back analysis in soil slope stability

PRESENTATION ON

BACK ANALYSIS IN SLOPE

STABILITY

Prof. Samirsinh P Parmar

Research Scholar - Geotechnical Engineering

Roll No. : 14103277

Department of Civil Engineering

INDIAN INSTITUTE OF TECHNOLOGY, KANPUR

1

Course: Advance Geotechnical Engineering

INTRODUCTION

When Slope Fails by sliding it gives useful information

on

The conditions in the slope at the time of the failure, and

Opportunity to validate the stability analysis method.

The factor of safety is

considered to be unity

(1.0) at the time of

failure. Ref: Google image

2

INTRODUCTION

To validate or to develop model at the time of failure

following are the requirements..

1) Unit weight of soil

2) Shear strength properties of soil.

3) Groundwater and pore water pressure conditions.

4) Method of analysis including failure mechanism.

The model helps in understanding failure mechanism , used as a

Basis for analysis of remedial measures. 3

DEFINITION : BACK ANALYSIS

The process of determining the conditions and

establishing a suitable model of the slope from a failure

is termed back analysis or back –calculation.

Back analysis of slope failures can provide functional relations

between shear strength parameters c and ϕ for slopes of

homogeneous materials with linear failure envelopes provided all

the other parameters are known.

• Back analysing a failed slope usually involves trying to

establish what conditions existed at the time of failure.

• That is, what was the strength mobilized or what was the

pore-water pressure condition.

4

BACK ANALYSIS:

To back-analyze multiple sets of slope stability

parameters simultaneously under uncertainty, the

back-analysis can be implemented in a probabilistic

way, in which uncertain parameters are modelled

as random variables, and their distributions are

improved based on the observed slope failure

information.

5

HISTORICAL REVIEW

Researchers Write et al. (1973), Fredlund and Krahn (1977),Duncan and Write (1980), Leshchinsky (1990), and Duncan(1992) shown stability methods that satisfy all conditions ofequilibrium ( Horizontal and vertical force equilibrium andmoment equilibrium) result in factor of safety with accuracy of± 5 % .

Leroueil and Tavenas, 1981;

Azzouz et.al., 1981;

Leonards, 1982;

Duncan and Stark, 1992;

Gilbert et. al. 1998;

Tang, et. al. 1998;

Stark et. al. 1998.

6

FACTORS AFFECTING BACK ANALYSIS

Structural fabric of soil

Nonhomogenity

Influence of fissures on soil strength.

Effects of pre-existing shear planes within soil

mass.

7

FACTOR OF SAFETY IN BACK ANALYSIS

Eq (1)

Ref: Rick Deschamps and Greg Yankey

8

In the back analysis of failure, the assumption is made

that the safety factors is 1.0 so that the forces equal the

driving forces.

For the simple case of wedge system with no cohesion

eq (1) becomes:

The right side of eq (2) is dictated by equilibrium and

can be considered “ Known” for a given Geometry and

Rupture surface.

The objective of back-analysis is to determine the

strength components on the left side of eq (2).

By fixing the FS at 1.0, leads to condition that

conservative design assumptions are un-conservative

in back analysis.

Eq (2)

9

Ref: Rick Deschamps and Greg Yankey

Assuming c and ϕGeological site exploration

Slope stability

analysis method

Assume FS =1

Calculate Factor of safety for

positional parameter of

critical slip surface L

Positional Parameter

of landslide La

L-La/La

<ε ?

Calculate Ca and ϕa

Change design of slope

and Corresponding FS

Determining FS

Flow Chart of Back Analysis of

Shear strength ParametersRef: K Zhang and P Cao

10

STEPS TO PERFORM BACK ANALYSIS

1) Several pairs of values of cohesion (c’) and friction angle

(ϕ’) were assumed.

2) The pairs of values were chosen such that they

represented a range in the dimensionless parameter λcϕ,

but the values did not necessarily produce a factor of safety of

1.

3) The critical circles and the corresponding minimum factor of

safety were calculated for each pair of c and ϕ.

4) Values of the developed shear strength parameters (C’d and

ϕ’d) were calculated by following equations.

C’d= c’/ F _____(1) ϕ’d= arc tan ( tanϕ’/ F )_____(2) 11

λcϕ = γtanϕ/c

STEPS TO PERFORM BACK ANALYSIS CONT…

5) The depth of the critical slip

surface for each pair of

values of strength

parameters was calculated.

6) Draw graph of depth of slip

surface(ft) vs ϕ’ and depth of

slip surface(ft) vs c’.

7) The developed cohesion

and friction angle represent

back calculated values

required to produce a factor

of safety 1.

Depth of slip surface(ft)

Depth of slip surface(ft)

Co

hesio

n c

’ (p

sf)

Fri

cti

on

an

gle

ϕ’

(deg

ree)

12

BACK ANALYSIS STEPS CONT…

Calculations for back

analysis described

here, can be

simplified by the use

of dimensionless

stability charts that

allow the cohesion

and friction angle to

be back calculated

directly.

Ref: Duncan and Wright, fig-12.7 pg:187

13

EXAMPLE : EMBANKMENT ON SOFT SATURATED CLAY

FOUNDATION

30 ft

6 ft

Slope 1v: 2H

Failed during construction due to the

underlying weak clay foundation

Saturated Clay

Fill (sand): γ= 125 pcf, ϕ=35˚

14


EXAMPLE: CONT…

Estimated friction angle ϕ=35˚.

