### Earthquake Analysis

```SEISMIC ANALYSIS
Stability of a slope can be affected by seismicity in two ways: earthquake and
blasting. These seismic motions are capable of inducing large destabilizing inertial
forces.
•
Pseudostatic Method: The earthquake’s inertial forces are simulated by the
inclusion of static horizontal and vertical forces in limit equilibrium analysis.
•
Newmark’s Diaplacement Method: This method is based on the concept that the
actual slope accelerations may exceed the static yield acceleration at the expense
of generating permanent displacements (Newmark, 1965).
•
Dynamic Finite Element Analysis: This is a coupled two or three dimensional
analyses using appropriate constitutive material model that will provide details of
concerning stresses, strains, and permanent displacement.
Types of seismic wave
The main seismic wave types are
• Compression (P)
• Shear (S)
• Rayleigh (R)
• Love (L)
P and S waves are known as body waves, because they propagate outward in all
directions from source (such as an earthquake) and travel through the interior of
the earth. Love and Rayleigh waves are surface waves and propagate
approximately parallel to the earth’s surface.
Typical seismogram ( www.geo.mtu.edu)
definition of earthquake terms (www.culcanhammer.net)
Dynamic Soil Properties
Important elements in a seismic response analysis are:
input motions,
site profile,
static soil properties,
dynamic soil properties,
methods of analysis using computer programs.
Simulation of seismic effect
there are two basic approaches to incorporate the seismic effect on slope
stability
Inertia slope stability analysis
weakening slope stability analysis
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.
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 Fh is calculated as follows:
Where,
Fh = 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
amax = peak ground acceleration
amax/g=seismic coefficient
Inertia Slope Stability – Newmark Method
Newmark’s method assumes: existence of a well-defined slip surface, a rigid,
perfectly plastic slide material, negligible loss of shear strength during
shaking, and that permanent strains occur if the dynamic stress exceeds the
shear resistance. Also, the slope is only presumed to deform in the downslope
direction, thus implying infinite dynamic shear resistance in the upslope
direction. The procedure requires that the value of a yield acceleration or
critical seismic coefficient, ky, be determined for the potential failure surface
using conventional limit equilibrium methods.
Pseudo-static approach
Magnitude of slope displacement depends on variety of factors. Higher the ay value, more stable
the slope is for a given earthquake. Greater the difference between peak ground acceleration amax
due to earthquake and ay, larger the down slope movement. Longer the earthquake acceleration
exceeds ay, larger the down slope deformation. Larger the number of acceleration pulses
exceeding ay, greater the cumulative down slope movement during earthquake. Most common
method used in Newmark method is as follows:
Where,
d= estimated downslope movement due to earthquake in cm.
yield acceleration and
peak ground acceleration of design earthquake.
Essentially
must be greater than
. While using Eq. (9.3), pseudostatic factor of safety is
determined first using the technique described in Fig. 9.2. If it is less than 1,
pseudostatic factor becomes equal to 1. This value of
and
are used to determine slope deformation.
is used to determine
is reduced till
using Eq. (9.1).
```