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Design Of Stiffened Slabs-On-Grade On Shrink-Swell Soils 
 
C. Magbo- Graduate Assistant Research, Texas A&M University, College Station, Texas 77843-
3136, USA. Email: charlesmagbo@gmail.com 
 
R. Abdelmalak- Geotechnical & Heavy Civil Engineering Department, Dar Al-Handasah., 2 Lebnan 
St. Mohandessin, Giza, Cairo, Egypt. Email: remonisaac@gmail.com 
 
 SUMMARY: 
 
Stiffened slabs-on-grade are one of the most 
efficient and inexpensive foundation solutions 
for light structures on shrink-swell soils. This 
paper presents a simple design procedure and 
associated for calculating the depth of the 
beams required to limit the differential 
movement of the foundation due to bending to 
an acceptable amount. This bending of the 
foundation is due to the shrinking and 
swelling of the soil during the dry and wet 
seasons under the edges of the structure. The 
procedure consists of determining the 
unsaturated soil diffusivity in the field from 
the free shrink test, simulating the effect of the 
weather on the soil, parameters obtained from 
the soil-weather simulation model like the 
change in suction or the change in water 
content and the anticipate depth of influence 
are used in conjunction with the unsaturated 
diffusivity to determine the mound shape 
developed using the modified Peter Mitchel’s 
moisture diffusion theory. The final step 
involves performing the soil-structure 
interaction using ABAQUS STANDARD to 
determine the moment, shear and deflection 
profile which are used to develop design 
charts. These charts are subsequently used to 
select the beam depth, width and spacing 
required to adequately resist foundation 
movements due to the shrinking and swelling 
of the soil for a given weather and soil 
properties. If the distortion is too large for 
the type of structure considered, the beam 
depth is increased until the acceptable value is 
reached. 
 
 
 
 
 
1 INTRODUTION 
 
Stiffened slabs-on-grade are one of the most 
efficient and inexpensive foundation solution 
for light structures on shrink-swell soils. After 
removing the top soil, the stiffening reinforced 
concrete beams, say 1m deep and 0.3 m wide, 
are formed in the natural soil and placed every 
3 m in both directions. The slab is typically 0.1 
m thick. Such stiffened slabs are often called 
waffle slabs because of the geometric analogy 
with a waffle. They are commonly used in 
the USA for the foundation of houses or any 
light weight structure on shrink-swell soils and 
cost about 100$/m2 (2010). This paper presents 
a simple design procedure, associated charts 
and spread sheets for calculating the depth of 
the beams required to limit the differential 
movement of the foundation due to bending to 
an acceptable amount. Some of the other 
foundation solutions used for buildings on 
shrink-swell soils are thin post tension slab on 
grade, slab on grade and on piles, and elevated 
structural slab. The thin post tension slab on 
grade (say 0.1 m thick) is a very good solution 
for flat surfaces which are not carrying any 
structures such as tennis courts. The thin post 
tension slab on grade is not a good solution for 
the foundation of light and relatively rigid 
structures because, while post tensioning 
increases the maximum bending moment that 
the slab can resist compared to the same 
reinforced concrete slab and provides a minor 
improvement in stiffness, it is generally too 
flexible and leads to differential movements of 
the foundation incompatible with what a rigid 
structure can tolerate. This can lead to cracking 
in the walls of the structure. Of course, thick 
post-tensioned slabs can work well and post 
tensioning a reinforced concrete stiffened slab 
on grade increases the maximum bending 
moment that the slab can resist. The benefit 
associated with the added cost of post-
tensioning a reinforced concrete stiffened slab 
is not clear. The slab on grade and on piles is 
not a good solution either as it anchors the 
slab on grade while the soil may want to 
swell. In this case the soil pushes up on the slab 
and the piles hold it down at the connections 
between the pile and the slab. Under these 
conditions, the slab is likely to break if 
swelling is excessive. If the soil shrinks a gap 
can appear below the slab on grade which loses 
its support. Since such slabs are not designed 
to take the load in free span they can fail 
under these conditions as well. The elevated 
structural slab on piles is a very good solution 
but can be expensive (about 200$/m2 in 2010), 
and represents an unnecessary expense for 
light structures. It is the solution of choice for 
more expensive structures. In the case of the 
elevated structural slab on piles, the soil can 
move up and down without impacting the 
structure since a gap of sufficient magnitude 
(sometimes 0.3 m or more) exists under the 
beams and the slab. The load is taken up by the 
piles which must be designed for the tension 
generated by the swelling of the soil which is 
typically more severe than the shrinking design 
case. Of course no matter how well designed 
and constructed the foundation is for light 
structures on shrink-swell soils, some poor 
practices by the owner can be very detrimental 
to the structure including trees too close to the 
structure and poor drainage. Proper owner 
maintenance is important and requires some 
education of the owner. 
 
