The Pennsylvania State University The Graduate School Department of Civil and Environmental Engineering IMMEDIATE LOAD-SETTLEMENT RESPONSE OF STRIP FOOTINGS BEARING ON GEOGRID-REINFORCED CLAY A Thesis in Civil Engineering by Yuhao Ren 2015 Yuhao Ren Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2015
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The Pennsylvania State University
The Graduate School
Department of Civil and Environmental Engineering
IMMEDIATE LOAD-SETTLEMENT RESPONSE OF STRIP FOOTINGS
BEARING ON GEOGRID-REINFORCED CLAY
A Thesis in
Civil Engineering
by
Yuhao Ren
2015 Yuhao Ren
Submitted in Partial Fulfillment of the Requirements
for the Degree of
Master of Science
May 2015
The thesis of Yuhao Ren was reviewed and approved* by the following:
Prasenjit Basu Assistant Professor of Civil Engineering Thesis Advisor Swagata Banerjee Basu Assistant Professor of Civil Engineering MS Thesis Committee Member Tong Qiu Assistant Professor of Civil Engineering MS Thesis Committee Member Peggy Johnson
Professor of Civil Engineering Head of the Department *Signatures are on file in the Graduate School
ii
ABSTRACT
Footings on reinforced soil have long been considered as an effective solution to
enhance foundation bearing capacity and reduce settlement. Notwithstanding the fact
that footings bearing on reinforced clays can be an economic alternative to other
expensive foundation solutions, studies focusing on such foundations are rather limited
in number. In addition to consolidation and long-term creep settlement, which are most
frequently quantified for footings on clay, immediate settlement (i.e., settlement at a
time shortly after load application) of foundations bearing on reinforced clay should be
studied adequately to establish serviceability criteria that may govern the design.
The present research quantifies immediate settlement of strip footings bearing
on geogrid-reinforced clay. Finite element analyses of a strip footing bearing on
unreinforced and reinforced clay are performed to evaluate and quantify the effects of
several material (e.g., soil and reinforcement properties) and geometric (i.e., those
pertaining to reinforcement layout) parameters on load-settlement response of the
footing. A nonlinear elastic, perfectly plastic constitutive model obeying a non-
associated flow rule is used to represent mechanical behavior of clay. geogrid
reinforcement is modeled as a linear elastic material. Soil-reinforcement interaction is
modeled using cohesive interface elements above and below the reinforcement layers.
The clay constitutive model is also used as the material model for the cohesive interface
element and a contact interaction model is utilized to define the connection between the
cohesive interface and reinforcement layer.
Results show that settlement influence factor, which can be used for calculation
iii
of immediate settlement under varying net stress applied at the footing base, reduces
with increase in number of reinforcement layers and with increase in undrained shear
strength of clay. An increase in plasticity index of clay causes an increase in immediate
settlement and the same can be significant for foundations bearing on clays with high
plasticity. Optimal values of different reinforcement arrangement factors obtained from
this research are in agreement with those reported in literature.
