Methods for assessing the stability of slopes during earthquakes have evolved steadily since the early twentieth century, when the first attempts at modeling the effects of seismic shaking on slopes were developed.

These early efforts, based simply on adding an earthquake force to a static limit-equilibrium analysis, were formalized by Terzhagi (1950)

Methods developed to date to assess

the stability or performance of slopes

during earthquakes thus fall into three

general categories:

(1) pseudostatic analysis

(2) stress-deformation analysis, and

(3) permanent-displacement analysis.

Each of these types of analysis has

strengths and weaknesses, and each

can be appropriately applied in different

situations

The stability of a slope is represented by a factor of safety, which is the ratio of the shear strength along a critical failure surface and the shear stress induced on that failure surface by the slope.

Evaluation of seismic slope stability revolves principally around four key issues:

1) identification of the critical mechanism of failure

2) the geometry of the slope 3) the seismicity and dynamic response of the site,

and

4) the resistance of the slope to the critical failure.

Seismic slope stability is evaluated using

a “pseudostatic” analysis where the

failure mass is assumed to be horizontally

accelerated by the seismic coefficient, k

(in units of gravity), appropriately chosen

for the expected seismicity of the site.

Terzaghi (1950) originally recommended

using

k = 0.1, for severe

0.2, violent destructive

0.5, and catastrophic earthquakes,

Selection of k is the most important, and most difficult, factor to determine in a pseudostatic analysis.

An earthquake may be capable of producing a certain maximum acceleration, but this acceleration may act for less than a portion of a second.

The factor k in a pseudostatic analysis is almost always less than the anticipated maximum acceleration, thus it is very possible that a slope with a factor of safety greater than 1 for a chosen k, will fail because the slope was analyzed with a horizontal acceleration less than the acceleration experienced in the field.

Static Coefficient, k vs Recommended Pseudo-Static Factor of Safety

A pseudostatic analysis is simple to do,

and very straightforward. However, the

difficulty of interpreting k and the factor

of safety warrant the use of other

methods.

Newmark’s Sliding Block Analysis

Newmark (1965) first attempted to

analyze seismic slope stability by

quantifying the amount of displacement

due to a failure.

Newmark made the analogy that the sliding mass on the failure surface is similar to a block resting on an inclined plane.

He found that increasing the amount of shaking decreased the factor of safety, as expected, and that for a given frictional resistance, there was one particular k that produced a factor of safety of 1.

Further studies using the sliding block

analogy show that the displacement is

sensitive to the yield acceleration, and

small differences in this can cause large

differences in the predicted

displacement.

Makdisi and Seed’s Simplified Procedure (1978)

Makdisi and Seed (1978) used a sliding block analysis to compute permanent deformation of earth dams and embankments by making assumptions about the dynamic response of the soil.

Newmark’s sliding block analogy assumes that the deformation will be rigid and perfectly plastic, as shown in the stress strain curve.

A slope, however, is compliant and will

deform during shaking. Thus, it is possible

for adjacent portions of the sliding mass

to be out of phase; different areas of the

slope may be accelerating in different

directions.

Assumption of constant acceleration in

height of slope is opposite of real behaviour

of dams and it leads to errors in results.

Because the earthquake acceleration

imposes in both horizontal and vertical

direction and their magnitudes varies with

time, therefore, this method can't

completely consider the dynamic effective

of earthquake and thus, pseudo static

methods are approximate ways.

The result of pseudo static method is strongly depended to seismic factor (K) that choosing of a good factor is one of the most difficult procedures.

Analysis by pseudo static method similar to all limit equilibrium ways, exhibits an index for stability, but it doesn’t represent any information about strains in failure mode.

The more the K, S.F reduces, if S.F releases to less than one, this can't mean failure and instability in slope, because, pseudo static method applies forces as a permanent force on slopes, while in earthquake situations, slopes are under this forces in a limited period.

Pseudo static methods can't predict

effects of increases in pore water

pressure due to earthquake on deposits

that have a liquefaction risk. Thus, it is

better not to use this method in design of

earth dams on sandy deposits.

Pseudostatic analysis is still very widely

used in practice and has a deep

reservoir of engineering judgment

behind it. It is conceptually simple, but

the process of selecting a seismic

coefficient commonly lacks a rational

basis, and the analysis tends to be over

conservative.

Therefore, the most appropriate

applications for pseudostatic analysis are

probably limited to preliminary analyses

and screening procedures that precede

a more sophisticated analysis.

Terzaghi, K, (1950), Mechanics of Landslides, Engineering Geology (Berkey) Volume, Geological Society of America

Seed, R.B., (2000), Class Notes, Evaluation and Mitigation of Seismic Hazards Seminar, UC Berkeley Extension, Berkeley, California

Kramer, S.L., (1995), Geotechnical Earthquake Engineering, Prentice Hall, Upper Saddle River, New Jersey

Dismuke, J., (extracted 2014), Seismic Slope Stability And Analysis Of The Upper San Fernando Dam, from: sokocalo.engr.ucdavis.edu/~jeremic/ECI284/.../2002/JDismuke.doc

M. Ghazavi, et al.,(extracted 2014), Limitations of Pseudo Static Methods in Stability Analysis of Earth Dams-Case History, from : http://irandanesh.febpco.com/FileEssay/omran-1386-12-22-agh(222).pdf