 
 
 
2 DEVELOPMENT OF THE DESIGN 
APPROACH 
 
The primary design issues for stiffened slabs on 
grade are the sizing of the beams that stiffened 
the slab and the spacing of the beams. The 
beams are typically from 0.6 to 1.2 m deep, 0.15 
to 0.3 m wide, and the spacing varies from 3 to 
6 m. The slab itself is usually set at a thickness 
of 0.1 m. Any quality design for such a 
foundation must include the parameters related 
to the soil, the weather, the foundation, and the 
super-structure. The goal of such a design is to 
ensure that the stiffness of the foundation is such 
that the movements due to swelling and 
shrinking of the soil under a given weather 
condition do not distort the super-structure 
excessively. The development of the design 
approach to size the beams and their spacing 
consisted of a number of research tasks which 
took place over the last 10 years. These tasks 
were. 
 Task 1: This consisted of performing 
numerical simulations to develop the percent 
diffusion vs. time factor curves for the free 
shrink test much like the percent consolidation 
vs. time factor curves for the consolidation 
theory. These curves were used in conjunction 
with the free shrink test to obtain the coefficient 
of unsaturated diffusivity of the intact soil. 
Then other numerical simulations were used 
to develop a correction factor for including 
the influence of cracks on the intact value of 
the diffusion coefficient. 
Task 2: This consisted of using an advanced 
form of Mitchell’s theory (1979) to develop a 
more realistic solution for the equation 
describing the shape of the mound created when 
a flexible membrane covers partially a 
shrinking or swelling soil. 
 Task 3: This required special numerical 
simulations using the FAO 56-PM method with 
weather input and soil input to obtain the 
maximum change in suction for several cities in 
the USA. These cities were selected because 
they have the most significant problems with 
shrink swell soils: San Antonio, Austin, Dallas, 
Houston, and Denver. College Station was 
added because it is the home of Texas A&M 
University. The weather input over the 20 year 
period considered included the rain fall, the air 
temperature, the wind speed, the relative 
humidity, and the solar radiation. An average 
vegetation cover was selected and the soil 
diffusion was varied over a reasonable rangeTask 4: This consisted of running 
simulations with the foundation on top of the 
deformed mound. The maximum bending 
moment in the stiffened slab and the deflections 
were obtain in a series of cases where many 
parameters were varied. This thorough 
sensitivity analysis gave a very clear indication 
of what parameters were most important and 
what parameters could be neglected within the 
precision sought. 
Task 5: This took advantage of all the results 
obtained to select the major factors and 
organize design charts and spreadsheets which 
gave the beam depth for a given weather-soil 
index. This paper covers Task 4 and Task 5 of 
the research effort and details the steps of the 
proposed design procedure with the charts. The 
results of the other tasks can be found in the 
work of Abdelmalak (2007) with further 
background found in Zhang (2004). Many 
design methods have been established for the 
design of stiffened slabs on shrink-swell soils; 
they include the Building Research Advisory 
Board method (BRAB 1968), the Wire 
Reinforcement Institute method (WRI 1981), 
the Australian Standards method (AS 2870 
1990, 1996), and the Post-Tensioning Institute 
method (PTI 1996, 2004). These design 
methods handle this problem by implementing 
different moisture diffusion, soil-weather 
interaction, and soil-structure interaction 
models. They all have advantages and 
drawbacks which lead the authors to develop 
this new method.
3 NUMERICAL SIMULATION OF SOIL SLAB INTERACTION 
After concluding steps 1 to 3 as discussed in 
section 2, a 2D finite element simulation was 
carried out for a flat foundation slab centered on 
the mound. The output of this simulation was 
the deflected shape of the slab, the bending 
moment diagram across the slab and the shear 
force diagram across the slab. 
Abdelmalak (2007) used the finite element 
package, ABAQUS/STANDARD, to simulate 
the problem for a uniform slab pressure. 
However, with the inclusion of a line load 
around the slab perimeter the output of the 
simulation is slightly different. The mesh for 
this problem is shown in Figure 3a for the case 
where the soil is swelling around the edges of 
the slab (edge lift) as would happen in the 
winter time. Figure 3b shows the mesh for the 
case where the soil is shrinking around the 
edges of the slab (edge drop) as would happen 
in the summer time. A two dimensional plane 
strain condition was simulated and boundary 
conditions are shown in Figures 3a and 3b. If L 
is the width of the slab, the mesh was 3L wide 
and 1.5 L deep and half the problem was 
simulated because of symmetry. 
 