iv
TABLE OF CONTENTS
LIST OF FIGURES.................................................................................................................. vi LIST OF TABLES .................................................................................................................. vii ACKNOWLEDGEMENTS .................................................................................................. viii Chapter 1 Introduction .............................................................................................................. 1
1.1. Background .......................................................................................................... 1 1.2. Motivation and Research Objectives ................................................................... 4 1.3. Thesis Outline ...................................................................................................... 5
Chapter 2 A Review of Existing Literature ............................................................................... 6 2.1. Reinforcing Mechanisms and Bearing Capacity Equations for RSF ................... 6 2.2. Model-scale Experiments .................................................................................. 11 2.3. Numerical Studies .............................................................................................. 17
Chapter 3 Finite Element Modeling ........................................................................................ 23 3.1. Clay Constitutive Model .................................................................................... 23 3.2. Geometric Model for the Soil Domain .............................................................. 25 3.3. Modeling of the Reinforcement Layers ............................................................. 28 3.4. Modeling of the Clay-Reinforcement Interface ................................................. 29 3.5. Convergence Study ............................................................................................ 30 3.6. Validation for the FE Model .............................................................................. 32
Chapter 4 Analyses and Results .............................................................................................. 37 4.1. Influence Factor Iq ............................................................................................. 37 4.2. Effect of Number of Reinforcement Layers N on Influence Factor Iq ............... 39 4.3. Effect of Undrained Shear Strength su on Settlement Influence Factor Iq ......... 45 4.4. Effect of Plasticity Index PI on Settlement Influence Factor Iq ......................... 46 4.5. Optimal Depth for Placement of the Top Reinforcement Layer ........................ 47 4.6. Optimal Reinforcement Width LR for a Single Layer of Reinforcement ........... 48 4.7. Optimal Vertical Spacing between Two Reinforcement Layers ........................ 50 4.8. Effective Total Reinforcement Depth de ............................................................ 51 4.9. Influence Zone ZR below the Footing Base ....................................................... 52 4.10. Optimal Number of Reinforcement/Interspacing for Multi-layer ...................... 55 4.11. Influence of Reinforcement Bending Stiffness .................................................. 56 4.12. Effect of Clay Layer Thickness on Settlement Influence Factor Iq .................... 57
Chapter 5 Discussion and Conclusions ................................................................................... 59 5.1. Comparison with Results Reported in Previous Numerical Studies on Footings on Reinforced Clay ......................................................................................................... 59 5.2. Comparison with Previous Experimental Studies .............................................. 61 5.3. Conclusions ........................................................................................................ 62
Figure 1-1 Representative layout of a reinforced soil foundation ............................................. 4 Figure 3-1 FE mesh for footing on unreinforced clay ............................................................. 27 Figure 3-2 FE mesh for footing on reinfnorced clay ............................................................... 27 Figure 3-3 Initial geostatic vertical effective stress contour ................................................... 28 Figure 3-4 Coulomb friction model (adapted from ABAQUS 6.12 User’s Manual) .............. 30 Figure 3-5 FEA convergence study of strip footing with W/B=20 ......................................... 31 Figure 3-6 FEA convergence study for different mesh densities ............................................ 32 Figure 3-7 Comparison of load-settlement curve reported in Davidson and Chen (1997) with
the one obtained using FE model used in the present research ....................................... 33 Figure 3-8 Comparison of load-settlement data reported in Das and Shin (1994) with that
predicted using the FE modeling scheme employed in the present research: (a) unreinforced clay; (b) reinforced clay ............................................................................. 35
Figure 3-9 Comparison of influence factor reported in Foye et al. (2008) with the one obtained based on FE modeling of the present research ................................................................ 36
Figure 4-1 Variations of settlement influence factor Iq with number of reinforcement layers N for G0/su=200: (c) PI=50, G0=3.2MPa. ........................................................................... 42
Figure 4-2 Variations of settlement influence factor Iq with number of reinforcement layers N for G0/su=100: (d) PI=60 ................................................................................................. 44
Figure 4-3 Variations of settlement influence factor Iq with number of reinforcement layers N for G0/su=50: (b) PI=60, G0=2.2MPa. ............................................................................. 45
Figure 4-4 Variations of settlement influence factor Iq with su based on PI=50, G0=3.2MPa: G0/su=200, 133, 100 and 71, respectively. ....................................................................... 46
