Sarma method
Encyclopedia
The Sarma method is a method used primarily to assess the stability of soil slopes under seismic
conditions. Using appropriate assumptions the method can also be employed for static slope stability
analysis. It was proposed by Sarada K. Sarma
in the early 1970s as an improvement over the other conventional methods of analysis which had adopted numerous simplifying assumptions.
worked in the area of seismic analysis of earth dams under Professor Ambraseys
at Imperial College for his doctoral studies in the mid 1960s. The methods for seismic analysis of dams available at that time were based on the Limit Equilibrium approach and were restricted to planar or circular failures surfaces adopting several assumptions regarding force and moment equilibrium (usually satisfying one of the two) and about the magnitude of the forces (such as interslice forces being equal to zero).
Sarma looked into the various available methods of analysis and developed a new method for analysis in seismic conditions and calculating the permanent displacements due to strong shaking. His method was published in the 1970s (the very first publication was in 1973 and later improvements came in 1975 and 1979 ).
. It is called advanced because it can take account of non-circular failure surfaces. Also, the multi-wedge approach allows for non vertical slices and irregular slope geometry. It is called a rigorous method because it can satisfy all the three conditions of equilibrium, horizontal and vertical forces and moments. The Sarma method is nowadays used as a verification to finite element programs (also FE limit analysis
) and it is the standard method used for seismic analysis.
When the method is used in the analysis of earth dams (i.e. the slopes of the dam faces), the results of the analysis, i.e. the critical acceleration is used in the Newmark's sliding block
analysis in order to calculate the induced permanent displacements. This follows the assumption that displacements will result if the earthquake induced accelerations exceed the value of the critical acceleration for stability.
methods (e.g. the 51st Rankine Lecture
).
software employing usually the finite element
, finite difference
and boundary element
methods are more widely used for special case studies. Particular attention has been recently given to the finite element method which can provide very accurate results through the release of several assumptions usually adopted by the conventional methods of analysis. Special boundary conditions and constitutive laws can model the case in a more realistic fashion.
Earthquake
An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...
conditions. Using appropriate assumptions the method can also be employed for static slope stability
Slope stability
The field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock-fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock...
analysis. It was proposed by Sarada K. Sarma
Sarada K. Sarma
Dr Sarada Kanta Sarma, BTech PhD DIC MASCE is a Geotechnical Engineer, Emeritus Reader of Engineering Seismology and Senior Research Investigator at Imperial College London...
in the early 1970s as an improvement over the other conventional methods of analysis which had adopted numerous simplifying assumptions.
History
SarmaSarada K. Sarma
Dr Sarada Kanta Sarma, BTech PhD DIC MASCE is a Geotechnical Engineer, Emeritus Reader of Engineering Seismology and Senior Research Investigator at Imperial College London...
worked in the area of seismic analysis of earth dams under Professor Ambraseys
Nicolas Ambraseys
Professor Nicolas Neocles Ambraseys Dip.Eng DIC PhD FICE FREng is a Greek Engineering Seismologist...
at Imperial College for his doctoral studies in the mid 1960s. The methods for seismic analysis of dams available at that time were based on the Limit Equilibrium approach and were restricted to planar or circular failures surfaces adopting several assumptions regarding force and moment equilibrium (usually satisfying one of the two) and about the magnitude of the forces (such as interslice forces being equal to zero).
Sarma looked into the various available methods of analysis and developed a new method for analysis in seismic conditions and calculating the permanent displacements due to strong shaking. His method was published in the 1970s (the very first publication was in 1973 and later improvements came in 1975 and 1979 ).
Assumptions
The method satisfies all conditions of equilibrium, (i.e. horizontal and vertical force equilibrium and moment equilibium for each slice. It may be applied to any shape of slip surface as the slip surfaces are not assumed to be vertical, but they may be inclined. It is assumed that magnitudes of vertical side forces follow prescribed patterns. For n slices (or wedges), there are 3n equations and 3n unknowns, and therefore it statically determinate without the need of any further additional assumptions.Advantages
The Sarma method is called an advanced and rigorous method of static and seismic slope stability analysisSlope stability analysis
The slope stability analyses are performed to assess the safe and economic design of a human-made or natural slopes and the equilibrium conditions. The term slope stability may be defined as the resistance of inclined surface to failure by sliding or collapsing...
. It is called advanced because it can take account of non-circular failure surfaces. Also, the multi-wedge approach allows for non vertical slices and irregular slope geometry. It is called a rigorous method because it can satisfy all the three conditions of equilibrium, horizontal and vertical forces and moments. The Sarma method is nowadays used as a verification to finite element programs (also FE limit analysis
Finite element limit analysis
A finite element limit analysis utilises optimisation techniques to directly compute the upper or lower bound plastic collapse load for a mechanical system rather than time stepping to a collapse load, as might be undertaken with conventional non-linear finite element techniques...
) and it is the standard method used for seismic analysis.
Use
The method is used mainly for two purposes, to analyse earth slopes and earth dams. When used to analyse seismic slope stability it can provide the factor of safety against failure for a given earthquake load, i.e. horizontal seismic force ir acceleration (critical acceleration). Besides, it can provide the required earthquake load (force or acceleration) for which a given slope will fail, i.e. the factor of safety will be equal to 1.When the method is used in the analysis of earth dams (i.e. the slopes of the dam faces), the results of the analysis, i.e. the critical acceleration is used in the Newmark's sliding block
Newmark's sliding block
The Newmark's sliding block analysis method is an engineering method used to calculate the permanent displacements of soil slopes during seismic loading. It is also simply called Newmark's analysis or Sliding block method of slope stability analysis.-History:The method was proposed by Nathan M...
analysis in order to calculate the induced permanent displacements. This follows the assumption that displacements will result if the earthquake induced accelerations exceed the value of the critical acceleration for stability.
General acceptance
The Sarma method has been extensively used in seismic analysis software for many years and has been the standard practice until recently for seismic slope stability for many years (similar to the Mononobe-Okabe method for retaining walls). Its accuracy has been verified by various researchers nad it has been proved to yield results quite similar to the modern safe Lower Bound numerical stability Limit AnalysisPlasticity (physics)
In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...
methods (e.g. the 51st Rankine Lecture
Rankine Lecture
The Rankine Lecture is hosted in March each year by the British Geotechnical Association. It is widely viewed as the most prestigious of the invited lectures in Geotechnics.The lecture commemorates W. J. M...
).
Modern alternatives
However, nowadays modern numerical analysisNumerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
software employing usually the finite element
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
, finite difference
Finite difference method
In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.- Derivation from Taylor's polynomial :...
and boundary element
Boundary element method
The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations . It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture...
methods are more widely used for special case studies. Particular attention has been recently given to the finite element method which can provide very accurate results through the release of several assumptions usually adopted by the conventional methods of analysis. Special boundary conditions and constitutive laws can model the case in a more realistic fashion.
See also
- Slope stabilitySlope stabilityThe field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock-fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock...
- Slope stability analysisSlope stability analysisThe slope stability analyses are performed to assess the safe and economic design of a human-made or natural slopes and the equilibrium conditions. The term slope stability may be defined as the resistance of inclined surface to failure by sliding or collapsing...
- Earthquake engineeringEarthquake engineeringEarthquake engineering is the scientific field concerned with protecting society, the natural and the man-made environment from earthquakes by limiting the seismic risk to socio-economically acceptable levels...
- Finite element analysis