Interfacial friction between soils
and solid surfaces
Dr. R. G. Robinson
Assistant Professor
Department of Civil Engineering
IIT Madras
Typical field situations
Shallow foundation
Tip resistance
Deep foundation
Typical field situations
Retaining walls
Typical field situations
Reinforced earth walls
Typical field situations
Geosynthetic reinforced earth slopes
Typical field situations
Geotextiles
www.geosyntheticssociety.org
Definition of coefficient of friction and friction angle
P
P
Normal Force
T
Shear Force
Coefficient of friction,
m=tand=T/P
where, d is the friction angle
T
Soil
Solid material
Shear stress = T/A
P
T
Normal stress=P/A
Apparatus used for evaluating friction angle
Potyondy (1961)
Ingold (1984)
Rowe (1962)
Silberman (1961)
Ingold (1984)
Apparatus used for evaluating friction angle
Jewell and Wroth (1987)
Murthy et al. (1993)
Coyle and Sulaiman (1967)
Apparatus used for evaluating friction angle
Brumund and Leonards (1973)
Heerema (1979)
Ingold (1984)
Yoshimi and Kishida (1981)
Apparatus used for evaluating friction angle
Desai et al. (1985)
Uesugi and Kishida (1986)
Paikowsky et al. (1995)
Abderrahim and Tisot (1993)
Some Terminologies
Three Phases in Soils
S : Solid
W: Liquid
A: Air
Soil particle
Water
Air
Void ratio, e = Vv/Vs
Water content, w = Mw/Ms
Relative Density (Dr)
Loosest
emax = 0.92
(Lambe and Whitman, 1979)
emax  e
Dr 
100
emax  emin
Densest
emin = 0.35
Particle shapes-- Sand
Coarsegrained
soils
Rounded
Subrounded
Subangular
Angular
(Holtz and Kovacs, 1981)
Maximum and minimum void ratio
ASTM D 4253; ASTM D 4254
Maximum void ratio
Minimum void ratio
Direct shear test
 f  c   n tan 
f
n
c

shear strength of soil
Normal stress
cohesion intercept
angle of internal friction
Typical direct shear test results
Dense sand
Loose sand

cv
Displacement
n1
n2
n3
Displacement
n1
n2
n3
Angle of repose
Fcv ~ Angle of repose
Interface friction in sands
Factors influencing interfacial friction angle of Sand







Surface Roughness
Density of sand
Normal stress
Rate of deformation
Size of apparatus
Grain size and shape
Type of apparatus
Influence of sand density and surface Roughness
1
d / cv
0.75
0.5
0.25
Soma sand
Steel Dr = 40%
Steel Dr = 60%
Steel Dr = 90%
Brass Dr=65%
Aluminium Dr=65%
Steel
Wood
Concrete
Toyoura
sand
0
1
10
100
Surface roughness, Rmax, mm
1000
Influence of sand density……
Results of triaxial and soil-steel friction tests (after Noorany, 1985)
Soil Type
Soil Condition

d
Silica sand
loose
dense
35
40
21
20
Calcareous
sand from
Guam
loose
dense
loose, crushed
loose, ground
dense, crushed
46
49
46
46
48
18
18
21
22
Calcareous
sand from
Florida
loose
medium
dense
medium, crushed
medium, ground
dense, crushed
44
45
47
45
45
49
20
20
23
23
23
Influence of sand density……
Acar et al. 1982
Levacher and Sieffert 1984
1.2
Steel
Wood
1
Concrete
tan(  ord )
Sand
0.8
0.6
0.4
0.2
0
20
40
60
80
Relative Density (% )
100
Limiting values of d
I Maximum Values:
Potyondy (1961), Panchanathan and
Ramaswamy (1964), Uesugi and co-workers
reported the limiting maximum value of d is the
peak angle of internal friction p
Yoshimi and Kishida (1981) report that the
maximum limiting value is the critical state
friction angle cv
Minimum Values of d Reported by Various Authors
d
Interface
Sand-material
Sand-smooth surface
Sand-smooth material
Sand-normal glass
Sand-pyrex glass
Sand-stainless steel
Sand-steel
Sand-steel
Glass beads-steel
Material-Material
Diamond-diamond
Sapphire-sapphire
Metal-diamond
Steel-sapphire
m
0.5 m
7 - 10
5–6
7
tan -1 (0.07/Ri) §
0.5 m
5
3
11
3
7
Notes: 
m
Particle-to particle friction angle
§
Ri
Modified roundness
Source
Lambe and Whitman (1969)
Yoshimi and Kishida (1981)
Tatsuoka and Haibara (1985)
Tatsuoka and Haibara (1985)
Tatsuoka and Haibara (1985)
Uesugi and kishida (1986b)
Tejchman and Wu (1995)
Paikowsky et al. (1995)
Bowden and tabor (1986)
Bowden and tabor (1986)
Bowden and tabor (1986)
Bowden and tabor (1986)
Influence of normal stress
Potyondy (1961); Acar (1982):
Both δ and Φ decreases with normal stress
but the ratio (δ/) remains constant
Heerema (1979), Uesugi and Kishida (1986),
O’Rourke et al. (1990)
d is independent of normal stress
For soft materials:
d increases with normal stress due to
indentation of sand into the material
(Panchanathan and Ramaswamy, 1964;
Valsangkar and Holm (1997)
Influence of Rate of deformation
 Heerema (1979)
– Rate of deformation from 0.7 to 600 mm/s
– No influence
 Lemos (1986)
– Rate of deformation 0.0038 to 133 mm/min
– No influence
Influence of Size of apparatus
 Brumund and Leonards (1973)
– Rods with interface area of 225 cm2 and 400 cm2
– No appreciable difference
 Uesugi and kishida (1986)
– Simple shear apparatus, 40 cm2 and 400 cm2
– No influence
 O’Rourke et al (1990)
– Direct shear apparatus of size equal to 6cm x 6 cm, 10
cm x10 cm, 28 cm x28 cm and 30.5x30.5 cm
– No significant influence
Rowe (1962), Uesugi and Kishida
(1986), Jardine and Lahane (1994):
d decreases with increase in grain size
Friction angle (degrees)
Influence of grain size and shape
Rowe (1962)
Particle diameter (mm)
Angular particles give higher friction angle
(Uesugi and Kishida 1986; O’Rourke et al. 1990; Paikowski et al. 1995)
Influence of type of apparatus
 Kishida and Uesugi (1987)
– Simple shear versus direct shear
– No difference
 Thandavamurthy (1990)
– Direct shear versus model pile tests
– Direct shear gives 20% higher
 Abderrahim and Tisot (1993)
– Direct shear- Ring torsion-Pressuremeter probe
– Direct shear > Pressuremeter probe >Ring shear
QUANTIFICATION OF
INTERFACE ROUGHNESS
d versus Roughness (Bosscher and Ortiz 1987)
Normalized Roughness (Kishida and Uesugi 1987)
Rmax ( L  D50 )
Rn 
D50
Correlation with Normalized Roughness (Kishida &Uesugi 1987)
Definition of modified roundness (Uesugi and Kishida 1986)
Modified roundness of a particle
1  r2  r4 r1  r3 