Figure 4-5 Variations of settlement influence factor Iq with PI based on su=32kPa: G0=6.9MPa, 4.8MPa, 3.2MPa and 2.2MPa for PI=30, 40, 50 and 60, respectively. ........................... 47
Figure 4-6 Variations of BCR with depth d0 (measured from the footing base) of the top reinforcement layer; based on FEAs with PI =56 (i.e., G0=2.5MPa) and su=50kPa ....... 48
Figure 4-7 Variations of BCR (at different levels of footing settlement) with normalized reinforcement width LR/B for a single layer of reinforcement; based on FEAS with PI = 40 (i.e., G0=5MPa) and su=50kPa. .................................................................................. 50
Figure 4-8 Variation of BCR (for different settlement levels) with normalized vertical spacing h/B between reinforcement layers; based on FEAs with PI = 60 (i.e., G0=2.2MPa) and su=30kPa. ........................................................................................................................ 51
Figure 4-9 Increase in BCR with number of reinforcement layer N; based on FEAs with PI = 60 (i.e., G0=2.2MPa) and su=22kPa. ............................................................................... 52
Figure 4-10 Variation of vertical effective stress change ratio at different depths z below the footing base depth: (c) z = 1.7B and (d) z = 2.9B. .......................................................... 54
Figure 4-11 Variation of BCR (at s/B=3.2%) for different N-h combinations; based on FEAs with PI =50 (i.e., G0=3.2MPa) and su=32kPa.................................................................. 56
Figure 4-12 Influence factors for different reinforcement stiffness; based on FEAs with PI =30 (i.e., G0=6.9MPa), su=34.5kPa, N=4, and E=1.2GPa. ..................................................... 57
Figure 4-13 Influence factor for different clay thickness (N=4) ............................................. 58
vi
LIST OF TABLES
Table 2-1 Summary of finite element analyses of RSFs ......................................................... 19 Table 2-2 Summary of optimum parameters for reinforced soil foundations ......................... 20 Table 3-1 Reinforcement properties ........................................................................................ 29 Table 4-1 Soil input parameters used in the FEAs .................................................................. 40 Table 5-1 Summary of optimal parameters as reported in different numerical studies ........... 60 Table 5-2 Comparison of optimal parameters reported in past experimental studies with those
obtained from the present research.................................................................................. 61
vii
ACKNOWLEDGEMENTS
First of all, I want to thank my mom for the birth and love she gave to me; life is hard,
but yet interesting. There’s still a long way in front of me.
Secondly, I want to thank my father for his early education, I actually started to
understand him after I came to the United States and began to think that pursing a PhD
degree in physics overseas is never an easy thing although he has passed away already
for more than 12 years.
Next, I would like to thank my advisor Dr. Prasenjit Basu for his guiding toward
my research; most of his suggestions are indeed really helpful and may still work for
me in the future. Dr. Swagata Banerjee Basu and Dr. Tong Qiu have asked me some
good questions during the defense and they also offered me some constructive
suggestions that would be definitely beneficial to me, so I really appreciate their time
and help on this research.
Additionally, Mr. Yin Gao helps me a lot as an upperclassman in the department
of civil engineering and I sincerely express my gratitude to him here.
Finally, please allow me to end up with a line from the movie ‘Blackjack’:
“Yesterday is a history and tomorrow is a mystery; it’s all what you do in the moment.”
viii
Chapter 1 Introduction
1.1. Background
Geosynthetics are polymeric products, commonly available in the form of geogrids,
geotextiles, geomembranes and geocells, which are frequently used in civil engineering
practice. The polymeric nature of the material makes different geosynthetics products
durable under different ground and environmental conditions. Common applications of
geosynthetics in the field of geotechnical engineering include improving strength and
stiffness of subsurface soil beneath shallow foundations and pavements, providing
stability to earth retaining structures and slopes, ensuring dam safety, to name a few.
Early applications of geosynthetics in 1960s were about their use as filters materials in
the United States and as soil reinforcement in Europe.
A geogrid is one of the most common geosynthetic products that are often used
for improving mechanical performance of subsurface soil under external loadings.
Geogrids are widely used as reinforcement layers in mechanically stabilized earth
(MSE) and geosynthetic reinforced soil (GRS) walls, as a measure of slope
stabilization and as reinforcement in subsurface soil below pavements and footings.
Soils are weak in tension; good tensile capacity of geogrids allows the reinforcement
layers to take over a significant part of tensile stresses generated within a soil mass due
to the action of external loading. Thus, geogrids act as “reinforcing” element and
enhance load-deformation behavior of reinforced soil mass. Geogrids are commonly
made of polymers; nowadays different a variety of geogrids are made of polypropylene
1
or high density polypropylene (HDPP).
Based on manufacturing process, geogrids can mainly be categorized in three
distinct types. The first type is commonly known as homogenous or punched geogrid.
Bundles of polyethylene-coated polyester fibers contributing to the flexibility, are used
as reinforcing material in the second type. The third type is made by bonding
polypropylene rods together in a grid-like pattern using laser or ultrasonic technology.
Geogrids can also be classified into three types according to grid structure: uniaxial,
biaxial and triaxial. As the name suggests, while uniaxial geogrids are able to sustain
mainly uniaxial stress (along the direction of longer gird dimension), biaxial and
triaxial geogrids are capable of sustaining loads from two and three directions,
respectively.
