Simple Techniques for Estimating
the Shear Strength and the Coefficient of Permeability
of Unsaturated Soils
By
Sai K. Vanapalli
Lakehead University, Thunder Bay
Canada
Unsaturated Soil Engineering: Applications in Pavements
Maplewood, Minnesota: 5th August, 2002
Today’s Presentation
Establish: Need for unsaturated soil mechanics
in pavement designs
Theory: Simple extensions of classical soil
mechanics
Simple Techniques/Procedures for Interpreting
the Engineering Behavior of Unsaturated Soils:
Using conventional soil mechanics lab facilities
Pavement Design Procedures
●
Present /conventional procedures: Experience and
and Empirical procedures
●
Rational procedure: Take into account of the influence
of wet-dry and freeze-thaw cycles (Use principles of
unsaturated soil mechanics)
●
Rational Approach: Use stress state variable approach
(Two stress state variables: Net normal stress, (σ – ua)
and matric suction, (ua – uw))
●
Key engineering properties: Shear strength and the
Coefficient of permeability
Unsaturated Soils Testing
Shear Strength of
Unsaturated Soils
Coefficient of Permeability
of Unsaturated Soils
Unsaturated Soils Testing
Need extensive laboratory facilities
Time consuming and expensive
Need simple techniques: for practical applications
such as the design of pavements
Focus: Estimating the shear strength and the
coefficient of permeability of unsaturated soils
Key information: Soil-Water Characteristic Curve
(SWCC)
Soil-Water Characteristic Curve (SWCC)
A useful tool in the interpretation of USM
100
Residual
air content
80
Degree of
saturation
(%)
Desaturation
zone
Wetting curve (Adsorption)
60
Drying curve (Desorption)
Capillary
saturation
zone
20
Residual conditions
Air entry
value
0
1
10
100
1000
10000
Soil suction (kPa)
100000
1000000
Measurement of the SWCC
Tempe Cell/ Pressure plate
(liquid phase flow)
Osmotic Desiccators
(Vapor phase flow)
Small - Scale
Beckman
Centrifuge
J6 – HC
(Simple and fast technique
for SWCC measurement)
Saturated Soil Specimens and
Saturated Ceramic Cylinders in the
Specimen Holders
Soil Specimen Holders
Ready to Centrifuge
Gravimetric water
content, %
Indian Head Till Test Results
24
16
Centrifuge curve
Tempe cell curve
8
0
1
10
100
Matric suction (kPa)
Centrifuge test, ρd = 1.77 Mg/m3, w = 19.2%
Tempe cell test, ρd = 1.77 Mg/m3, w = 19%
1000
Time Required to Obtain a SWCC
Test method
used
Silt
Indian Head Till
Regina Clay
Centrifuge
time (days)
0.5
1
2
Tempe cell
time (days)
14
42
112
Pore Water Distribution
Shear strength and Volume Change: Related to the interphase contact
area controlling stress transfer
Coefficient of permeability : Related to the continuity and tortuosity of
liquid phase
S = 100
1 > S > Sr
S = Sr
Shear Strength of
Unsaturated Soils
Relationship Between SWCC and
Shear Strength versus Matric Suction
Commencement of
desaturation
Water
content
w (%)
Clayey silt
Sand
Matric suction (kPa)
φ′ clayey silt
Shear
strength
τ c′
φ′ sand
Matric suction (kPa)
Unsaturated Soils Shear Strength
Prediction (Vanapalli et al. 1996)
κ
τ = c ′ + (σn − ua) tanφ′ + [Θ (ψ)] (u a− u w )tanφ ′
where: Θ(ψ) = θ(ψ)/θs
θ(ψ) = volumetric water content at any suction
κ= fitting parameter to account for non-linearity
between area and volume representation of the
amount of water contributing to the
shear strength
Comparison between Predicted and
Measured Shear Strengths
Shear Strength, kPa
(Vanapalli and Fredlund, 2000)
1000
750
500
250
Red silty clay
(σ - ua) = 120 kPa
0
0
2500
5000
7500
10000
Soil Suction, kPa
12500
15000
Relationship between κ vs Ip
(Vanapalli and Fredlund, 2000)
Fitting
parameter, κ
4
3
2
1
0
0
10
20
Plasticity Index, Ip
30
40
• Useful relationship to estimate the fitting parameter
value, κ
Degree of Saturation, S,
(%)
Pre-shear and Post-shear SWCC data from
