1070
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
2 BACKGROUND
2.1 The constitutive relationship for estimating the vertical
movements of expansive soils
The volume change behavior of any expansive soil deposit
relative to the changes in site conditions can be rationally
interpreted by extending continuum mechanics principles in
terms of two independent stress state variables of unsaturated
soils; namely, matric suction (u
a
–
u
w
), and net normal stress
(σ –
u
a
) (where, u
a
= the pore-air pressure, u
w
= the pore-
water pressure, and σ
= the total stress). Water movement into
/ out of an unsaturated expansive soil leads to a change in
suction and contributes to soil volume change predominantly in
the vertical direction (i.e., the soil lateral deformations are
negligible). In other words, the K
0
-loading was assumed in the
present study. In the MEBM, the incremental vertical
movement, dh, was related to changes in matric suction
neglecting the limited influence of the net normal stress within
the surficial active zone as follows:
s
2 a
w
dh m d(u u )
(1)
where,
s
2
m (1 ) / (H( 1))
= the soil
structure
compressibility modulus associated with a change in suction
(u
a
˗ u
w
) (where H = elasticity modulus with respect to
change in suction
and μ =
P
oisson’s ratio
).
To calculate the vertical soil movement for a given site, the
soil within the active zone was divided into n layers. The
vertical movement for each layer,
Δ
h
i
, was computed by
multiplying the incremental vertical movement at the mid-layer
(Equation 1) and the layer thickness, h
i
. The total vertical
movement for the soil profile,
Δ
h, was then calculated by
adding the vertical movement of all layers within the active
zone.
n
n
s
i
i
2 a w i
i 1
i 1
h
h
h m d(u u )
(2)
Oh et al. 2009 studies show that the value of the modulus
of elasticity with respect to change in net normal stress, E,
varies significantly with soil suction. In the proposed
MEBM, the semi-empirical model introduced by Vanapalli
and Oh (2010) was used to estimate the modulus of
elasticity, E, associated with any value of the soil suction.
a
w
unsat
sat
a
(u u )
E E 1
(S)
(P 101.3)
(3)
where E
unsat
and E
sat
= the soil moduli of elasticity under
unsaturated and saturated conditions, respectively, P
a
=
atmospheric pressure (i.e., 101.3 kPa), S = degree of
saturation, and
and
= the fitting parameters.
To calculate the soil structure compressibility
modulus,
s
2
m
, the modulus of elasticity with respect to
change in suction, H, was estimated using the relationship
below:
H E / 1 2
(4)
The relationship between H and E may be more complex
for soils in a state of unsaturated condition; however, this
relationship which is valid for saturated soils has been
extended for unsaturated soils in the present study. Similar
assumptions were suggested by Geo-Slope International Ltd. for
modeling soil heave due to infiltration using SIGMA/W.
2.2 VADOSE/W for estimating the changes in soil suction
Estimation of soil suction changes due to soil water migration
(infiltration/evaporation) in the active zone is important in
predicting the vertical movement of expansive soils. The
computer program VADOSE/W, a product of Geo-studio, was
used as a tool to estimate the net changes in soil suction with
respect to time and depth (Geo-Slope 2007). The program
couples the flow of water, heat and vapor through both saturated
and unsaturated soils
to provide a direct evaluation of
soil water
storage and suction
.
Critical to the formulation of VADOSE/W
is its ability to predict actual evaporation as a function of
climate data, applied as an upper boundary condition, using the
rigorous Penman-Wilson method (Wilson, 1990).
The input parameters required for VADOSE/W include soil
properties such as the SWCC and the coefficient of permeability
function, climate and vegetation data. The climate data include
the daily precipitation, the maximum and minimum daily
temperature, the maximum and minimum daily relative
humidity, the average daily wind speed and net radiation. The
vegetation data include the leaf area index (LAI), the plant
moisture limiting point, the root depth and the length of the
growing season.
The output from VADOSE/W includes modeled data such as
temperature, evaporation, suction, and volumetric water content.
In the present study, only the modeling results for soil suctions
versus time are presented and compared with the published data
of Ito and Hu (2011).
3 CASE STUDY: REGINA EXPANSIVE CLAY (ITO AND
HU 2011)
The city of Regina, SK, Canada is located on highly expansive
clay deposits that exhibit large volume changes as the soil
moisture changes. Failures in light infrastructures buried in the
soil have increased greatly in recent years, especially in older
areas with asbestos cement (AC) water mains (Hu et al. 2008).
As a part of a program of study the performance of AC water
mains in Regina expansive clay, Ito and Hu (2011) modeled a
site located in a residential area with a high water main
breakage rate. It includes a park area with thick grass of 100
mm and a wide paved road with 150 mm thick asphalt
pavement. Infiltration due to precipitation and park watering
and evapotranspiration from the grass were considered to model
the soil suction fluctuations for this site.
The results from the Regina test site were used to validate
the proposed MEBM in estimating the vertical soil movements
over time considering the field condition (vegetated park area
and asphalt-paved area). The stratigraphy of the site consists of
approximately 6.4 m of highly plastic clay, 1.8 m of elastic silt
and 6.8 m of till as shown in Figure 1. The choice of thickness
and soil properties for each layer was guided by field
observations made by Vu et al. (2007). The climate data
obtained from a weather station at the Regina international
airport was applied at the vegetative cover over a period of one
year (from 1 May, 2009 to 30 April, 2010). Figures 2 and 3
show the SWCCs and the coefficient of permeability functions,
respectively, for Regina and other materials used in the
numerical modelling. Ito and Hu (2011) provide more details
about the soil, the climate, and the vegetation data of the site.
4 RESULTS AND DISCUSSIONS
4.1 Estimation of the soil suctions
The soil profile shown in Figure 1 was modeled using the
fully coupled transient analysis with the 2-D software
package (VADOSE/W) to estimate the suction changes
associated with the environmental changes for a period of
one year. Beside the soil properties, the initial and boundary
conditions are needed as input data to run the program.
The
initial conditions for all nodes of the model domain, including
pressure and temperature, were derived from implementing a
steady-state analysis using the same model.
Based on the field
suction data measured by Vu et al. (2007),
the
initial
pressure head
during the steady-state analysis
was set up to be
-163.15 m for the top 3 m of the clay layer, -101.97 m for
the rest of the clay, -61.18 m for the silt, and -203.94 m for
the till. T
he temperatures of nodes at the lower boundary were
set up to be 10
o
C
.
Figure 1. Soil profile and soil properties (Ito and Hu 2011)