R  

2  l1
l2 
Correlation between m, Rn and R
(0.27)
(0.19)
(0.17)
Summary of some published interface friction tests
Author(s)
Type of testing apparatus
Results of investigation
Potyondy (1961)
Direct shear apparatus
with the sand on the top
of test material
d increases with density and
dlim=p
Broms (1963)
Direct shear mode by
sliding the material over
the sand
A d value of 23o was obtained
irrespective of sand density
Yoshimi and
Kishida (1981)
Ring shear with the test
material on top of sand
Density has no influence and
dlim=cv
Acar et al. (1982) Similar to Potyondy
d increases with density
Noorany (1985)
Similar to Broms
Influence of density is negligible
Uesugi et al.
(1990)
Simple shear with the
sand on top of the test
material
d increases with density dlim=p
Analysis of past studies
From the review the following three conclusions
can be drawn:
(1) d increases with surface roughness and
reaches a maximum limiting value
(2) For very rough surfaces, d tends to a limiting
maximum value which could be either the peak
angle of internal friction p or the critical state
friction angle cv.
(3) d can either increase or remain constant with
the increase in sand density.
Summary of some published interface friction tests
Author(s)
Type of testing apparatus
Results of investigation
Potyondy
(1961)
Direct shear apparatus
with the sand on the top
of test material
d increases with density
and dlim=p
Broms (1963)
Direct shear mode by
sliding the material over
the sand
A d value of 23o was
obtained irrespective of
sand density
Yoshimi and
Kishida (1981)
Ring shear with the test
material on top of sand
Density has no influence
and dlim=cv
Acar et al.
(1982)
Similar to Potyondy
d increases with density
Noorany
(1985)
Similar to Broms
Influence of density is
negligible
Uesugi et al.
(1990)
Simple shear with the
sand on top of the test
material
d increases with density
dlim=p
Schematic of Type A and Type B apparatus
Loading cap
SAND
Type A apparatus
Material
SAND
Type B apparatus
Features of Type A and Type B apparatus
Sl.No.
Features
Type A
Type B
Relative position of
Soild material is on the top of
The sand specimen is
solid material and sand
sand. The sand specimen is
on the top of solid
and sample
prepared
material surface. The
preparation.
surface
I Apparatus configuration
1
first
is
and
placed
the
solid
over
the
prepared leveled surface.
sand
is
prepared
directly on the solid
surface.
2
Application of normal
Normal stress is applied through
Normal stress is
stress to the interface.
the material to the interface.
applied through the
sand the interface.
3
Apparatus type in
Ring torsion apparatus, direct
Direct shear apparatus
literature
shear apparatus by sliding solid
by sliding soil over solid
material over sand.
material, simple shear
apparatus, translational
test box etc.
….. Features of Type A and Type B apparatus
Sl.No.
Features
Type A
Type B
II Influence of type of apparatus on the results obtained
4
Influence of
d increases with
d increases with
roughness
roughness
roughness.
d increases with
5
Influence of
Negligible.
density.
density of sand.
6
the increase of
Maximum limiting
The maximum limiting
The limiting
value of d
value for very rough
maximum value is
interface is critical state of the peak angle of
angle of internal friction of internal friction of
sand
sand.
Experiments in Direct shear
apparatus
Solid materials used
Material 1– Stainless steel
Material 2– Mild steel
Material 3– Mild steel
Material 4– Ferrocement
Material 5– Ferrocement