the Triaxial Shear Test Results on Dhanauri
clay specimens (derived from Satija 1978)
100
Post-Shear SWCC
80
60
Pre-Shear SWCC
40
1
10
100
1000
Matric suction, (ua -uw), kPa
10000
Shear Strength due to Suction,
kPa
Measured and Predicted Shear Strength of
Dhanauri clay for Low Suction Range (Using
Pre and Post-shear SWCC)
200
Predicted from pre-shear SWCC
100
Predicted from post-shear SWCC
0
0
100
200
300
Matric Suction (ua-uw), kPa
400
500
Shear Strength due to Suction,
kPa
Measured and Predicted Shear Strength
of Dhanauri clay for High Suction Range
(Using Pre and Post-shear SWCC)
400
Predicted from pre-shear SWCC
200
Predicted from post-shear SWCC
0
0
500
1000
Matric suction (ua - uw), kPa
1500
Simple Test Procedures
Conventional test procedures: Unconfined
compression test and Direct shear tests
Estimate of soil suction from simple tests?
Based on indirection estimation:
– Determine the degree of saturation (from
volume-mass properties)
– Use SWCC information and estimate suction
for corresponding degree of saturation
Degree of Saturation, S (%)
Estimation of Suction from the SWCC
100
80
60
40
20
0
0.01
1
100
Suction, Ψ (kPa)
10000
1000000
Shear Strength Interpretation from
Unconfined Compression Test Results
rd
(53 Canadian Geotech Conf: Vanapalli et al. 2000)
Specimen preparation for a
silt specimen (Ip = 8)
– statically compacted
saturated specimens
prepared using
constant volume molds
– air dried for varying
time intervals so that
fully saturated to fully
dry samples would be
tested
– suctions estimated
from SWCC
Unconfined Compression Test
Testing
– Quickly loaded at a
strain rate of approx.
1.2 mm/min
– stress readings taken
at every 0.2 mm
interval travel
Assumptions
– Suction in the
specimen does not
change during
loading
– Interpretation based
on initial suction
values in the
specimens
Predicted and Measured Unconfined
Compressive Strengths (Silt)
Unconfined
compressive strength, kPa
10000
*Symbols are experimental
results
1000
100
Shear strength prediction
using fitting parameter, κ =
1.8
10
1
0.1
1
10
100
1000
Soil suction, kPa
10000
100000
Determination of Shear Strength of
Compacted Till Using Conventional
Direct Shear Apparatus (Vanapalli & Lane
2002)
Shear strength of Indian
Head till
– Three different compaction
water contents
– Provide comparisons
between CDST and MDST
Assumption
– Suction in the specimen
does not change during
loading
Compacted Soil Specimen Extraction
from Constant Volume Mould
Soil Specimen Saturation Procedure
Soil Specimen & Cutter
Comparison between Shear Strength Test Results
Using MDST and CDST (Vanapalli & Lane 2002)
Shear Strength Contribution due
to Suction (kPa)
150
125
100
Modified Direct Shear Test
Results Best-Fit Curve
75
50
25
0
0
100
200
300
Matric Suction (kPa)
400
500
Coefficient of Permeability of
Unsaturated Soils
Relationship Between the
SWCC and Coefficient of Permeability
Clayey silt
50
40
Water
content 30
w (%) 20
Sand
10
0
1
10
Sand
10-5
100
1000
Matric suction (kPa)
10-6
Coefficient of
permeability 10-7
kw (m/s)
Clayey silt
10-8
Permeability functions
10-9
10-10
1
10
100
1000
Matric suction (kPa)
Predicting the Unsaturated
Coefficient of Permeability of Soils
Several procedures available in the literature
Key information: SWCC and ksat
Several parameters influence the SWCC and the kunsat :
- applied stress
- compaction energy
- soil structure (function of initial
compaction water content) (important
particularly in fine-grained soils)
Normalization Technique for
Estimating the Coefficient of
Permeability of Unsaturated Soils
Time consuming and expensive to measure
SWCC taking into account the influence of
parameters such as the stress state and soil
structure
Useful to the practicing engineers if a simple
technique can be proposed.
