Bearing Capacity of shallow foundation on slopes, a comprehensive seminar for the registration of PhD degree.

1. BEARING CAPACITY OF SHALLOW FOUNDATIONS ON SLOPES
A report submitted for the comprehensive Seminar for the registration
for the degree
of
Doctor of Philosophy
by
NABAM BUDH
(PhD/FT/16/CE/01)
Under the guidance of
Dr. Sukumar Baishya
Prof. Deptt. of Civil Engg.



DEPARTMENT OF CIVIL ENGINEERING
NORTH EASTERN REGIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY
(DEEMED TO BE UNIVERSITY)
NIRJULI, ARUNACHAL PRADESH-791109 INDIA
DECEMBER 2017

2.  Introduction
 Literature Review
◦ Analytical Techniques
◦ BC of shallow foundation on horizontal ground
◦ BC of shallow foundation on slopes
◦ Comparison of available methodologies
◦ Failure mechanism of shallow foundation on slopes
◦ Factors affecting BC of shallow foundation on slopes
◦ BC using Finite element analysis (FEA)
 Why FEA Method?
 Acharyya & Dey (2015, 2017)
 Critical comments
 Proposed work and research objectives
 Methodology
 Work Plan
 References

3.  GENERAL BACKGROUND
 BRIEF LITERATURE REVIEW
 BEARING CAPACITY OF SOIL
 Definition of BC & Ultimate BC
 In foundation, soil is the weakest construction material.
 BC depends on mechanical characteristic of soil and physical
characteristic of foundation.
 First developed by Prandtl (1920), and later extended by Terzaghi
(1943), Meyerhof (1951), Hansen (1970), Vesic (1973)
 Terzaghi (1943) qu =cNc +qNq +γBNγ
 BEARING CAPACITY OF SOIL ON SLOPES
 Land limitations
 NO BIS guidelines
 Overall stability & BC failure makes it more critical
 First undertaken by Meyerhof (1957) and later on by Hasen (1970),
Vesic (1975), Kusakabe et. al. (1981), etc.
 qu,slope =cNcq +γBNγq
 Theories of Ultimate BC was developed using analytical techniques.
 SUMMARY

5.  The theories of the ultimate bearing capacity of shallow foundations
were developed by employing one of the following analytical techniques:
Limit equilibrium analysis
Considers equilibrium of forces ,an approximate method,
trial and error, simple, most widely used till date.
 Terzaghi (1943), Meyerhof (1957), Azzouz and Baligh (1983), Narita and
Yamaguchi (1990) and Castelli and Motta (2008)
Slip line analysis
Slip line represent the direction of the maximum shear
stresses.
 Sokolovski (1960), Buhan and Garnier (1994, 1998)
Limit analysis
Considers the stress-strain relationship in an idealized
manner. Ben Leshchinsky (2015,2017), Mofidi et.al. (2014),
Chakraborty (2012)
Finite element analysis
A numerical technique
 Kai Wing Ip (2005), Loukidis et.al.(2008), Georgiadis (2010), Shaiau et. al.(2011),
Nyugen et.al. (2011), Abbas & Sabbar (2011), Acharyya & Dey (2015, 2017),

6. BEARING
CAPACITY THEORY
FOR STRIP
FOUNDATION ON
HORIZONTAL
SURFACE
 Terzaghi (1943) proposed a
theory for determination of
the ultimate bearing capacity
of shallow ,rough, rigid &
continuous foundation
supported by a homogenous,
isotropic soil.
 qu =cNc +qNq +γBNγ
 Used limit equilibrium
analysis
 Moment in equilibrium was not
considered
 Elastic zone is responsible
for resistance against
sliding
due to self weight of the soil.
 passive force is due to
 surcharge (q),
 cohesion (c),
 unit weight of the soil (γ),
 the angle of shear resistance (Φº),
 the solution is not exact

7.  Meyerhof (1957)
 qu,slope =cNcq +γBNγq
◦ Plastic zone on the side of the slope is relatively smaller
◦ The ultimate BC of the foundation is reduced.
BC depends on
 the distance of the foundation from the top of the slope (b),
If b˃ 2 to 6B, BC is independent of (α°).
 the angle of the slope (α°),
 the angle of shearing resistance of the soil
 the depth/width ratio (Df/B), of the foundation