The soil and the concrete were simulated as 
elastic materials and a load was imposed on the 
slab in addition to its weight. As a simulation 
example, consider a plane strain problem for a 
foundation slab on an edge drop mound: The 
foundation slab has a width of L=16 m, an 
equivalent thickness of 0.38 m, a modulus Econc 
= 20000 MPa, and it is loaded with a uniform 
slab pressure of 7.5 kPa and a line load of 
20kN/m around its perimeter. The foundation 
rests on an edge drop mound with a shape 
obtained from the equation derived from Task 
2. The input parameters for the mound shape 
equation were the depth of active zone (H) 
=3.5m, a free field imposed suction change of 
1.90 pF and a soil with a field coefficient of 
diffusivity αfield=0.02042m2/day. The 
modulus of the soil for the finite element 
simulation was taken as Esoil=60MPa. The 
initial and final mound profiles and the final 
slab profiles for the example cited above are 
presented in figure 3c. Due to the slab weight 
and the load, the surface of the soil mound 
settles. Because the slab is stiff, a gap exists 
near the edge between the soil surface and the 
underside of the slab. The length of the 
unsupported slab or gap length Lgap is 
approximately 5.8 m in this example. This 
overhanging of the slab creates a significant 
bending moment and associated deflection. The 
bending moment and the shear force diagram 
across the slab are shown in Figure 3d. Note 
that the distance from the edge of the slab to the 
point of separation between the soil and the 
slab, Lgap does not coincide with the distance 
between the edge of the slab and the point of 
maximum bending moment. The reason being 
that the overhanging slab does not behave as a 
pure cantilever. 
 
 
 
 
Figure 3c 
Figure 3d 
 
4 RESULTS OF THE SENSITIVITY 
STUDY 
 
The reference case for this study was chosen to 
correspond to the median values of the 
parameters. To reduce the number of simulation 
involved in developing the proposed design 
chart, the influence of the variation of each 
parameter will be compared to the reference 
case. The equivalent cantilever length Leqv was 
chosen as the parameter of greatest significance 
as it directly affects the maximum bending 
moment and the maximum deflection the two 
main considerations in the sizing and the design 
of the beam. In order to account for the 
combined effect of the uniform slab pressure 
and the line load on the design of slab on grade, 
sensitivity studies were performed for both the 
slab uniform pressure load and the line load. 
Results from these studies for line loads showed 
very insignificant moment, shear and deflection 
values for the edge-lift case and as such the 
edge-lift case for line loads was omitted in this 
section. 
 
4.1 Sensitivity Study For Pressure Load 
Table 4: Reference Case 
H(m) Iss 
(%) 
Δu0(pF) D(m) L(m) w 
(kN/m) 
3.5 45 1.3 0.9 8 6.25 
 
4.1.1 Influence Of The Soil-Shrink-Swell 
Potential 
Fig 4.1 shows the relationship between the 
normalized shrink swell index and the 
normalized equivalent cantilever length. It can 
be seen that an increase in shrink-swell index 
results in a non-linear increase in the 
equivalent cantilever length. The reason being 
that an increase in shrink-swell causes an 
increase the mound curvature which 
subsequently increases the foundation 
distortion and the equivalent length. The 
average slope of the normalized shrink-swell 
index curve being 0.32 for edge-drop and 0.388 
for edge-lift respectively. 
 