Shallow foundations are often used in practice to transfer loads coming from
the structure to the underlying ground at relatively shallow depth (usually less than five
times the width of the foundation). Shallow foundations range from small isolated
foundations, which support load from an individual column, to large foundation
elements that support several columns, or even all the loads from structure. Shallow
foundations are easy to build, requiring little to no specialized equipment. For shallow
foundations, foundation-to-soil load transfer takes place predominantly through the
base of the foundation element, and only a small fraction of the total load can be
transferred through the sides of an embedded shallow foundation element (in most
cases these are reinforced concrete blocks); however, such contribution is often
The foundation is assumed to be rigid. This is a practical assumption for any
reinforced concrete footing bearing on clay because the rigidity of foundation element
is much greater than that of underlying soil. Uniform displacement is expected at the
base of a rigid foundation and thus displacement-controlled method is used to simulate
the loading process. Analyses are performed for a surface footing and owing to the fact
that the foundation is a rigid one, small displacement increment (in the order of 0.5mm)
was applied at all nodes lying at the foundation base.
3.3. Modeling of the Reinforcement Layers
Most of the geogrids nowadays are made out of Polypropylene (PP) or High Density
Polypropylene (HDPP) that has a Possion’s ratio of around 0.4 and Young’s modulus
about 1.0 GPa (Ashby 2012). The thickness of commonly used geogrid is close to 1
mm and therefore, the mechanical behavior of geogrid layers can be regarded as that
of an Euler–Bernoulli beam instead of a Timoshenko’s beam since the aspect ratio of
the geogird is really high and thus the transverse shear (out-of-plane shear) can be
28
ignored. The related beam type element in ABAQUS is B23. The geogrid
reinforcement layers are modeled as linear elastic material with properties listed in
Table 3-1.
Table 3-1 Reinforcement properties
Material Possion’s
ratio v Young’s
modulus E Thickness
h Moment of Inertia I Element Type
Polypropylene (HDPP)
0.4 1.2GPa 1mm bh3/12
(b=unit out-of-plane thickness)
B23
3.4. Modeling of the Clay-Reinforcement Interface
The soil-reinforcement interface needs particular attention for successful solution of
the problem. Two interface layers are used for each reinforcement layer: one is at the
top of the geogrid and the other one is at the bottom. The interface layers are modeled
using traction-separation type cohesive element (COH2D4) built in ABAQUS. For
such interface element, the thickness of the interface layer is essentially zero. The clay
constitutive model described in section 3.1 is used as the material model for the
cohesive interface element. A contact interaction model is utilized to define the
connection between the cohesive interface and reinforcement layer. The normal
behavior of the interaction is selected as a ‘hard contact’, which implies that the
cohesive element will move with the reinforcement in the vertical direction. For the
transverse behavior, Coulomb friction model with friction coefficient = 0.6 is used with
a shear stress limit equal to the undrained shear strength su of clay. Figure 3-4 shows
the mechanical behavior of the friction model. The sticking friction increases with 29
increase in contact pressure at a constant rate (equal to the constant friction coefficient)
and the sticking friction becomes slipping friction after it reaches the shear stress or
shear stress limit (equal to the undrained shear strength su). The slip displacement limit
was set to be 10% of the geogrid thickness (1mm) beyond which the sticking friction
changes into slipping friction.
Figure 3-4 Coulomb friction model (adapted from ABAQUS 6.12 User’s Manual)
3.4. Convergence Study
A series of convergence study is performed for the unreinforced case in order to
ascertain reasonable mesh size and dimensions of the analysis domain. The right
boundary of the analysis domain is set at a distance w = 20B measured from the footing
centerline. Results from the analysis performed as part of the convergence study
confirmed that vertical displacement at the right boundary is indeed negligible (less
than 5% of the displacement below the footing base) and, therefore, W/B =20 is
selected for all analyses. The vertical distance (clay thickness) plays an important role
in quantification of footing settlement. Analyses are performed with H varying from
30
5B to 20B (H/B=5, 10 and 20). It is clear that the computed bearing stress at the footing
base converges to a constant value and there is no significant difference between
H/B=10 and H/B=20 (based on the mesh for which the number of elements below the
footing base is 20), as is shown in Figure 3-5. Thus, H/B=10 is used for all analyses in
the present study.
