1. Predicting Unsaturated Shear Strength of
Residual Soil Based on Basic Soil
Properties
TRB 95th Annual Meeting
January 12th 2016
Chien-Ting Tang, PhD candidate, North Carolina State University
Roy Borden, Professor, North Carolina State University
Mo Gabr, Professor, North Carolina State University

2. Organization
• Introduction
• Background
• Experimental program
• Experimental data
• The proposed empirical model
• Summary and conclusion
1

3. Introduction
• The increase of shear strength in unsaturated
soil provides advantages in geotechnical design.
• The concept of unsaturated shear strength has
been studied for years, but not widely applied.
• A number of prediction models have been
developed, but do not give good predictions for
soils with various properties.
2

4. Test Site in Greensboro, NC
3

5. Organization
• Introduction
• Background
• Experimental program
• Experimental data
• The proposed empirical model
• Summary and conclusion
4

6. Soil Water Retention Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1 1 10 100 1000 10000
Volumericwatercontent
Matric suction (kpa) (Vanapalli, et al., 1996) 5

7. (Fredlund, et al., 1987)
6

8. 7
Author Predicting formula Parameters
Fredlund, et
al. (1996)
Vanapalli, et
al. (1996)
Khalili and
Khabbaz
(1998 )
Houston, et
al. (2008)
Grain size
distribution:
Diameter of 30 %, 60
% and percentage of
sand
+1
= Plasticity Index
= Volumetric
water content
= Saturated
= Residual
= Normalized θ

9. Organization
• Introduction
• Background
• Experimental program
• Experimental data
• The proposed empirical model
• Summary and conclusion
8

10. 9

11. Picture of the Test System
Pressure panel
(Confining pressure)
Air regulator
(pore air pressure)
Water pumps
(pore water pressure)
10

12. Organization
• Introduction
• Background
• Experimental program
• Experimental data
• The proposed empirical model
• Summary and conclusion
11

13. Soil Properties of the Four Test Soils
Symbol
SoilType
(AASHTO)
SoilType
(USCS)
Depth
(ft)
Gs
LL
(%)
PI
(%)
<#200
(%)
Clay
(%)
Silt
(%)
Sand
(%)
φ'
(deg)
c'
(psi)
G1 A-7-5 MH 5- 12 1.11 2.76 61 22 88 15 73 12 27 1.9
G2 A-4 ML 24-50 1.61 2.70 40 6 60 4 56 45 30 2.8
G3 A-4 ML 13-27 1.65 2.73 45 10 84 6 78 16 28 2.5
G4 A-2-6 SC 2- 7 1.75 2.68 34 11 32 10 22 68 36 0
(g/ )
12

14. Soil Water Rentention Curves
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1 1 10 100 1000 10000
Volumetricwatercontent,θ
Matric suction, ψ (kPa)
G1 (A-7-5)
G2 (A-4)
G3 (A-4)
G4 (A-2-6)
13

15. Applied Models
14
Number Author Predicting formula Parameters
Method
1
Method
2
Method
3
Vanapalli, et
al. (1996)
Method
4
Houston, et
al. (2008)
Grain size
distribution:
Diameter of 30 %, 60
% and percentage of
sand
Fredlund, et
al. (1996)
+1
= Plasticity Index
= Volumetric
water content
= Saturated
= Residual
= Normalized θ
: best fit from test data
= Normalized θ

16. G1 soil , A-7-5, MH
0
3
6
9
12
0 3 6 9 12 15 18 21
Totalcohesion(psi)
Matric suction (psi)
Test Data
Method 1
Method 2
Method 3
Method 4
Location 404 + 50, 3LT
Number ST-49A
Depth 7.5-9.5
Specific Gravity 2.77
% of Clay 31
% of Silt 49
% of Fine Sand 17
% of Coarse Sand 3
Passing #200 85
Passing #40 99
Passing #10 100
Liquid Limit 61
Plastic index 22
AASHTO Classification A-7-5
Water content 33.5%
Degree of saturation 65.8%
Matric suction 10.8 psi
Position of
the soil
speciman
Soil
properties
and
classifiction
Initial
measured
parameters
15

17. G2 soil, A-4, ML
0
3
6
9
12
0 3 6 9 12 15 18 21
Totalcohesion(psi)
Matric suction (psi)
Test Data
Method 1
Method 2
Method 3
Method 4
Location 404 + 50, 86RT
Number ST-87-a
Depth 37.5-39.5 ft
Specific Gravity 2.68
% of Clay 9
% of Silt 44
% of Fine Sand 18
% of Coarse Sand 29
Passing #200 57
Passing #40 78
Passing #10 99
Liquid Limit 38
Plastic index 6
AASHTO Classification A-4
Water content 27.9%
Degree of saturation -
Matric suction 3.5 psi
16

