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Indian Institute of Technology Roorkee,Roorkee, UttharaKhand

Seismic Slope Stability

Dr. R S Jakka

Contests

Introduction Landslides Slope failures

Types of Earthquake Induced Landslides

Earthquake Induced Landslide Activity

Evaluation of Slope Stability

Static Slope Stability Methods

Seismic Slope Stability Methods

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(Contd..)Static Slope Stability Methods

Wedge MethodMethod of Slices

Ordinary or Fellenius Method (Swedish Circle Method)Bishops MethodJanbus Simplified MethodSpencer MethodMorgenstern price methodSarma MethodGeneral limit equilibrium method

Stress deformation analysis (Finite element stress based method)

Seismic Slope Stability Methods Inertial slope stability methods

Pseudostatic AnalysisDisplacement AnalysisNewmark Sliding Block AnalysisMakdisi-Seed Analysis Dynamic analysis (Dynamic FEM Analysis)

Weakening slope stabilityFlow slide analysisDeformation failures/lateral spreads

Advanced FEM

Introduction Landslidesare nothing but slope instabilitiesof natural s lopes Landslidesoccur ona regular basis Landslides can cause tremendous damage to properties , lives of

people Landslides have been responsible for as much or more damage than

all otherseismic hazards combined Slidescanalsooccur in man-made s lopes, such as ?.. Earthquake very oftentrigger slope failures/landslides

Due to ground shaking (inertial forces) Due to raise in the pore water pressures/liquefaction

Slope failures influenced by number of phenomenon ..

Slopesexist in states ranging fromvery stable to marginally stable

There are many examples of slope failures (e.g. Lower San FernandoDam, SheffieldDam, many examplesof roadand rail embankments;

Landslidesduring Alaska 1964, Sikkim2011)

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Computer simulation of a "slump" landslide in San Mateo County, Calif ornia (USA) in January 1997

Typical failures of Landslides

Photo of the 2005 La Conchita Landslide

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2005 La Conchita Landslide - John Lehmkuhl

300 Ton Topanga Cany on Boulder - 2005 Landslide - (AP Photo)

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Holbeck Hall Landslide - England 1993 - British Geological Surv ey

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October 2, 1978 Bluebird Cany on landslide in Orange County California

Landslide & Debris Flow Scars in the San Gabriel Mountains - USGS

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National Highway 1-D connecting Srinagar with Leh town

Typical failures of Embankments

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Damage to kerb of highway pavement due to lateral spreading of soil, Bhuj 2001

ypThis rail embankment at Vaka Nala damaged due to

occurrence of Liquefaction at the base

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Types of Earthquake Induced Landslides

1. Disrupted slides and falls

2. Coherent slides

3. Lateral spreads and flows

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Earthquake-Induced Landslide Activity Magnitude Effects

Distance Effects

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Evaluation of Slope Stability Review of available documents Reconnaissance Ins trumentation: Slope movement monitoring Surface investigations Laboratory tests Performing stability analysis

Static slope stability analysis Seismic slope stability analysis

Slope Stability: Introduction Why is water not stable when we force a slope on it?

Why are some soils stable at gentle slopes and others at steeper slopes?

When does a stable soil cease to be stable and then slides?

What causes instability?

What ensures stability?

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Static Slope Stability Analysis

Types of Slopes Infinite Finite

Types of Failure Surfaces Translational Circular

Toe failure, slope failure, base failure Log-spiral Compound failure Wedge failure Two-way wedge failure

Stability Analysis for Infinite s lopes -----Simple, hand calculations Stability Analysis for finite s lopes

Limit Equilibrium Analysis: Wedge method, Method of slices, Stress Deformation Analysis: FEM, FDM, DEM,

Stability of Infinite Slopes

A ty pical element below an inf inite slope

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Condition of Failure:

Case 1: Dry Cohesionless soil

Case 2: Cohesive soil

Condition of Failure:

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Case 3: C and Phi Soils

Condition of Failure:

Case 4: Down-ward Seepage

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Various Steps in the Stability Analysis:

i. Identifying the critical failure surface,

ii. Estimating the driving forces/stress,

iii. Estimating the resisting forces/stress, and

iv. Comparing the two stresses to determine the Safety Factor.

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Stability of Finite Slopes

C ritical F.S (Failure Surface) ?