Figure 4.1 
 
‐0.06
‐0.04
‐0.02
0.00
0.02
0.04
0.06
0.08
0.0 2.0 4.0 6.0 8.0
y‐c
oo
rd
in
at
e (
m
)
x‐coordinate (m)
Soil mound and foundation elevation
initial
mound
elevation
final found
elevation
final mound
elevation
‐100
‐50
0
50
100
150
0.0 2.0 4.0 6.0 8.0
M
om
en
t (k
N
m
) o
r S
he
ar
 (k
N
)
x‐coordinate (m)
Bending moment and Shearing forces
Moment
Shear
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5
N
or
m
al
iz
ed
 L
 e
qv
(L
eq
v/
 L
 e
qv
 ( 
re
fe
re
nc
e)
)
Normalized Iss
( Iss/Iss (reference case))
edge drop
edge lift
 
4.1.2 Influence Of The Depth Of Active Zone 
Fig 4.2 shows the relationship between the 
normalized depth of active zone and the 
normalized equivalent cantilever length. 
Increasing the depth of the moisture active zone 
causes a non-linear increase in the equivalent 
cantilever length with the slope of the curve 
averaging 0.492 for edge-drop and 0.150 for 
edge-lift respectively. 
 
Figure 4.2 
4.1.3 Influence Of The Suction Change At 
The Ground Surface 
Fig 4.3 shows the relationship between the 
normalized change in surface suction and the 
normalized equivalent cantilever length. 
Similarly an increase in the change in surface 
suction resulted in a non-linear increase in the 
equivalent cantilever length. The average slope 
of the curve is approximately 0.369 for edge-
drop and 0.308 for the edge-lift cases 
respectively.Figure 4.3 
 
4.1.4 Influence Of Slab Stiffness 
Fig 4.4 shows the relationship between the slab 
stiffness, represented by the depth of the 
stiffening beams and the equivalent cantilever 
length. It can be seen from Fig 4.4 that an 
increase in the beam depth leads to a significant 
increase in the equivalent cantilever length with 
the slope of the normalized equivalent 
cantilever length vs. normalized beam depth 
averaging approximately 0.615 for edge-drop 
and 0.725 for the edge-lift cases respectively. 
This represents the greatest effect on the 
equivalent cantilever length. 
 
Figure 4.4 
4.1.5 Influence Of Slab Load 
Fig 4.5 shows the relationship between the 
equivalent cantilever length and the slab load w 
(kN/m), it can be seen that unlike the other 
parameters, increasing the slab load causes a 
decrease in the equivalent cantilever length. 
This can be explained by the fact that increasing 
the slab load compresses the soil mound 
causing a decrease in mound curvature and 
subsequently a decrease in the equivalent 
cantilever length. Fig 4.5 shows also that the 
normalized equivalent cantilever length vs. the 
normalized slab load curve has an average slope 
of -0.425 and -0.671 for the edge-drop and 
edge-lift cases respectively. For this reason, 
different charts were developed for a range of 
pressure loads. 
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5
N
or
m
al
iz
ed
 L
 e
qv
(L
eq
v/
 L
 e
qv
 ( 
re
fe
re
nc
e)
)
Normalized H
( H/H (reference case))
edge drop
edge lift
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.4 0.8 1.2 1.6
N
or
m
al
iz
ed
 L
 e
qv
(L
eq
v/
 L
 e
qv
 ( 
re
fe
re
nc
e)
)
Normalized ∆U0
( ∆U0/∆U0 (reference case))
edge drop
edge lift
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2
N
or
m
al
iz
ed
 L
 e
qv
(L
eq
v/
 L
 e
qv
 ( 
re
fe
re
nc
e)
)
Normalized D
( D/D (reference case))
edge drop
edge lift
 
Figure 4.5 
The effect of change in soil modulus was 
neglected in this study as it was shown to have 
the least effect on the equivalent cantilever 
length from previous research (Abdelmalak 
2007). Sensitivity analysis for line loads was 
also carried out but not included in this report. 
4.2 Conclusion of the sensitivity study 
 
The sensitivity study showed that the following 
factors influence the design of slabs on grade 
on shrink- swell soils. These factors are cited 
in order of significance starting with the most 
significant factor: 
 
Point load simulation: the slab stiffness, depth 
of active moisture zone, soil surface suction 
change, shrink-swell index, slab length and the 
imposed point load p. 
 
Uniform slab pressure simulation: the slab 
stiffness, slab uniform pressure, the depth of 
the active zone (edge-lift), the shrink-swell 
index, the change in surface suction and the 
slab length. The edge drop cases were also 
found to be the controlling factor for the line 
load case as very insignificant moment, shear 
and deflection values were obtained for the 
edge-lift simulations. 
 