Figure 3-5 FE convergence study – effect of clay layer thickness on footing
settlement (for w/B=20)
The mesh density below the footing base is also varied to see the effect of
number of elements Nb below the footing base on foundation load-settlement behavior.
Analyses are performed with three different mesh densities with Nb=10, 20 and 50,
results are plotted in Figure 3-6. A convergence of load-settlement response is observed
for all values of Nb considered. However, the analysis terminates earlier as Nb increases
because element size decreases and mesh distortion becomes more severe with increase
0 1 2 3 4Normalized net stress at the footing base qb,net/su
0
10
20
30
40
Settl
emen
t s (m
m)
H=5BH=10BH=20B
31
in Nb. Based on the convergence study, H/B=20, W/B=20 and Nb=20 were chosen for
the analyses presented in Chapter 4.
Figure 3-6 FE convergence study – effect of different mesh densities on footing
settlement (for w/B = 20, H/B = 10)
3.5. Validation for the FE Model
Davidson and Chen (1977) performed finite element analyses for load-settlement
response of unreinforced clay due to loading from footings under plain-strain condition.
A linear elastic perfectly plastic soil constitutive model with Von-Mises yield criterion
and associated flow rule was used. In one of their analyses, the Young’s modulus E of
the clay was set to 14.4MPa with an undrained shear strength su=144kPa (E/su=100),
Possion’s Ratio v=0.48, effective (submerged) soil unit weight γ = 6kN/m3 and
coefficient of lateral earth pressure at rest K0 = 1. The value of initial Young’s modulus
E (or shear modulus G) reported in Davidson and Chen (1977) is a constant value
0 1 2 3 4Normalized net stress at the footing base qb,net/su
0
10
20
30
40Se
ttlem
ent s
(mm
)
Nb=10Nb=20Nb=50
32
following a linear elastic response (which is in contrast to a nonlinear elastic response
for the constitutive model used in the present study). Thus for a comparison to be
possible, the constant shear modulus G value reported in Davidson and Chen (1977) is
considered as an average shear modulus G during the shear modulus degradation
captured in the constitutive model used in the present research. Therefore, G0=2G is
used in this comparison study. Figure 3-7 shows a comparison of results reported by
Davidson and Chen (1977) and that predicted using FE model developed and used
(both geometric and constitutive model are same) in the present research.
Figure 3-7 Comparison of load-settlement curve reported in Davidson and Chen
(1997) with the one obtained using FE model used in the present research
The load settlement curve predicted using the present FE model matches well
with the initial part of the results reported by Davidson and Chen (1977); however, the
present analysis terminates early because of excessive distortion of the elements near
0 2 4 6Normalized net stress at the footing base qb,net/su
0
0.04
0.08
0.12
Nor
mal
ized
imm
edia
te s
ettle
men
t s/B Davidson and Chen (1977)
Present study
33
the footing base. Such early termination of analysis is certainly a drawback of present
study; the point of analysis termination varies with soil input parameters. Nonetheless,
it is anticipated that the results presented in this thesis can be used for practical range
of qb,net/su ratio that is allowed at the footing base.
Das and Shin (1994) conducted load tests on strip footing resting on
unreinforced and reinforced clay bed prepared within a laboratory-scale soil tank (229
mm wide, 607 mm high and 915 mm long). An average undrained shear strength su =
12 kPa and plasticity index PI = 20 was reported for the clay used in this study. The
footing width B was equal to 76mm. For the reinforced clay, the top layer spacing d0
was set to be equal to 0.4B and number of reinforcement layers N=5 with interlayer
spacing h=0.333B. A FE model was developed using these geometric details and the
soil properties provided in Das and Shin (1994) were used in the soil constitutive model.
However, Das and Shin (1994) does not provide the value of G0 for use in the soil
constitutive model. Comparison results shown in Figure 3-8 (a) (unreinforced clay) and
Figure 3-8 (b) (reinforced clay) are based on a G0 value equal to 250 kPa, which is
significantly low (almost 1/6 times) compared to that calculated (based on Viggiani
and Atkinson 1995) at a representative depth 2B below the footing base. The value of
G0 used in comparisons shown in Figure 3-8 are same as that would be calculated at a
depth (=0.2B) immediately below the footing. It is thus realized that although the
present FE solution scheme can successfully predict results from laboratory-scale
experiments such prediction is subjected to the uncertainty in ascertaining relevant soil
input parameters.