A f inite slope with possible f ailure surfaces

Assume some failure surface(FS) as possible failure surface and estimate FOS

A f inite slope with a circular arc as a f ailure surf ace

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Weight of soil =

Driv ing Force =

Total Driv ing Force along the F.S =

Driv ing Moment

Ef f ective Normal Stress Acting on ds =

Resisting Force =

Total Resisting Force =

Resisting Moment,

Factor of Saf ety = Md/Mr

Method of Slices Analytical techniques not feasible Numerical techniques are to be adopted Summation of small but finite elements (ie number of

slices)

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Fellenius (1927) made simplest assumption about inter-slice forces

Each inter-slice force is zero (ie ignored the existence of inter-slice forces)

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C = 10kN/m2Phi = 350 . 17kN/m3. 14kN/m3

5m

1:2.5

25m

Assume number of FS, and then estimate FOS for each of the FS..FS with Min FOS is the Critical FS

21m

Embankment Ht.= 5m

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Mathematical Equations For Factor of Safety (FOS)

The summation of Moments, about center of rotation (an axis point) of the forces acting on slices. Typical FOS eq.

Resolving forces acting on slices in horizontal direction and summing for all slices. Typical FOS eq.

Moment Equilibrium Condition

Force Equilibrium Condition

Where, c' = effective cohesion ' = effective angle of friction = pore-water pressure N = slice base normal force W = slice weight D = line load , R, x, f, d, = geometric parameters = inclination of slice base

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Swedish Method of Slices (or)Ordinary or Fellenius method

The simplicity of the method made it possible to compute factor of safety using hand calculations.

In this method, all inter-slice forces are ignored. For homogenous soil slopes with circular failure surfaces,

usually this method provides conservative FOS (low FOS) compared to other methods of slope stability

However, due to the poor force polygon closure, this method can sometimes give unrealistic factor of safety and consequently should not be used in practice.

F.S is the total available shear strength along slip surface divided by summation of gravitational driving forces.

SmobilizedSresistace

WNC

SF)sin*(

tan.

Where,c = cohesion, = slice base length,N = base normal (W cos ), = friction angle,W = slice weight, and = slice base inclination

SmobilizedSresistace

WNC

SF)sin*(

tan.

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2

Bishops simplified method This method include interslice normal forces, but ignores

inters lice shear forces This resulted the base normal becomes a func tion of the factor of

safety. The fac tor of safety equation becomes nonlinear (i.e. F.S appears

on both s ides of the equation).

To find fac tor of safety, it is necessary to s tart with a guess for FS. The initial guess is taken as the ordinary factor of safety .

The force polygon c losure is now fairly good with the addition of the interslice normal forces.

)sin*(

}].tansin{costan[

.

WSF

WCSF

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Janbus simplified method This method is similar to the Bishops method (No

horizontal interslice shear force is considered) This method satisfies only overall horizontal force

equilibrium, but not overall moment equilibrium The slice force polygon closure is usually better than

that for the Bishops method There is a significant difference in FS from Janbu and

Bishop methods. Factor of safety is actually too low compared to

Bishops method This is due to the fact that force equilibrium is

sensitive to the assumed interslice shear, ignoring the interslice shear makes the resulting factor of safety too low for circular slip surfaces

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Spencer method It is an advanced method. It considers both shear and normal interslice forces It considers both factor of safety related to Moment equilibrium condition

and force equilibrium condition. It satisfies both conditions of equilibrium It assumes a constant interslice force function.

(ie. a constant relationship between the interslice shear (X) to normal (E) forces between all slices)

Where, f(x) = 1 (i.e. the interslice shear normal ratio is the same between all slices) is interslice shear force to normal force ratio

It is an iterative procedure altering the interslice shear and normal ratio until the two factors of safety were the same.

Spencers method was presented originally for the analysis of circular slip surfaces, but it is easily extended to non-circular slip surfaces.

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Morgenstern-price method Morgenstern-Price (M-P) method similar to the

Spencer, but this method allows use of various user-specified interslice force functions like Constant, Half-sine, Clipped-sine, Trapezoidal.

Selecting the Constant function makes the M-P method identical to Spencer method.

M-P method considers both shear and normal interslice forces satisfies both moment and force equilibrium.

As with the Spencer method, the force polygon closure is very good with the M-P method, since both shear and normal interslice forces are included.

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Comparisons of various methods

= X /[E f(x)]

f(x)= Interslice force functionE = Interslice normal forceX = Interslice shear force = % of function used (decimal form)

Sarma method This 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 also.

This 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 called advanced because it can take account of non-circular failure surfaces

Sarma method is now a day used as verification to finite element programs.

It is the standard method used for seismic analysis.

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General limit equilibrium methods The GLE method provides a framework for discussing,

describing and understanding all the other methods. The GLE formulation is based on two factors of safety

equations and allows for a range of inter slice shear-normal forces assumptions. One equation gives the factor of safety with respect moment equilibrium (Fm), while the other equation gives the factor of safety with respect to horizontal force equilibrium (Ff).

