**
8.8 Pseudo-static approach**

In pseudo-static methods, the cyclic earthquake motion is replaced with a constant horizontal acceleration equal to kc(g), where kc is the seismic coefficient, and g is the acceleration of gravity. A force is applied to the soil mass equal to the product of the acceleration and the weight of the soil mass.

The limit equilibrium method is modified to include horizontal and vertical static seismic forces that are used to simulate the potential inertial forces due to ground accelerations in an earthquake. In pseudostatic slope stability analyses, a factor of safety against failure is computed using a static limit equilibrium stability procedure, in which a pseudostatic, horizontal inertial force, which represents the destabilizing effects of the earthquake, is applied to the potential sliding mass.

This method is easy to understand and is applicable for both total and effective
stress slope stability analyses. The method ignores cyclic nature of earthquake.
It assumes that additional static force is applied on the slope due to
earthquake. In actual analysis, a lateral force acting through centroid of
sliding mass, is applied which acts out of slope direction. This pseudostatic
lateral force F_{h} is calculated as follows:

Where,

F_{h }=_{ }horizontal pseudostatic force acting through centroid
of sliding mass out of slope direction.

m=total mass of slide material

W=total weight of slide mass

a= acceleration, maximum horizontal acceleration at ground surface due to earthquake

a_{max }= peak ground acceleration

a_{max}/g=seismic coefficient

A considerable limitation of the pseudostatic approach is that the horizontal force representing the effects of seismicity is constant and acts in only one direction. With dynamically applied loads, the force may be applied for only a few tenths of a second before the direction of motion is reversed. The result of these transient forces will be a series of displacement pulses rather than complete failure of the slope.

Seismicity subjects sliding mass to vertical as well as horizontal pseudostatic
forces. However, the effect of vertical pseudostatic force on sliding mass is
ignored as it has very little effect on its slope stability. Although, the
weight of the sliding mass *W* can be readily estimated, selection of
seismic coefficient requires considerable experience and judgement. Certain
guidelines regarding selection of seismic coefficient are as follows:

· Higher the value of peak ground acceleration, higher is the value of

· is also determined as function of earthquake magnitude.

· When items 1 and 2 are considered, should never be greater than .

· Sometimes local agencies suggest minimum value of seismic coefficient.

· For small slide mass, =.

· For intermediate slide mass, =0.65.

· For large slide mass, =0.1 for sites never generating 6.5 magnitude earthquake and, =0.15 for sites near faults generating 8.5 magnitude earthquake.

· =0.1 for severe earthquake, = 0.2 for violent and destructive earthquake and=0.5 for catastrophic earthquake.

**
Wedge Method**

This is simplest type of slope stability analysis. A wedge failure has planar slip surface, inclined at an angle α to horizontal. Analysis could be performed for the case of planar slip surface intersecting the face of slope or passing through toe of slope. Factor of safety for pseudostatic analysis is obtained as follows:

Where,

FOS= factor of safety for pseudostatic analysis

u= average pore water pressure along slip surface

c’ and ’ are the effective cohesion and friction angle material

For total stress analysis, total stress parameters of soil should be known and
is often performed for cohesive soils. For effective stress analysis, effective
stress parameters of soil should be known and is often performed for
cohesionless soils. For this purpose pore water pressure along slip surface
should also be known. For soil layers above water table, pore water pressure is
assumed zero. If the soil is below water table and water table is horizontal,
pore water pressure below water table is hydrostatic. In case of sloping water
table, flow net can be used to estimate pore water pressure below water table**.**

**
Method of Slices**