THREE DIMENSIONAL NUMERICAL SIMULATION OF RESIDENTIAL
BUILDINGS ON SHRINK-SWELL SOILS
This work is finished by Dr. Xiong Zhang under the supervision of Dr. J.L.
Briaud and R.L. Lytton.
Reference:
Zhang, X.(2004) Consolidation theories for saturated-unsaturated soils and numerical
simulations of residential buildings on shrink-swell soils. Ph.D. Dissertation,
Department of Civil Engineering, Texas A&M University, College Station, TX.
Shrink-swell soils can cause distress in buildings. Every year the economic loss
associated with this problem is very large. This research presents an integrated simulation
of the soil-foundation-building system and its response to daily weather condition. The
weather data includes rainfall, solar radiation, air temperature, relative humidity and wind
speed, all of which are readily available from local weather station or the internet. These
data are used to determine the flux boundary conditions for the simulation. Different
methods are proposed to simulate different boundary conditions such as bare soils, trees,
and vegetation. The coupled hydro-mechanical stress analysis is used to simulate the
coupled volume change (consolidation) of shrink-swell soils due to both mechanical
stress and water content variations. The coupled hydro-mechanical stress jointed
elements are used to simulate the soil-structure interaction between the soil and the slab.
The general shell elements are used to simulate the structure behavior. All these models
are combined together to solve the worldwide natural hazard. Some other techniques such
as the pseudo moisture variation simulation and the thermodynamic analogue are used to
make the simulation applicable. Theory regarding the proposed system is described first.
Two examples to illustrate the application of the proposed system are then presented.
Evaluation of Evapotranspiration
Two primary reasons make it extremely difficult to simulate the evaporation
process at the interface between the ground surface and the atmosphere: (1). Too many
influencing factors must be included in the process. The mechanical stress, pore water
pressure, pore air pressure, temperature and salt concentration must be used as stress state
variables which require five or more constitutive relations. More than 30 material
parameters are needed to handle the fully coupled problem. For example, the soil
deformation is influenced by the mechanical stress, pore water pressure, pore air
pressure, water vapor, and salt concentration. Similar considerations are needed for the
water, water vapor, air, heat and salt phases in the soils and many other phenomena such
as conduction, convection, radiation must be included. (2). the boundary conditions at the
soil-atmosphere interface are extremely difficult to determine.
By contrast, the soil at a certain depth is mainly influenced by the mechanical
stress and moisture (pore water pressure) variation whereas the other factors such as
temperature, salt concentration and pore air pressure usually remain constant and their
influences are negligible. Consequently, if the evapotranspiration process at the soilatmosphere interface can be determined, the soil behavior can be simulated by a coupled
hydro-mechanical stress analysis. The FAO 56 Penman –Montieth method is “well
established as the most accurate and robust method to estimate the reference ET, and the
past decade of research has solidified its status as the international standard (Allen et al.
1998).” The following information is required: location of the site, elevation, daily or
hourly weather data including solar radiation, relative humidity, air temperature and wind
speed. This information can be readily obtained from local weather stations or from the
internet. Figs.1a through 1d show mean daily air temperature, relative humidity, wind
speed, and rainfall over a two year period between August 1, 1999 and October 2001 at a
Date
(a)
10/01/01
08/01/01
06/01/01
04/01/01
02/01/01
12/01/00
10/01/00
08/01/00
06/01/00
04/01/00
02/01/00
12/01/99
10/01/99
100
90
80
70
60
50
40
30
20
10
0
08/01/99
Mean Daily Temperature (oF)
site at Arlington, Texas, respectively.
Date
(c)
02/01/01
04/01/01
06/01/01
08/01/01
10/01/01
02/01/01
04/01/01
06/01/01
08/01/01
10/01/01
08/01/00
06/01/00
04/01/00
02/01/00
12/01/99
10/01/99
08/01/99
Mean Daily Relative Humidity (%)
12/01/00
10
9
8
7
6
5
4
3
2
1
0
12/01/00
(b)
10/01/00
Date
10/01/00
08/01/00
06/01/00
04/01/00
02/01/00
12/01/99
10/01/99
08/01/99
Mean Daily Wind Speed (mm/s)
120
100
80
60
40
20
0
110
Rainfall and ET0 (mm/day)
90
70
Rainfall
50
30
10
-10
ET0
04/01/02
02/01/02
12/01/01
10/01/01
08/01/01
06/01/01
04/01/01
02/01/01
12/01/00
10/01/00
08/01/00
06/01/00
04/01/00
02/01/00
12/01/99
10/01/99
08/01/99
-30
(d)
Fig.1. Daily Weather Data Over Two Years At Arlington, TX. (a.) Mean Daily
Temperature; (b.) Mean Daily Relative Humidity. (c.) Mean Daily Wind Speed
The soil stratigraphy, the average soil properties and the parameters for each soil
layers at the site are shown on Fig.2. There are two soil layers, which are the dark gray
silty clay from 0-1.80m and the brown silty clay for the depth greater tan 1.8m. Four
footings called RF1, RF2, W1, and W2 were constructed at the site. A benchmark was
installed to a depth of 10m following the standard procedure for Class A Rod Marks. The
water level in the 7m deep standpipes varied between 4m and 4.8m below the ground
surface over a period of 2 years. The soil outside of the footings is covered by
Johnsongrass (Sorghum halepense), which is the most widely distributed naturalized
warm-season, perennial grass in North America. Starting on August 11, 1999, the vertical
movement of the footings with respect to the benchmark was recorded every month with
a digital level until November 2001.
