Introduction to back analysis; Definition- Back analysis; Historical Review- back analysis; Factors affecting back analysis; Steps to perform back analysis; Solved numerical for demonstration of back analysis; Practical Problems and limitations of back analysis; Advantages of back analysis How to make back analysis accurate?; Concluding remarks; Selected References; back analysis procedure; Back analysis in slope stability problems

1. PRESENTATION ON
BACK ANALYSIS IN SLOPE
STABILITY
Samirsinh P Parmar
Roll No. : 14103277
Department of Civil Engineering
INDIAN INSTITUTE OF TECHNOLOGY, KANPUR
1
Course: CE 631: Advance Geotechnical Engineering
Instructed By: Dr. Sarvesh Chandra
IIT Kanpur

2. CONTENT OF THE PRESENTATION
 Introduction to back analysis
 Definition- Back analysis
 Historical Review- back analysis
 Factors affecting back analysis
 Steps to perform back analysis
 Solved numerical for demonstration of back analysis
 Practical Problems and limitations of back analysis
 Advantages of back analysis
 How to make back analysis accurate?
 Concluding remarks
 Selected References 2

3. 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
3

4. 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. 4

5. 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.
5

6. 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.
6

7. 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 of
equilibrium ( Horizontal and vertical force equilibrium and
moment 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.
7

8. FACTORS AFFECTING BACK ANALYSIS
 Structural fabric of soil
 Nonhomogenity
 Influence of fissures on soil strength.
 Effects of pre-existing shear planes within soil
mass.
8

9. FACTOR OF SAFETY IN BACK ANALYSIS
Eq (1)
Ref: Rick Deschamps and Greg Yankey
9

10.  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)
10
Ref: Rick Deschamps and Greg Yankey

11. Assuming c and ϕ
Geological 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 Parameters
Ref: K Zhang and P Cao
11

12. 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)
12
λcϕ = γtanϕ/c

13. 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)
Cohesion
c’
(psf)
Friction
angle
ϕ’
(degree)
13

14. 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
14

15. 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˚
15
Ref: Duncan and Wright, fig-12.8 pg:188

16. 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
Depth
below
original
ground
surface-
ft
Undrained Shear Strength
profiles from back analysis of
embankment on soft clay
78
16
Ref: Duncan and Wright, fig-12.9 pg:188

17. 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
17
Ref: Duncan and Wright, fig-12.10 pg:189

18. CRITICAL CIRCLES FROM BACK ANALYSIS
18
Critical Circes obtained from back Analysis
( ref: Yamagami & Ueta 1996)

19. 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.
19

20. 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 %)
20

21. PRACTICAL PROBLEMS AND LIMITATIONS OF
BACK ANALYSIS
 Progressive failure.
- back calculated values represent only an average,
of the shear strength parameters that were mobilized
on the failure surface. ( avg. may not be the actual
failure surface parameters).
 Decreasing Shear strength with time.
• Undrained conditions assumed and used to back
calculate shear strength for such a slope.
• The stability and shear strength will continue to
decrease after failure occurs.
• For redesign , strength significantly lower then the
one determined by back analysis my be
appropriate.
21

22. PRACTICAL PROBLEMS AND LIMITATIONS OF
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.
22

23. 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 23
William Kitch, Cal Poly Pomona,UC Riverside, May 12, 2012

24. 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.
24

25. 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
25

26. HOW TO MAKE BACK ANALYSIS MORE
ACCURATE
26
 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

27. 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.
27

28. 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.
28

29. 29