Unit weight of fill material γ= 125pcf

Average undrained shear strength calculated from assumed parameters = 137 pcf

0

200 400

10

20

30

10 psf/ft

137 pcf

Undrained Shear Strength-psf

De

pth

be

low

ori

gin

al g

rou

nd

su

rfa

ce

-ft

Undrained Shear Strength

profiles from back analysis of

embankment on soft clay

78

15


Saturated Clay

Fill (sand)

Constant Strength (137psf)

Linear increase in strength with

depth (10psf/ft)

Critical Circles from Back

Analysis

Assuming

Constant shear strength and

Linear increase in undrained

Shear strength with depth of

foundation

16


CRITICAL CIRCLES FROM BACK ANALYSIS

17Critical Circes obtained from back Analysis

( ref: Yamagami & Ueta 1996)

FROM THE CRITICAL CIRCLES….

For increase in FS from 1 to 1.5

Decrease the slope ht.6 ft to 10 ft with the constant

shear strength of 137 psf.

If shear strength increases linearly with depth as

second shear strength profile, the factor of safety is

only increased to 1.3 by reducing the slope height

to 4 ft.

Now a days it is possible to represent accurate shear

strength then the average shear strength calculated,

hence able to remove uncertainty in back analysis.18

PRACTICAL PROBLEMS AND LIMITATIONS OF

BACK ANALYSIS

Presence of seam or weak layer.

- Strength of each layer must be known.

Knowledge of the pore water pressure

- pre-failure piezometric data at selected location

are not available.

Practically all slopes have a three dimensional

component. (Plain Strain Condition assumed)

- Neglecting this component in back-analysis will

lead to an overestimation of strength. (5% to 30 %)

19


BACK ANALYSIS

Progressive failure.

- back calculated values represent only an average,of the shear strength parameters that were mobilizedon the failure surface. ( avg. may not be the actualfailure surface parameters).

Decreasing Shear strength with time.

• Undrained conditions assumed and used to backcalculate shear strength for such a slope.

• The stability and shear strength will continue todecrease after failure occurs.

• For redesign , strength significantly lower then theone determined by back analysis my beappropriate.

20


BACK ANALYSIS

Complex shear strength parameters.

• - Complex phenomenon : shear strength

• - with respect to failure plane: anisotropic shear

strength.

• - Shear strength varies nonlinear with depth.

• - It is essential to know weather the shear strength

should be represented by undrained shear strength

parameters and total stress analysis or by drained

shear strengths and effective stresses.

21

PRACTICAL PROBLEMS AND LIMITATIONS OF BACK

ANALYSIS

Limitations of Factor of safety

Does not contain information about the variability or

uncertainty of shear strength or mobilized shear stress.

Same factor of safety can have different reliability

Probabilistic methods are available to estimate

reliability of slopes 22

William Kitch, Cal Poly Pomona,UC Riverside, May 12, 2012

ADVANTAGES OF BACK ANALYSIS

It avoids many of the problems associated with

laboratory and in-situ tests.

Back calculated strengths are representative of the

soil in natural state.

Provides strength values representative of failure

plane.

It gives a measure of shear strength of soil mass that

reflects the influences of soil fabric, fissures and pre-

existing shear planes.

It involves a much longer time to failure than the

laboratory or in-situ tests.23

THERE ARE A VARIETY OF METHODS FOR

CARRYING OUT BACK ANALYSIS:

Manual trial and error to match input data with

observed behaviour

Sensitivity analysis for individual variables

Probabilistic analysis for two correlated variables

Advanced probabilistic methods for simultaneous

analysis of multiple parameters

24

HOW TO MAKE BACK ANALYSIS MORE

ACCURATE

25

For Data Acquisition

Pore Pressure

Transducers

Strain Gauges

Load Cells

RS / GIS real time data

monitoring.

For back analysis

Slope Stability

Software's

Ann models

Fuzzy logic application

CONCLUSION:

Successful back-calculation requires accurate

information regarding geometry, material properties, and

pore pressure distribution.

It is important to remember that all assumptions that are

conservative in design are un-conservative in back

analysis.

Application of modern technology in terms of hardware

and software's can lead back analysis to an exact tool to

analyze the slope stability.

26

REFERENCES:

J. M. Duncan ,A. L. Buchignani, March,( 1987), An Engineering manual for

slope stability studies.

J.M. Duncan, Stark, (1992), “Stability performance of slopes and

embankments-II Proceedings”-Berkeley, CA, June 29-July1, 1992, pp.890-

904.

Y. Okui; A. Tokunaga; M. Shinji; S. Mori, (1997), “New back analysis

method of slope stability by using field measurements”, Int. J. Rock Mech. &

Min. Sci. Vol. 34, No. 3-4, 1997.

Duncan, J.M. and Wright, S.G. (2005), Soil Strength and Slope Stability

(chapter 12), John Wiley and Sons Inc.

R Deschamps G Yankey, (2006), “Limitations in the Back-Analysis of

Strength from Failures”, pp. 01-10.

Ke Zang , Ping, Rui ( 2012) “ Rigorous back analysis of shear strength

parameters of landslide slip”, Elsevier , Science Direct. Trans. Nonferrous

Met. Soc. China. pp.1459-1464.

27

back analysis in soil slope stability

Technology