Sarma method

Key takeaways

Sarma method belongs to earth science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Sarma method to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Sarma method from memory before moving on to harder problems.

Reference excerpt

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.

History Sarma worked in the area of seismic analysis of earth dams under 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 ).

Method

Assumptions The method satisfies all conditions of equilibrium, (i.e. horizontal and vertical force equilibrium and moment equilibrium 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 analysis. 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.

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 or 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 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.

Accuracy

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 and it has been proved to yield results quite similar to the modern safe Lower Bound numerical stability Limit Analysis methods (e.g. the 51st Rankine Lecture).

Modern alternatives However, nowadays modern numerical analysis 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.

See also Earthquake engineering Finite element method Slope stability analysis

References

Bibliography Kramer, S. L. (1996) Geotechnical Earthquake Engineering. Prentice Hall, New Jersey.

External links Dr Sarada K Sarma

Worked examples

Example 1 — a first encounter with Sarma method

Start with the simplest possible case. Write down what Sarma method claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In earth science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Sarma method before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Sarma method ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Sarma method

In research: Sarma method appears in earth science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Sarma method in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Sarma method is common in secondary-school and first-year university syllabi. It links to neighbouring topics Earthquake engineering, Landslide analysis, prevention and mitigation, so understanding it makes those chapters shorter.
In everyday life: Look for Sarma method outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Sarma method in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Sarma method means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Sarma method out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sarma method in simple terms?

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.

Why does Sarma method matter?

Because it connects several earth science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Sarma method?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Sarma method.