34
(a)
(b)
Figure 3-8 Comparison of load-settlement data reported in Das and Shin (1994) with that predicted using the FE modeling scheme employed in the present research: (a) unreinforced clay; (b) reinforced clay
For strip footings resting on unreinforced clay, the immediate load-settlement
0 1 2 3 4 5Normalized net stress at footing base qb,net/su
0
2
4
6
8
Settl
emen
t s (m
m)
Data from Das and Shin (1994)Present study
0 2 4 6 8Normalized net stress at footing base qb,net/su
0
4
8
12
16
Settl
emen
t s (m
m)
Data from Das and Shin (1994)Present study
35
response is also compared with that reported by Foye et al. (2008) [for PI=20,
G0=10MPa and su=50kPa, G0/su=200]. The coefficient of lateral earth pressure at rest
K0 is varied from 0.3 to 1.2 (K0=0.3, 0.5, 0.7, 0.9 and 1.2). The result of this comparison
is shown in Figure 3-9. Note that the vertical axis in Figure 3-9 represents immediate
settlement influence factor Iq, which is a direct reflection of immediate footing
settlement. The theoretical background for calculation of Iq is and is discussed in detail
in Chapter 4. Figure 3-9 confirms the validity of present FE modeling approach in
reproducing results from Foye et al. (2008) for K0 values lying between 0.7 and 0.9.
Figure 3-9 Comparison of influence factor reported in Foye et al. (2008) with the one
obtained based on FE modeling of the present research
0 1 2 3 4 5Normalized net stress at the footing base qb,net/su
2
4
6
8
Influ
ence
Fac
tor I
q
Foye et al. (2008)Present study K0=0.3Present study K0=0.5Present study K0=0.7Present study K0=0.9Present study K0=1.2
36
Chapter 4 Analyses and Results
Results from a series of finite element analysis (under undrained condition) of a strip
footing bearing on reinforced clay are presented in this chapter. A normalized
settlement influence factor Iq, which is a direct reflection of immediate settlement of
the footing, is introduced. A parametric study is performed to quantify the effects of
important input parameters factors (e.g., the number of reinforcement layers, undrained
shear strength, plasticity index, bending stiffness of reinforcement) that may affect Iq,.
Besides, several parameters related to the reinforcement arrangement and influence
depth beyond which the change in vertical stress becomes insignificant are also studied
and related results are shown in the subsequent sections.
4.1. Influence Factor Iq
Based on elastic FEAs Christian and Carrier (1978) developed design charts to estimate
immediate settlement of footings bearing on clay. These charts suggest that the
immediate settlement ρ can be expressed as:
ρ = 𝐼𝐼1𝐼𝐼0𝑞𝑞𝑏𝑏𝐵𝐵𝐸𝐸𝑢𝑢
(4.1)
where I1 is the influence factor related to footing shape and clay layer thickness beneath
the footing base; I0 is the influence factor related to the embedment depth; qb is unit
load (or stress) at the footing base; B is the footing width; and Eu refers to the
representative Young’s modulus of the foundation soil. However, the correction factor
I0 accounting for the embedment depth of the footing may not be conservative because
the reduction is settlement with increase in embedment depth is insignificant (Christian
37
and Carrier 1978; Burland and Burbidge 1985). Therefore, the factor I0 may be
excluded from Eq. (4.1), and the expression for ρ can be written as (Foye et al. 2008):
ρ = 𝐼𝐼𝑞𝑞𝑞𝑞𝑏𝑏,𝑖𝑖𝑛𝑛𝑖𝑖𝐵𝐵𝐸𝐸0
(4.2)
where Iq is settlement influence factor, E0 is a representative value of initial (small
strain) Young’s modulus of the subsurface soil, qb,net is the net applied stress at the
footing base. Eq. (4.2) can be rearranged to define the settlement influence factor Iq.