5 NEW DESIGN CHARTS 
The design parameter necessary to size the 
beams and their spacing are the maximum 
bending moment Mmax, the maximum shear 
force Vmax, and the maximum deflection Δmax of 
the slab. In the proposed design charts these 
quantities are presented by using the equations 
for a cantilever beam with a modification factor 
to make them applicable for slab on grade. The 
method adopted here was to develop a set of 
design charts for two distinct categories of 
loads. Numerical simulations were performed 
using ABAQUS STANDARD for these two 
categories: 
1. Slab with uniform pressure 
2. Slab with Line load (perimeter walls) 
 
5.1 Slab With Uniform Pressure 
Design charts were developed for this category 
to cover a wide range of pressure values usually 
encountered in practice. Numerical simulations 
were performed for four (4) slab pressures 
2.5kPa, 5kPa, 7.5kPa and 10kPa for the edge-
drop cases and edge lift cases. Maximum 
moment, Shear and deflection values obtained 
from the numerical simulations were used to 
obtain modification factors presented in a 
cantilever equation. For a true cantilever beam, 
the equivalent length Leqv would be the length 
of the cantilever beam, the maximum shear 
force factor Fv would be 1, and the maximum 
deflection factor FΔmax would be 8.The 
modification factors are presented below. 
ܮ௘௤௩ሺ௤ሻ ൌ ሺ2ܯ௠௔௫/ݍሻ଴.ହ (5.1) 
F௩ሺ௤ሻ ൌ 	 ௏ౣ౗౮	ሺ೜ሻ௤௅೐೜ೡ (5.2) 
F∆୫ୟ୶	ሺ௤ሻ ൌ ௤௅೐೜ೡሺ೜ሻ
ర
∆೘ೌೣாூ (5.3) 
 
5.2 Slab With Line Load 
In a similar vein, design charts were produced 
for line loads ranging from 5kN/m to 20kN/m. 
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.5 1 1.5
N
or
m
al
iz
ed
 L
 e
qv
(L
eq
v/
 L
 e
qv
 ( 
re
fe
re
nc
e)
)
Normalized w imposed
( w imposed/w imposed (reference case))
edge drop
edge lift
This range was chosen to cover values of line 
loads encountered in practice for light-medium 
structures. Numerical simulations were 
performed for 5kN/m, 10kN/m, 15kN/m and 
20kN/m loads. 
As before moment, shear and deflection values 
obtained from numerical simulations were 
presented in a cantilever equation with 
modification factors to make the applicable to 
slab on grade. For a true cantilever beam, the 
equivalent length (Leqv) would be the actual 
length of the beam, the maximum shear force 
factor (Fv) would be 1 and the maximum 
deflection factor (FΔmax) would be 3. The 
modification factor are as shown below: 
ܮ௘௤ሺ௣ሻ ൌ ெౣ౗౮	ሺ೛ሻ௣ (5.4) 
F௩ሺ௣ሻ ൌ 	 ௏ౣ౗౮	ሺ೛ሻ௣ (5.5) 
F∆୫ୟ୶	ሺ௣ሻ ൌ ௣௅೐೜ೡሺ೛ሻ
య
∆೘ೌೣாூ (5.6) 
 
5.3 Super-Positioning 
The output from these two categories of design 
charts, maximum moments (Mmax), maximum 
shear (Vmax) and the maximum deflection 
(Δmax) should be super–positioned to obtain the 
final moment, shear and deflection values for 
design purpose. 
Final design moment = Mmax (q) + Mmax (p) 
Final design shear = Vmax (q) + Vmax (p) 
Final deflection = Δmax (q) +Δmax (p) 
Subscript (q) denotes values obtained from the 
uniform pressure (q) charts while (p) denotes 
values obtained from the line load (p) charts 
 
 
5.4 Validation Of Super-Positioning 
For validation of super-positioning, numerical 
simulation were performed for the following 
cases: 
I) Slab supporting uniform pressure (q) 
II) Slab supporting line load (p) 
III) Slab with uniform pressure (q) + line load 
(p) combined in a single simulation 
IV) Slab with uniform pressure (q) + slab with 
line load (p) in two different simulations (super-
positioning) 
The parameters used were: slab pressure (q) = 
7.5kPa, line load (p) = 20kN/m, slab equivalent 
depth deqv = 0.3975m, 
H= 3.5m, ΔU free field = 1.90, Iss = 45, modulus 
of soil (Esoil) = 60MPa, slab length (L) = 16m. 
Result from simulations showed that the 
maximum design moment, maximum design 
shear and the maximum deflection were 
greatestfor case IV (super-positioning). Fig 
5.1, Fig 5.2 and Fig 5.3 – show a plot of 
moment, shear and deflection profiles for the 
four (4) cases. These profiles represent 
simulation values for a given mound shape. 
 