The idea of using two factors of safety equations follows from the work of Spencer (1967).

The inter slice shear force in the GLE method are handled with an equation proposed by Morgenstern and price (1965). The equation is

X = E f(x)

S.No

Methods MomentEquilibrium

ForceEquilibrium

Interslice Shear Forces

Interslice NormalForces

MomentFactor of

safety

Force Factor of

safety

IntersliceForce

Function1. Culman Wedge

Block method (no-slice)

NO YES NO NO NO YES NO

2. Fellenius, Swedish Circle or Ordinary

method (1936)

NO YES NO NO NO YES NO

3. Bishop Simplified

method (1955)

YES NO YES NO YES NO NO

4. Janbu simplified method (1954)

NO YES YES NO NO YES NO

5. Spencer method(1967)

YES YES YES YES YES YES Constant

6. Morgenstern-price method

(1965)

YES YES YES YES YES YES ConstantHalf-Sine

Clipped-SineTrapezoid

7. Sarma method (1973)

YES YES YES YES YES YES YES

Comparison of limit equilibrium slope stability methods (Abramson et al, 2002; Sinha, 2008)

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Various Steps in the Slope Stability Analysis of Finite Slopes:

i. Assume a possible failure surface,ii. Divide it into small finite slices

iii. Estimating the driving forces/stress for each slice,

iv. Estimating the resisting forces/stress for each slice,

v. Sum up all driving forces and resisting forces on all the slices

vi. Comparing the two quantities to determine the Safety Factor

vii. Repeat steps i to vi with other possible failure surfaces

viii. Identify critical failure surface

Wedge MethodIt occurs when a soil deposit has a specific plane of weakness

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What is the minimum required FOS for the design of embankments?

For long term loading conditions = 1.5For temporary or end of construction conditions = 1.3

Limitations of Method of Slices

Stress distributions are not necessarily representative of the actual field stresses.

Stress distributions are obtained considering equilibrium conditions of each slice.

All the slices are assumed at the same state of equilibrium (ie FOS is assumed to be the same for each slice)

Many other assumptions about inter-slice forces No information on slope deformations (Soil above potential

failure surface is assumed to be rigid-perfectly plastic) In actual conditions, strength of soil at all points doesnt

reach failure surface at the same time.

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Stress-Deformation Analysis

(FEM Analysis)

This analysis allows consideration of actual stress-strain behavior of the soil

FEM analysis of slopes provides magnitudes and patterns of stresses, movements, and pore pressures in slopes during and after the construction/deposition

Non-linear stress-strain behavior, complex boundary conditions, irregular geometries, and a variety of construction operations can all be simulated/considered in this analysis (advanced FEM analysis).

Analysis can identify most likely mode of failure by locating most critically stressed zones within a slope

Provides the slope deformations up to the point of failure

Finite Element Method (FEM) Analysis

The finite element-computed stresses can be imported into a conventional limit equilibrium analysis. The stresses x, y and xy are known within each element, and from this information the normal and mobilized shear stress can be computed at the base mid-point of each slice

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Procedure1. The known x, y and xy at the Gauss numerical integration point in each element

are projected to the nodes and then averaged at each node. With the x, y and xyknown at the nodes, the same stresses can be computed at any other point within the element.

2. For Slice 1, find the element that encompasses the x-y coordinate at the base mid-point of the slice.

3. Compute x, y and xy at the mid-point of the slice base.4. The inclination () of the base of the slice is known from the limit equilibrium

discretization.5. Compute the slice base normal and shear stress using ordinary Mohr circle

techniques.6. Compute the available shear strength from the computed normal stress,7. Multiply the mobilized shear and available strength by the length of the slice base to

convert stress into forces.8. Repeat process for each slice in succession up to Slice # n

Once the mobilized and resisting shear forces are available for each slice, the forces can be integrated over the length of the slip surface to determine a stability factor. The stability factor is defined as:

where, Sr is the total available shear resistance and Sm is the total mobilized shear along the entire length of the slip surface.

Typical Finite element mesh for Computing insitu stress

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Computed Stress Distributions

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Analysis of complex boundary conditions

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Advantages of FEM Based Slope

Stability Analysis

There is no need to make assumptions about intersliceforces

The stability factor is deterministic once the stresses have been computed, and consequently, there are no iterative convergence problems.

The issue of displacement compatibility is satisfied The computed ground stresses are much closer to reality. Stress concentrations are indirectly considered in the

stability analysis. Soil-structure interaction effects are readily handled in the

stability analysis Dynamic stresses arising from earthquake shaking can be

directly considered in a stability analysis.

