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