Surface profiles of the materials
Stainless steel
Mild steel
Mild steel
Concrete surface
Concrete surface
Grain size distribution curves of the sands used
Properties of sands used
Sand
No.
Gs
D50
1
2
3
4
5
6
7
2.64
2.64
2.64
2.64
2.65
2.64
2.65
Cu
mm
1.60
1.10
0.74
0.42
0.27
0.78
2.20
1.3
1.3
1.5
1.4
1.6
3.4
8.3
Note:
Gs
Specific gravity of soil grains
(d)max
Maximum dry density
(d)min
Minimum dry density
Dav
(d)max
(d)min
mm
kN/m3
kN/m3
1.53
1.01
0.69
0.41
0.27
1.10
1.92
15.9
16.0
16.1
16.0
16.2
18.0
18.6
13.0
12.9
13.1
13.0
13.0
14.0
14.5
Raining Technique--Calibration curves
Schematic of Type A apparatus
Type A apparatus
Schematic of Type B apparatus
Type B apparatus
Typical shear stress-movement curves
Sand 6, ’n = 140 kPa
150
150
Type A
Sand/Material 5
Type B
Sand/Material 4
Sand/Material 3
100
Shear stress, kPa
Shear stress, kPa
Sand/Material 2
Sand/Material 1
50
0
100
50
0
0
2
4
Shear movement, mm
6
0
2
4
Shear movement, mm
6
Shear stress, kPa
80
Sand 4
Material 5
60
40
n’ = 70 kPa
Type B (Plate below)
20
Type A (Plate above)
0
0
1
2
3
Shear movement, mm
0
1
4
Volume change, %
1.6
1.2
0.8
0.4
0
-0.4
2
3
-0.8
Shear movement, mm
4
Typical failure envelopes (Type B)
Peak
Critical state
(dpB/) versus Relative density (Type B)
Thandavamurthy (1990)
Variation of (dpB/) with Dav (Type B)
Proposed Roughness index
Relative Roughness (R)
Ra
R
Dav
Ra Average Roughness
Dav Average particle size
Variation of (dpB/) with R
Variation of dcvB with R
Comparison of dcvA with dcvB
Drained shear strength of finegrained soil-solid surface
interfaces
Clays are sheet like and
possess plasticity
characteristics
Grain size distribution curves of the soils used
Properties of cohesive soils used
Soil
Property
Red Earth
Kaolinite
Illite
Liquid limit (%)
33
55
131
Plastic Limit (%)
19
33
78
Plasticity index (%)
14
22
53
Sand (%)
44
0
0
Silt size (%)
47
80
36
Clay size (%)
9
20
64
88.4
12.0
8.5
1.09 x 10 -3
1.37 x 10 -2
4.59 x 10 -4
Atterberg Limits
Grain Size
Average particle size (mm)
Coefficient of consolidation, Cv (cm2/sec)
Variation of shear stress with deformation rate of illite
Deformation rates calculated and adopted for tests under drained condition
Deformation rate (mm/min.)
Soil
Calculated
Adopted
Red Earth
0.05
0.05
Kaolinite
0.63
0.25
Illite
0.02
0.05
Shear stress
OC
NC
nc
’
c’
p’c
Normal stress
Failure envelope of a soil at constant preconsolidation pressure
FAILURE ENVELOPE WITH CONSTANT OCR
Red earth
OCR=1
n’=100, 200 and 300 kPa
OCR=5
’p=500 kPa ’n = 100 kPa
’p=1000 kPa ’n = 200 kPa
’p=1500 kPa ’n = 300 kPa
Illite
OCR=10
’p= 500 kPa ’n = 50 kPa
’p=1000 kPa ’n = 100 kPa
’p=1500 kPa ’n = 150 kPa
Typical shear stress-movement curves
0
2
4
Shear movement, mm
6
8
Shear movement, mm
Typical failure envelopes
Normal stress
Normal stress
DB/F
DB o
Variation of D’B and (D’B/F’) with OCR
Variation of (DB/F) with Ra
Variation of (DB/F) with R
Comparison of D values from Type A and Type B
SUMMARY
 Interfacial friction depends on mode of shear
for sands and the maximum value of friction
angle is controlled by the type of apparatus
used to evaluate the friction angle
 For clays, mode of shear has no influence
Research Issues
 Modeling of interface behaviour : shear
stress-movement curves
 Roughness
 Hardness of solid material
 Rigidity of materials
 Mode of shear
 Particle size and shape
Acknowledgements
1. Prof. K. S. SUBBA RAO
Department of Civil Engineering
IISc, Bangalore
2. Prof. M. M. Allam
Department of Civil Engineering
IISc, Bangalore
CSIR for funding
Thank you