 
Figure 5.1 
0
20
40
60
80
100
120
140
160
180
200
0.0 4.0 8.0
M
om
en
t (k
N
m
)
Beam Length (m)
CASE I
CASE II
CASE III
CASE IV
 
Figure 5.2 
 
Figure 5.3 
In a similar vein, numerical simulations were 
performed to include all the mound shapes for 
five (5) different slab equivalent depths deqv, for 
a uniform pressure of 7.5kPa and a Line load of 
20kN/m. A plot of case III against case IV for 
moment, shear and deflection are shown in Fig 
5.4, Fig 5.5 and Fig 5.6 respectively. It can also 
be seen that the moment, shear and deflection 
values are again greater for cases IV (super-
positioning) 
 
Figure 5.4 
 
Figure 5.5 
 
Figure 5.6 
It can be concluded from these simulations that 
super-positioning of the uniform pressure and 
line load charts represents a conservative 
approach to the design for slab on grade 
supporting a combination of line load and 
uniform pressure load. 
 
5.5 Soil-Weather Index 
The sensitivity studies for the uniform pressure 
load and the line load showed that the main 
parameters to be combined in the design charts 
should be the shrink-swell index ISS, the depth 
of the active zone H, the change of soil surface 
suction U0, and the slab stiffness deqv. The 
design parameters were the maximum bending 
moment, the shear force, and the slab 
deflection. Different charts of uniform pressure 
loads of 2.5kPa, 5kPa, 7.5kPa and 10kPa as 
‐60
‐50
‐40
‐30
‐20
‐10
0
10
20
30
0.0 4.0 8.0
Sh
ea
r (k
N
)
Beam Length (m)
CASE I
CASE II
CASE III
CASE IV
‐0.060
‐0.050
‐0.040
‐0.030
‐0.020
‐0.010
0.000
0.010
‐2.0 3.0 8.0
De
fle
ct
io
n (
m
)
Beam Length (m)
CASE I
CASE II
CASE III
CASE IV
0
50
100
150
200
250
300
350
400
0 100 200 300 400
CA
SE
 III
CASE IV 
Moment (kNm) 
0
10
20
30
40
50
60
70
80
0 20 40 60 80
CA
SE
 III
CASE IV 
Shear (kN) 
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.1 0.2 0.3
CA
SE
 III
CASE IV 
Deflection (m) 
well as for the line load 5kN/m, 10kN/, 15kN/m 
and 20kN/m were developed with each chart 
having the design parameters on the vertical 
axis and a combined soil weather index on the 
horizontal axis (Abdelmalak 2007). Each chart 
would contain several curves each one referring 
to a given slab stiffness. So the next step was to 
develop a combined soil weather index IS-W. 
Since the sensitivity study showed that the 
equivalent cantilever length increased with ISS, 
H, and U0, for the uniform pressure load and the 
line load it was decided to define the soil-
weather index as 
IS-W=ISS.H.U0 (5.7) 
 
5.6 Parametric Analysis 
 
Based on the success found in using the 
combined soil weather index, a parametric 
analysis was undertaken to develop the design 
charts. Seven representative mounds were 
chosen. For each mound, five slab stiffnesses 
were chosen and numerically simulated for the 
edge drop cases and edge lift cases. The slab 
stiffness was represented by the slab equivalent 
depth, deqv. The slab equivalent depth deqv 
represents the thickness of a flat slab which 
would have the same moment of inertia as that 
of a stiffened slab with a beam depth equal to 
D, a beam width equal to b and a beam 
spacing equal to S. The slab equivalent depth 
can be calculated by Equation 5.8 
 