18. G3 soil, A-4, ML
0
3
6
9
12
0 3 6 9 12 15 18 21
Totalcohesion(psi)
Matric suction (psi)
Test Data
Method 1
Method 2
Method 3
Method 4
Location 403 + 45, 3LT
Number ST-64A
Depth 25.2-27.1
Specific Gravity 2.74
% of Clay 10
% of Silt 65
% of Fine Sand 23
% of Coarse Sand 2
Passing #200 85
Passing #40 99
Passing #10 100
Liquid Limit 45
Plastic index 12
AASHTO Classification A-7-5
Water content 21.0%
Degree of saturation 97.7%
Matric suction 5.1
17

19. G4 soil, A-2-6, SC
0
3
6
9
12
0 3 6 9 12 15 18 21
Totalcohesion(psi)
Matric suction (psi)
Test Data
Method 1
Method 2
Method 3
Method 4
Location 403 + 45, 3LT
Number ST-59B
Depth 2.1-4.1
Specific Gravity 2.7
% of Clay 10
% of Silt 17
% of Fine Sand 18
% of Coarse Sand 55
Passing #200 92
Passing #40 56
Passing #10 31
Liquid Limit 37
Plastic index 13
AASHTO Classification
Water content 12.6%
Degree of saturation 72.0%
Matric suction 11 psi
18

20. Organization
• Introduction
• Background
• Experimental program
• Experimental data
• The proposed empirical model
• Summary and conclusion
19

21. Data Sets for Model Development
φ' c' Fines LL PI
USCS ASSHTO (deg)(psi) (%) (%) (%)
G1 in this research Residual soil in NC MH A-7-5 27 1.9 0.16 88 58 22 2.37 1.08
G2 in this research Residual soil in NC ML A-4 30 2.8 0.05 60 34 6 1.53 0.25
G3 in this research Residual soil in NC ML A-4 28 2.5 0.08 84 45 10 1.82 0.80
G4 in this research Residual soil in NC SC A-2-6 36 0 0.09 32 34 11 1.88 0.77
Miao, et al., 2002 Nanyang soil MH A-7-5 21 6.1 0.09 93 58 32 2.48 1.41
Lee, et al., 2004 Weathered granite SM A-2-4 42 2.8 n/a 12 1.00 1.40
Rahardgo, et al., 2004 Jurong sedimentary CL A-6 32 0.0 0.06 66 36 15 2.09 0.61
Kayadelen, et al., 2007 Residual clay MH A-7-5 22 3.6 0.05 95 77 32 2.48 1.85
Burrage et al., 2012 Residual soil ML A-4 32 2.3 n/a 71 38 3 1.28 0.42
Schnellmann, et al., 2013 Coasrse sand SM-SW A-2-4 33.6 0 0.08 11 1.00 1.34
= the value calculated fromEquation 3
= the value by best-fit analysis on measured data
NP
NP
Reference Soilname
SoilClassification
𝜅 𝑃 𝑃
20

22. An Empirical Expression for Predicting κ
• 𝜏 ′
𝜎 𝜑′
[ 𝛩 𝜅 𝜑′]
• Regression analysis to search
for variables to predict κ from
best-fit value
• 3 ∙
%𝑓𝑖𝑛𝑒
00%
8 ∙ 𝑃 33 ∙
−𝑃𝐼
−𝐿𝐿 0
1
2
3
0 1 2 3
κfrombest-fitonmeasureddata
κ from prediction equations
κ in literature
(Equation 3)
Proposed κ
(Equation 7)
21
(Method 2)
(Eq on the left)

23. Quality of the Modified Model
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14
Predictedcohesionduetomatric
suction(psi)
Measured cohesion due to matric suction (psi)
G1 (A-7-5)
G2 (A-4)
G3 (A-4)
G4 (A-2-6)
Miao, et al. (2002)
Kayadelen, et al. (2007)
Burrage, et al. (2012)
Rahardjo, et al.(2004)
Lee, et al. (2005)
Schnellmann, et al. (2013)
22

24. Organization
• Introduction
• Background
• Experimental program
• Experimental data
• The proposed empirical model
• Summary and conclusion
23

25. • The modified triaxial test device is able to
measure the increase of shear strength as a
function of matric suction.
• Different types of soil have different increases of
shear strength due to matric suction.
• The proposed empirical equation shows the
ability to estimate unsaturated shear strength
based on basic soil properties.
24

26. Thank you