Relative or the normalized coefficient of
permeability, krel = kunsat/ksat
Comparison of krel and S for a Typical
Sand and Clay Loam
1.E+00
Experimental
data points
1.E-01
Sand
Clay Loam
1.E-02
k rel
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.0
Degree of Saturation
0.1
krel versus S Using
Different γ Values
1.E+00
1.E-01
Sand
γ = 0.70
krel
1.E-02
Clay Loam
γ = 1.40
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.0
γ
(Degree of Saturation)
0.1
• Unique trend line for both the soils: Sand and Clay Loam through
the use of different fitting parameter, γ values
krel versus Sγ for Columbia Sandy Loam
1.E+00
Columbia Sandy Loam
1.E-01
Brooks & Corey, 1964
Ip = 5%
krel
1.E-02
Predicted
Experimental
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.0
0.1
γ
(Degree of Saturation)
krel versus Sγ for Touchet Silt Loam
1.E+00
Touchet Silt Loam
1.E-01
1.E-02
k re l
Predicted
Brooks & Corey, 1964
Ip = 6%*
Experimental
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.0
γ
(Degree of Saturation)
0.1
krel versus Sγ for Yolo Light Clay
1.E+00
Yolo Light Clay
1.E-01
Predicted
Moore, 1939
Experimental
k re l
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.0
0.1
γ
(Degree of Saturation)
Influence of Stress State on the
krel versus Sγ Relationship (Silt)
1.0E+00
Silt
1.0E-01
Huang, 1994
Ip = 5.6%
0 kPa
25 kPa
1.0E-02
krel
50 kPa
1.0E-03
100 kPa
200 kPa
1.0E-04
1.0E-05
1.0E-06
1.0E-07
1.0
γ
(Degree of Saturation)
0.1
krel versus Sγ for soils (Using Brooks &
Corey 1964 Results)
Relative Permeability, krel
1.E+00
Touchet Silt Loam (0.85)
Fragmented Mixture (0.75)
1.E-01
Volcanic Sand (0.70)
Fine Sand (0.60)
1.E-02
Normalizing Function
1.E-03
1.E-04
1.E-05
1.0
0.1
Adjusted Degree of Saturation, Sγ
krel versus Sγ wetting & drying for
London Clay (Croney & Coleman,
1954)
1.E+00
Relative Permeability, k
r el
Drying (1.55)
1.E-01
Wetting (1.90)
1.E-02
Normalizing
Function
1.E-03
1.E-04
1.E-05
1.0
0.1
Adjusted Degree of Saturation, Sγ
krel
The Relationship Between the krel versus Sγ
1.E+00
1.E-01
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.0
k rel ≈ S
7 . 9γ
(Degree of Saturation)
where:
krel = kunsat/ksat
γ
0.1
Relationship between Fitting
Parameter γ and Plasticity Index, Ip
F itti n g P a ra m e te r, γ
6.00
5.00
4.00
3.00
2.00
1.00
0.00
0%
10%
20%
30%
Plasticity Index, Ip (%)
40%
50%
60%
Estimation of Unsaturated
Coefficient of Permeability
•
The coefficient of permeability can be estimated using
the simple function.
k rel ≈ S
7 . 9γ
•
Required information: Saturated coefficient of
permeability, ksat, Water content, w or the degree of
saturation, S, and and the plasticity index, Ip.
•
More studies are in progress to test the validity and the
limitations of the proposed simple function.
Summary
•
SWCC can be used as a tool to propose simple
estimation techniques for interpreting the engineering
behavior of unsaturated soils.
•
SWCC can be measured using centrifuge techniques
reliably in a relatively shorter period of time compared to
conventional procedures.
•
The engineering properties of unsaturated of soils can be
estimated using simple techniques with the aid of
conventional experimental results.
•
These studies are useful to extend the principles of
unsaturated soils into engineering practice such as the
design of pavements
Thank you,
☺
Sai Vanapalli
August 5, 2002