9. Author Year Foundation
Position
Loadin
g
Geometr
y of
footing
Clay Sand C-Φ Constitutive
models used
Methods
used
Top of
Slope
On Slope
Meyerhof 1957 √ √ Strip
footing
√ √ X Limit
equilibrium
Hansen 1970 √ X √ √ √
Vesic 1975 √ X √ X X
Graham
et.al.
1988 √ X X √ X Analytical
method
Shields
et.al.
1988 √ X Strip
footing
X √ X Centrifugal
Test
Saran et.al. 1989 √ X Strip
footing
√ √ √ Limit
equilibrium
and limit
analysis
Sharma &
Chen
1995 √ X Strip
footing
√ √ √ Mohr-coulomb
failure criteria
Limit
equilibrium
Choudhury
& Rao
2006 X √ Strip
footing
√ √ √ Rigid perfectly
plastic
Limit
equilibrium
Georgiadis 2009 √ X Inclined Strip
footing
√ X X Mohr-coulomb
elastic perfectly
plastic
FEA
Yamamoto 2010 √ X √ √ √ Pseudo static
approach

10. Author Year Foundation
Position
Loading Geometry
of footing
Clay Sand C-Φ Constitutive
models used
Methods
used
Top of
the
Slope
On
Slope
Shiau et.al 2011 √ X √ X X Limit analysis
Nguyen et.al. 2011 √ X Strip footing √ X X Mohr-coulomb
failure criteria
FEA
Abbas &
Sabbar
2011 √ X Rectangular
footing
√ X X FEA
Castelli et.al. 2012 √ X Square &
Strip
X √ X Experimental
Chakrabort
y & Kumar
2013 √ Strip footing √ Mohr-coulomb
failure criteria
Limit analysis
Mofidi, et.al. 2014 √ √ Strip footing √ X √ Mohr-coulomb
yield function
Limit Analysis
Ben
Leshchinsky
2015 √ X Strip footing X X √ Perfectly plastic Upper bound
limit state
Ganesh et.
al.
2016 √ X Eccentric
and
oblique
Strip footing X √ √ Regression
analysis of
laboratory
model
Acharyya &
Dey
2015,
2017
√ X Square footing X √ X Mohr-coulomb
elastic perfectly
FEA

14. ◦ Bearing capacity
failure
◦ Overall stability of
the slope failure
◦ Combined failure
Figure: Failure modes: (a) and (b)
bearing capacity failure and (c) overall
slope failure

15.  The effect of slope
angle(β)
 BC decreases
 Height of slope (H)
 Geometry of footing
 Distance of slope
from edge of footing
(b)
 Cohesion (c)
 Angle of shearing
resistance (φ)
 Drainage conditions
in the slope.

17.  Kai Wing Ip (2005)
 Loukidis et al. (2008)
 Georgiadis (2010)
 Shaiau et. al.(2011)
 Nyugen & Merifield (2011)
 Abbas & Sabbar (2011)
 Acharyya & Dey (2015, 2017)

18.  A very powerful program that
◦ covers most of the problem in geotechnical engineering.
 FEA is capable to simulate
◦ the geometry of the foundation,
◦ the soil and
◦ the loading conditions
 Takes into account,
◦ the 3-D confinement effect at the site.
 Unlike others methods, no assumptions are made.
 Numerical simulation obtained from 3D models
gives
◦ accurate solutions
◦ consistently higher than that obtained from analytical
estimates
 Solutions obtained by finite element method of
analyses are
◦ widely acceptable in current industry.

19. Figure :Typical PLAXIS 3D representation of a footing resting on
the crest of a slope
Figure: Schematic representation of a model geometry for a
footing resting on sloping ground (not to scale)

20. Figure: 2.19. Standard fixities
applied in the numerical model
Fig. Typical meshing scheme
adopted in the numerical model
(Acharyya & Dey 2017)
(Acharyya & Dey 2017)

21. Figure: Formation of passive zones beneath the footing for various setback
ratios (b/B)
(Acharyya & Dey 2017)

22.  Coupled stress-deformation analysis
 BC increases with the increase in
◦ The angle of internal friction,
◦ Embedment depth,
◦ Footing width,
◦ Setback distance.
 The increase in BC due to increase of embedment depth
of the footing is
◦ due to increase in the degree of confinement restricting the
movement of the soil towards the sloping face.
 Beyond a critical setback ratio b/B = 3,
◦ the footing behaves similar to that on horizontal ground.
 Bearing capacity reduces
◦ with the increase of slope angle,
 which is associated with the increased soil movement towards the
slope.
 The variation of unit weight and modulus of elasticity of
soil
◦ has marginal effect on the bearing capacity.

23.  Theories of Meyerhof (1957) and Graham et al. (1987), and
the experimental work from Shields et.al (1977), Gemperline
(1988) and Garnier et al. (1994) ,etc.
◦ Provided a design chart needed
 to predict the magnitude of Nγq .
◦ Design chart valid for only
 a limited range of footing location and
 embedded depth.
 The experimental work of Meyerhof (1957) and Shield et al.
showed that
◦ soil with different value of ϕ° leads to
 BC with respect to the distance of the footing.
 While most of the theories developed for foundations near
slope are
◦ for cohesionless material,
◦ Meyerhof presented a solution for the case of
 pure cohesive soil (ϕ°=0°).
 Thus for cohesive-frictional material,
◦ equation qu,slope =cNcq +γBNγq may not be capable
 to predict the ultimate BC of footing on cohesive-frictional materials.