𝐼𝐼𝑞𝑞 =𝜌𝜌𝐸𝐸0
𝑞𝑞𝑏𝑏,𝑖𝑖𝑛𝑛𝑖𝑖𝐵𝐵 (4.3)
Note that Iq varies with the level of net load (or stress) applied at the footing base, and
thus quantification of Iq enables calculation of settlement at different levels of working
load. For a given footing dimension, load and subsurface condition a higher influence
factor indicates higher value of immediate settlement. Design charts containing
variations of Iq with qb,net/su would thus allow the designers to choose, without the need
for detailed analyses, different levels of net stress qb,net that can be applied on a footing
and directly obtain associated values of immediate settlement. Several factors may
affect immediate settlement influence factor Iq (and thus immediate settlement) for
footings bearing on reinforced clay. Such factors include the number of reinforcement
layers N, vertical spacing h between reinforcement layers, width LR of reinforcement
measured parallel to the footing width, total depth of reinforcement d, distance d0
between top layer of reinforcement and footing base, bending stiffness of
reinforcement (EI), undrained shear strength su and plasticity index PI of subsurface
clay. Therefore, it is important to quantify the effects of these parameters on the Iq –
qb,net/su variations. A prior knowledge of variation of Iq with reinforcement
38
arrangement parameters and reinforcement and clay properties will enable optimal
design of RSF on clay.
4.2. Effect of Number of Reinforcement Layers N on Settlement Influence Factor Iq
Past studies reported reduction in foundation settlement when the original foundation
soil (both sand and clay) is reinforced and more reinforcement layers are placed in the
soil layer. For all other input parameters being the same, a decrease in settlement
influence factor Iq is expected (from that for a footing on unreinforced soil) when one
and more number of reinforcement layers are placed below the footing base. Analyses
are performed for a strip footing bearing on reinforced normally consolidated clay with
different combinations of undrained shear strength su and plasticity index PI values and
the variations of Iq with N are reported. Following the relationship proposed by
Viggiani and Atkinson (1995), the initial shear modulus of clay G0 changes with change
in PI [see Eq. (3.3)]. For all analyses, G0 is calculated (based on an input value of PI)
at a depth 2B below the footing base. The zone of influence below a strip footing on
unreinforced clay is expected to extend down to a depth of 4B below the footing base
(Foye et al. 2008) and thus representative G0 values used in the present analyses are
calculated at a depth 2B below the footing base. Submerged unit weight for the
saturated normally consolidated clay layer is assumed to be equal to 7kN/m3. su values
used in the FEAs are decided based on assumed values of G0/su ratio. Table 4-1 lists
the soil input parameters used in the analyses.
39
Table 4-1 Soil input parameters used in the FEAs
PI G0 (MPa) G0/su su (kPa)
30 6.9 100 69
200 34.5
40 4.8 100 48
200 24
50 3.2 50 64
100 32
200 16
60 2.2 50 44
100 22
Number of reinforcement layers N are varied from 0 (unreinforced case) to 5
to quantify the reduction in settlement influence factor Iq with N (for a given set of soil
input parameters). The reduction of Iq is no longer significant when N reaches 4 for
most cases, indicating that four layers of reinforcement below the footing base is
perhaps most beneficial for immediate settlement reduction (Figure 4-1, Figure 4-2,
Figure 4-3). It is also observed that the reduction in Iq is more than 10% when the
number of reinforcement layers increases from 0 (unreinforced) to 4 for most cases
according to the figures below.
40
Figure 4-1 (a)
Figure 4-1 (b)
0 1 2 3 4Normalized net stress at footing base qb,net/su
2
2.4
2.8
3.2
3.6
4
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
0 1 2 3 4Normalized net stress at footing base qb,net/su
2.4
2.8
3.2
3.6
4
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
41
(c)
Figure 4-1 Variations of settlement influence factor Iq with number of reinforcement layers N for G0/su=200: (a) PI=30, G0=6.9MPa. (b) PI=40, G0=4.8MPa. (c) PI=50,
G0=3.2MPa.