S.deqv3=b.D3 (5.8) 
5.7 Water Content Based Design Charts 
The change in surface suction plays an 
important role in the mound shape equation; 
consequently it appears as an intrinsic 
component in the soil-weather index. However, 
measuring suction is more complicated than 
measuring water content, practitioners are more 
familiar with water content than with suction, 
and there is a much larger database of water 
content data than suction data. Therefore, it is 
convenient to have design charts in terms of 
water content in addition to having design chart 
in terms of suction. The soil water characteristic 
curve indicates that the change in suction U0 
(pF) and the change in water content w0 are 
linked by the specific water capacity Cw. 
w0=Cw.U0=2.∆wedge (5.9) 
Indeed the change in water content at the edge 
of the slab wedge is one half of the change in 
water content in the free field w0 since 
Equation 5.9 is linear and since U0 = 2.Uedge as 
mentioned before. Furthermore, Abdelmalak 
(2007) showed that there is a simple empirical 
relationship between the specific water capacity 
Cw and the shrink-swell index Iss: 
Cw=Iss/2, thus (5.10) 
 
IS-W = 2. H.w0 = H.wedge (5.11) 
With Equation 5.11 it was easy to transform the 
suction based design charts into water content 
based design charts by simply replacing the 
definition of the soil weather index on the 
horizontal axis. An advantage of the water 
content base design charts is that consultants 
may have sufficient water content data in their 
files to estimate the depth of the active zone H 
and the change in water content w0. As an 
example Briaud et al. (2003) organized a water 
content data-base which gave average values of 
w0 for three cities in Texas. Note that the design 
charts are given in terms of wedge which is equal 
to one half of w0. For a uniform pressure of 
5kN/m2, Figure 5.7, Figure 5.8, and Figure 5.9 
show the design charts for Leqv , F max, and Fv 
respectively. 
 
Figure 5.7 
 
Figure 5.8 
 
Figure 5.9 
 
REFERENCES 
Abdelmalak R. 2007. Soil structure interaction for 
shrink-swell soils -A new design procedure for 
foundation slabs on shrink-swell soils, Ph.D. 
dissertation, Department of Civil Engineering, Texas 
A&M University, College Station, TX. 
Australian Standard (AS2870). 1990. Residential Slabs 
and Footings, Part 2: Guide to Design by 
Engineering Principles AS 2870.2 Standard House, 
Sydney NSW, Australia. 
Australian Standard (AS2870). 1996. Residential Slabs 
and Footings, AS 2870 , Sydney NSW, Australia. 
Briaud, J.-L., Zhang, X., and Moon, S. 2003. Shrink Test 
Water Content Method for Shrink and Swell 
Predictions. ASCE Journal of Geotechnical and 
Geoenvironmental Engineering, 129(7): 590-600. 
Building Research Advisory Board (BRAB). 1968. 
National Research Council Criteria for Selection and 
Design of Residential Slabs- 
Holtz, R. D., and Kovacs, W. D. 1981. An Introduction 
to geotechnical Engineering, Prentice-Hall, 
Englewood cliff N.J., 180 
Mitchell, P. W. 1979. The structural analysis of footings 
on expansive soils. Research Report No. 1, K. W. G. 
Smith and Assoc. Pty. Ltd., Newton, South Australia. 
Post-Tensioning Institute (PTI) 2004. Design and 
construction of Post-Tensioned Slabs-on-Ground, 3 
Ed., Phoenix, AZ, USA. 
Wire Reinforcement Institute (WRI). 1981. Design of 
Slab-on-Ground Foundation, Findlay, Ohio, USA, 
August. 
Zhang, X. 2004. Consolidation theories for saturated-
unsaturated soils and numerical simulation of 
residential buildings on expansive soils, Ph.D. 
dissertation, Department of Civil Engineering,Texas 
A&M University, College Station TX 
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.00 0.50 1.00 1.50EQ
U
IV
AL
EN
T L
EN
G
TH
 Le
qv
 (m
)
SOIL WEATHER INDEX Is‐w= H.∆WEDGE
EDGE DROP (Q=5kPa)
d=0.632m
d=0.506m
d=0.379m
d=0.253m
d=0.127m
Mmax= qLeqv 2
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.00 0.50 1.00 1.50D
EF
LE
CT
IO
N
 FA
CT
O
R F
∆M
AX
SOIL WEATHER INDEX Is‐w= H.∆WEDGE
EDGE DROP (Q=5kPa)
d=0.632m
d=0.506m
d=0.379m
d=0.253m
d=0.127m
∆max = q leqv 4
F∆MAX EI
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.50 1.00 1.50
SH
EA
R F
AC
TO
R F
V
SOIL WEATHER INDEX Is‐w= H.∆W EDGE
EDGE DROP (Q=5kPa)
d=0.632m
d=0.506m
d=0.379m
d=0.253m
d=0.127m
Vmax=Fv q Leqv