24.  Method of Gemperline (1988) has provided a
mathematical solution, which is valid for
◦ different size of footing and
◦ different horizontal and vertical location of the
footing.
 The solutions of BC of shallow foundation on
slopes given by Saran et al. (1989) are
◦ valid only for Df/B=0 to 1 and b/B=0 to 1.
◦ For other footing locations and embedded depths,
the values of BC factors are
 not accurately predicted.

25.  All the approaches used by different
researchers for the evaluation of BC of
shallow foundation on slope or near the
slope
◦ have their own sets of assumptions and
◦ corresponding weaknesses also.
 Some investigations show that,
◦ in case of non cohesive soils,
 the BC is always governed by foundation failure,
◦ while in cohesive soil
 the BC of the foundation is dictated by the stability
of slope.

26.  Hybrid methods (viz. combination of FE method with Limit
analysis or FE method with Limit equilibrium)
◦ has been used successfully by many researchers
 use of finite element analysis has been very nominal
till date.
 Most of the research work has been carried
out on
◦ Strip footing
◦ but very few works has been reported on Square (Castelli et.al. 2012;
Acharyya & Dey 2015, 2017)
◦ and rectangular footing (Abbas & Sabbar 2011)
 Use of circular footing has not been reported so far.
 Most of the work was carried out for
foundation loaded with
◦ axial loads
 but the case of inclined load is very limited (Georgiadis 2009; Ganesh et.
al. 2016)

27.  To develop a numerical model
 simulate the case of shallow foundation with
strip/square/rectangular/circular footing on/near a
slope.
 Using Salome-Meca, FEA based software.
 To evaluate the ultimate bearing capacity
 the effect of slope angle,
 height of slope,
 geometry of footing,
 distance of slope from edge of footing,
 cohesion,
 angle of shearing resistance and
 drainage conditions in the slope.
 To evaluate the effect of the drainage on BC
 Undrained
 Drained

28.  To analyse BC
 considering 3D geometry of slopes
 To study the effect of different soil
constitutive models
on BC of shallow foundation on slopes.
 To compare the result obtained in this
investigation
◦ with the generally used existing theoretical values
available in literatures of Meyerhof (1957), Vasic
(1975), etc.

29.  Development of FE model
◦ of soil and foundation system on slopes covering wide range
of parameters identified in the objective of the studies.
 Development of load deformation curve
◦ of the footing under progressive loading.
 Determination of ultimate bearing capacity
◦ of the footing from step 2 above.
 Identification of pertinent failure mechanism
◦ in terms of deformation/strain/stress.
 Study of variation of failure mechanism if any,
vis-a-vis variation of different salient parameters
identified above.
 Development of non-dimensional (ND) charts
reflecting the effects of salient geotechnical/geometric
factors affecting bearing capacity of soil on slopes.

31.  Abbas & Sabbar (2011), Finite analysis for bearing capacity of
rectangular footing resting near sloped cohesive soil, Tikrit Journal
of Eng. Sciences/Vol.18/No.3/September 2011, (33-41).
 Acharyya R. & Dey R. (2015), Site characterization and bearing
capacity estimation for a school building located on hill slope, 50th
indian geotechnical conference, College of Engineering (Estd. 1854),
Pune, India.
 Acharyya R. & Dey R. (2017), Finite Element Investigation of the
Bearing Capacity of Square Footings Resting on Sloping Ground,
Springer; Indian National Academy of Engineering; INAE Lett (2017)
2:97–105; DOI 10.1007/s41403-017-0028-6.
 Ben Leschchinsky (2015), “Bearing capacity of footings placed
Adjacent to c-ϕ slopes” A.M.ASCE.
 Ben Leschchinsky and Xie Yonggui (2017), “Bearing capacity of
spread footings placed near c-ϕ slopes”, J. Geothech, Geoenviron,
Eng., 2017, 143(1):06016020; ASCE: DI10.1061/(ASCE)GT.1943-
5606.0001578
 Castelli, F. and Lentini, V. (2012), Evaluation of the bearing
capacity of footings on slopes, International Journal of Physical
Modelling in Geotechnics, 129(3), 112-118.
 Choudhury & Rao (2006), Seismic bearing capacity of shallow
strip footings embedded in slope, DOI:10.1061/(ASCE)1532-
3641(2006)6:3(176).

32.  Chakraborty & Kumar (2013), “Bearing capacity of foundations on
slopes”, Geomechanics and Geoengineering: An international Journal,
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 Ganesh et al. (2016), “Bearing capacity of shallow strip foundations in
sand under eccentric and oblique loads”, ASCE.
 Georgiadis, K., 2009. The influence of load inclination on the
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and Geotechnics, 37 (3), 311–322.
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