Fig.2. Soil Stratigraphy at the Site
Ho et al. (1992) proposed a method to construct the constitutive surfaces. A similar
method has been proposed by Fredlund and Rahardjo (1993). These methods require a
converged void ratio at the nominal origin of the constitutive surfaces. The constitutive
surfaces obtained have constant material properties in some regions and are usually
discontinuous. Sometimes these methods are not applicable. Zhang (2004) modified the
above methods and overcame the drawbacks by using the same assumptions as Ho. et al
(1992) and Fredlund and Rahardjo (1993). Continuous constitutive surfaces can be
obtained. The minimum laboratory tests needed for constructing the constitutive surfaces
of unsaturated soils are: the swell test-consolidation test, the suction test (pressure plate
test and salt concentration test), the free shrink test and the specific gravity test.
(a)Void Ratio
(b) water Content
Fig.3. Void Ratio and Water Content Constitutive Surfaces of a Soil at Arlington,
Texas.
The proposed method was used to simulate the movement of the four footings and
the simulation results are shown in Fig.4 A simulation is performed for every day of the
two year period. The displacements at the four corners of the concrete footing were
averaged and compared with the measurements at the site. As can be seen in Fig.4, in the
first year from 08/01/1999 to7/11/2000, both the measured and predicted movements are
relatively small. The explanation can be found in Fig.1d. It is found that in the first year,
the rainfall and the potential evapotranspiration are evenly distributed. This lack of
fluctuation leads to very small movements of the four footings. There are dramatic
settlements of the four footings from 7/11/2000 to 10/14/2000 in the second year,
followed by dramatic heaves from 10/14/2000 to 05/12/2001. After that the footings
move back to their original positions. This can be explained by a long dry summer from
06/19/2000 to 10/13/2000 with no rainfall, followed by a rainy winter and spring from
0/13/2000 to 06/30/2001 (Fig.1d) followed by relatively mild
rainfall and
evapotranspiration. The simulation results matched the observations reasonably well in
both tendency and magnitude, reflecting that the proposed method is good enough for
practical applications.
10
0
-10
-20
-30
-40
RF1 Movements
RF2 Movements
W1 Movements
-50
-60
-70
-80
W2 Movements
07/21/01
05/22/01
03/23/01
01/22/01
11/23/00
09/24/00
07/26/00
05/27/00
03/28/00
01/28/00
11/29/99
09/30/99
Predicted movements
08/01/99
Movements (mm)
40
30
20
Fig. 4. Comparisons between the Observation and Simulation Results
SIMULATION OF RESIDENTIAL BUILDINGS ON SHRINK-SWELL SOILS
It is extremely difficult to perform an uncoupled analysis for unsaturated soils.
Moreover, when a structure is constructed on the saturated soils, the magnitude and
distribution of the contact pressure between the soil and the foundation depends on the
volume change of the soils and are usually unknown. Variations in the mechanical stress
in the soil due to the applied contact pressure are much more complicated. Consequently,
it is nearly impossible to estimate the excess pore water pressure and use the uncoupled
consolidation theory to analyze the soil behavior accurately, still not to say to correctly
simulate the soil-structure interaction. To simulate the soil behavior and the soil-structure
interaction realistically, a fully coupled consolidation theory must be used to simulate the
volume change of the soils.
A complete system is proposed to simulate the behavior of residential buildings
on shrink-swell soils, which overcomes many shortcomings in the existing research.
Daily weather data such as air temperature, solar radiation, relative humidity, wind speed
and rainfall, which are readily available from local weather station or internet, are used to
determine the boundary conditions for bare soils, vegetations and trees in combination
with the FAO 56 PM method, which is a well established method in the agriculture
engineering. The fully coupled hydro-mechanical stress analysis is used to simulate the
volume change for shrink-swell soils. The coupled hydro-mechanical stress jointed
elements are used to simulate the soil-structure interaction at the soil-slab interface, and
the general shell elements are used to simulate the behavior of slabs and walls. Some
special techniques such as the thermodynamic analogue and the pseudo moisture
variation simulation are used to implement the proposed system. All the models and
techniques are integrated in a single system to simulate the influence of the weather on
the soil, foundation and superstructure, which makes a more realistic simulation possible.
Fig.5 shows a virtual residential building used in a simulation. Fig.6 shows the plane
view of the simulated domain. Figs.7 through 13 show some of the simulation results.
Figure 5. Residence Used in the Simulation
(Note: The roof is not included in this simulation to show the stress in the slab)
Figure 6. Floor Plan of the Residence
Figure 7. Deformations of the Ground Soils and the Building
Figure 8. Matric Suction Distribution in the Ground Soils
Figure 9. Separation between the Slab and the Ground Soils
Figure 10. Von Mises Stresses in the Structure
Figure 11. Shear Force between the Slab and the Ground Soils along X Direction
Figure 12. Relative Slip between the Slab and the Ground Soils along X Direction
Figure 13. Maximum & Minimum Moments in the Slab Over Two Years