Limitations/Disadvantages

Increased engineering time for problem formation

Detailed characterization of material properties and interpretation of results

Increased computational effort Accuracy of the analysis is strongly influenced by

the accuracy with which stress-strain model represents actual material behavior

Accuracy of simple models restricted to certain ranges of strain

Advanced models require a large number of input parameters, whose values can be difficult to determine

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SEISMIC SLOPE STABILITY METHODS

Seismic Slope StabilityMethods

Inertial Slope Stability Methods

Weakening Slope Stability Methods

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Inertial Slope stability methods

Pseudostatic Methods

Displacement Based Methods

Newmark Sliding Block Analysis Makdisi-Seed Analysis

Dynamic Finite Element Method

Pseudostatic Analysis: Introduction

Most commonly used method for analyzing seismic slope stability. This method is also recommended by IS code of practice.

This method is easy to understand and is applicable for both total and effective stress slope stability analyses.

Effects of earthquake are represented by constant horizontal and/or vertical accelerations

Several commercial software available: GeoStudio 2004/Slope W; Slide, etc..

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Pseudostatic Analysis: Methodology

Pseudostatic analysis represent the effects of earthquake shaking by considering pseudostatic accelerations that produce inertial forces, Fh and Fv, which act through the centroid of the failure mass.

Where, ah is horizontal pseudostatic acceleration, kh is dimensionless horizontal pseudostatic coefficients, W is the weight of the failure mass

Methodology Contd.. Selection of appropriate pseudostatic

accelerations/coefficients is very important step of the analysis

Magnitude of the pseudostaticaccelerations/coefficients should be related to the severity of the anticipated ground motion

After arriving at the appropriate horizontal & vertical forces, rest of the procedure is same as routine slope stability analysis: Resolve forces on the sliding mass in a direction parallel to the failure surface. Estimate driving and resisting forces and then FOS. Repeat for different possible failure surfaces, and then identify critical failure surface.

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Typical Example of PseudostaticAnalysis

Observations on Effects of Fh and Fv

Horizontal pseudostatic force, Fh reduces the resisting force and increases the driving force. Thereby FOS decreases.

Vertical pseudostatic force typically has less influence on factor of safety since it reduce both driving force and the resisting force

Thats why effects of vertical accelerations are frequently neglected in pseudostatic analysis.

This method can be used for planar, circular and noncircular failure surfaces.

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Selection of Pseudostatic Coefficient

If the slope material is rigid, the inertial force induced in the sliding mass, would be equal to the product of actual horizontal acceleration and the mass of the sliding mass.

According to Marcuson (1981): pseudostaticcoefficients for dams correspond to one-third to one-half of the maximum acceleration (including amplification or deamplification of crest acceleration)

Information Required For the Analysis

Peak design acceleration

Geometry of considered soil structure

Mohr-Coulomb strength parameters

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Earthquake Loading

Pseudostatic accelerations(related to the severity of the earthquake)

Pseudostatic Coefficients

Pseudo-static Methods

Modified Swedish Circle Method (IS Code suggested method)

Bishops Method Janbus Method Morgenstern-Price Method Wedge Method

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Procedure for calculation of seismic coefficients

Seismic coefficient is obtained using I.S code 1893(2002 and 1984) Initially, time period of the structure is to be calculated using IS 1893-1984 [clause

7.4.1.2(a)]

For this time period, Sa/g is to be obtained from response spectra given in IS1893-2002.

Seismic Coefficient is calculated from IS 1893-2002 (clause 6.4.2)

Where Z = Zone Factor (For Roorkee Zone IV) = 0.24 (From table-2 IS 1893-2002)I = Importance Factor (For Embankment) = 1.5 (From table-6 IS 1893-2002)R = Reduction Factor = 1.5 . Calculated seismic coefficient is scaled to appropriate damping of the structure.

Damping suggested for embankments in IS1893 (Table:3 IS 1893-1984) = 10% Multiplication factor = 0.8

Estimate equivalent uniform seismic coefficient (Section 7.4.2.2, IS1893-1984)

gSa

RIZ

h **2

GHT 9.2

Newmark Sliding Block Analysis (displacement analysis)

Pseudostatic method provides an index of stability but no information on deformations of slopes

This (NSBA) analysis provides the acceleration, velocity and displacement of the sliding mass under a given ground motion.

Major assumption of Newmark method is that the slope will deform only when peak ground acceleration exceeds yield acceleration.

Determining the yield acceleration is the most critical step in this analysis.

Analysis is most appropriate for wedge type failure.

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Forces acting on a block resting on an inclined plane under static conditions

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Forces acting on a block resting on an inclined plane under dy namic conditions

As Kh increases factor of safety reduces. There will be some positive value of Kh that will produce a factor of safety of 1.0. This coefficient, termed as the yield coefficient ky, corresponds to the yield acceleration, ay = ky*g

The yield acceleration is the minimum pseudostatic acceleration required to produce instability of the block.

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When a block on an inclined plane is subjected to a pulse of acceleration that exceeds the yield acceleration, the block will move relative to the plane.

Total relative displacement

(10.11)

Displacement depends upon: A, ay, dt

Characteristics of EQ influencing displacement are amplitude, frequency & duration.

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Displacement of the sliding mass under a single earthquake pulse loading,

A ssuming number of pulses in a earthquake motion are propitiate

to the ratio of A /ay, Newmark come up with following equation to obtain total displacement of the s liding mass produced during earthquake shaking,

The above equation usually, provides upper bound es timate of the permanent displacements produced by the earthquake motion

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(a) acceleration vs time (b) V elocity vs time for darkened portion of acceleration pulse

(c ) corresponding down s lope displacement vs time in response to velocity pulses

Diagram illustrating Newmark method

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Unlike Newmark, Yegian et al. (1991) come with the following expression which explicitly considers both frequency content and duration of ground motion on the total displacement of the sliding mass,

Sliding block displacement can also be correlated with arias intensity as follows

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Information Required For Analysis

Yield Acceleration/Critical Acceleration

Ground Motion Characteristics

Amplitude

Frequency

Duration

Accuracy of Displacement Method Depends on

Accuracy of input motion applied to the inclined plane.

Geometry of the slope and stiffness of slope materials.

Ground motion characteristics.

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Dynamic FEM analysis provides most accurate assessment of dynamic stresses/inertial forces

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Makdisi-Seed Analysis Makdisi and Seed (1978) improved upon Newmark

procedure by accounting for the dynamic response of the embankment.

Background: During the San Fernando Earthquake of 1971, the Upper San Fernando Dam, despite a large pseudostaticfactor of safety, failed. In 1973, Seed performed a dynamic analysis of the embankment and computed displacements that closely agreed with the observed deformations.

In Makdisi and Seeds procedure, the yield acceleration is computed for the failure surface using the dynamic yield strength, which is approximately 80% of the static strength.

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 .

M-S simplified procedure is widely used for estimation of permanent displacements in dams and embankments

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Weakening Slope Stability Analysis

Weakening Slope Stability Results in Flow slides Liquefaction induced lateral spreading

Reduction in shear strength is due to liquefaction.

This is the preferred method for those soils that will experience reduction in shear strength during an earthquake.

Reduction in shear strength is also due to excess pwps.

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Flow slide If liquefaction (flow liquefaction) occurs in or under a

sloping soil mass, the entire soil mass will flow or translate laterally to the unsupported slide in a phenomenon termed as flow slide.

Flow slides develop when static driving forces exceed weakened shear strength of soil along slip surface. Consequently, factor of safety is less than 1.

Occurrence of flow slides can be identified by carrying out slope stability analysis for end of earthquake conditions. Liquefied regions should be given residual strength. Effective stress analysis should be considered to include effect of development of excess pore water pressures.

Liquefaction Induced Lateral Spreading (or) Deformation

Failures Lateral spreading is caused due to the

liquefaction of embankment soil or soil behind a retaining wall. Occurrence of liquefaction subsequently increase pressures on the retaining wall or gently sloping or flat ground surfaces.

If the liquefaction induced lateral spreading is restricted to localized ground surface, it is called localized lateral spreading.

If it causes lateral movement over an extensive distance, it is called large scale lateral spreading.

Concept of cyclic mobility can be used to describe large scale lateral spreading

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Even though concept of cyclic mobility can be used to describe large scale lateral spreading. Its accurate quantification is very difficult due to complex stress strain behavior of soil during cyclic mobility. Simulation of cyclic mobility of soil in the field models is very difficult and complicated. Consequently, only empirical methods/formulae are only available currently to estimate lateral spreading/deformation failures.

Selection of appropriate method of analysis

For F.S against liquefaction < 1, soil is expected to liquefy due to earthquake. Flow slide analysis or lateral spreading analysis will be performed.

For F.S against liquefaction > 2, the pore water pressure due to earthquake is usually small. It can be neglected. Soil is not weakened by earthquake. So inertial slope stability analysis will be performed.

For F.S against liquefaction >1 and < or =2, soil is not expected to liquefy due to earthquake, but sufficient excess pore water pressures will be developed. Consequently, their effect is to be included in the analysis by carrying out effective stress analysis

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