Figure 4-2 (a)
0 1 2 3 4Normalized net stress at footing base qb,net/su
2.8
3.2
3.6
4
4.4
4.8
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
0 1 2 3 4Normalized net stress at footing base qb,net/su
1.6
2
2.4
2.8
3.2
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
42
Figure 4-2 (b)
Figure 4-2 (c)
0 1 2 3 4Normalized net stress at footing base qb,net/su
1.6
2
2.4
2.8
3.2
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
0 1 2 3 4Normalized net stress at footing base qb,net/su
2
2.4
2.8
3.2
3.6
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
43
(d)
Figure 4-2 Variations of settlement influence factor Iq with number of reinforcement layers N for G0/su=100: (a) PI=30, G0=6.9MPa. (b) PI=40, G0=4.8MPa. (c) PI=50,
G0=3.2MPa. (d) PI=60, G0=2.2MPa.
Figure 4-3 (a)
0 1 2 3 4Normalized net stress at footing base qb,net/su
2
2.4
2.8
3.2
3.6
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
0 1 2 3Normalized net stress at footing base qb,net/su
1.6
2
2.4
2.8
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
44
(b) Figure 4-3 Variations of settlement influence factor Iq with number of reinforcement
layers N for G0/su=50: (a) PI=50, G0=3.2MPa. (b) PI=60, G0=2.2MPa.
4.3. Effect of Undrained Shear Strength su on Settlement Influence Factor Iq
Love et al. (1987) reported that immediate settlement of footings on both unreinforced
and reinforced clays reduces with increase in undrained shear strength of undisturbed
soil. This observation could also be explained with the idea that the “stronger” clays
often tend to have stiffer responses in reaction to the load. Therefore, for footings on
clays with same PI but different values of su are expected to experience different levels
of immediate settlement. Figure 4-4 shows that for PI = 50 (corresponding calculated
G0 = 3.2 MPa) and for different levels of net normalized stress qb,net/su applied at the
footing base, Iq reduces by approximately 50% on an average as su increases from 16
kPa to 45 kPa.
0 1 2 3Normalized net stress at footing base qb,net/su
1.6
1.8
2
2.2
2.4
2.6
2.8
Settl
emen
t inf
luen
ce fa
ctor
I q
N=0N=1N=2N=3N=4N=5
45
Figure 4-4 Variations of settlement influence factor Iq with su based on PI=50,
G0=3.2MPa: G0/su=200, 133, 100 and 71, respectively.
4.4. Effect of Plasticity Index PI on Settlement Influence Factor Iq
The plasticity index PI, defined as the difference between liquid limit and plastic limit,
is a very routinely measured index parameter for clays. Foott and Ladd (1981)
concluded that the immediate settlement could be significant for highly plastic clays
(i.e., PI≥50). Thus it is necessary to perform a parametric study concerning the effect
of PI on immediate settlement of strip footings bearing on reinforced clay. Several
FEAs are performed (for N = 4 and su = 32 kPa) as part of the present research to
investigate the effect of PI on immediate settlement influence factor Iq and results are
shown in the Figure 4-5. While the absolute value of immediate settlement ρ increases
with increase in PI value, Iq decrease with an increase in PI (Figure 4-5). The value of
PI affects ρ and E0 in opposite ways. The rate of increase in ρ due to a ceratin increase
0 1 2 3 4Normalized net stress at footing base qb,net/su
1
2
3
4
5
Settl
emen
t inf
luen
ce fa
ctor
I q
Su=16kPaSu=24kPaSu=32kPaSu=45kPa
46
in PI is lower than the rate of decrease in E0 (or G0) for the exact same increase in PI.
Consequently, the net effect is reflected through a decrease in Iq [see equation (4.3)] as
a result of an increase in PI.
Figure 4-5 Variations of settlement influence factor Iq with PI based on su=32kPa: G0=6.9MPa, 4.8MPa, 3.2MPa and 2.2MPa for PI=30, 40, 50 and 60, respectively.
4.5. Optimal Depth for Placement of the Top Reinforcement Layer
The optimal depth d0, measured from the base of the footing, of placement of the top
reinforcement layer is determined through FEAs of a strip footing resting on clay bed
reinforced with a single layer of reinforcement (with width LR = 2B, B is the footing
width). Different combinations of G0/su are used for these analyses. Bearing capacity
ratio (BCR), i.e., the ratio of net vertical stress at the base of the footing on reinforced
soil to that for footing on unreinforced soil, is quantified for different levels of
0 1 2 3 4Normalized net stress at footing base qb,net/su
10
30
50
Settl
emen
t s (m
m)
4 3 2 1 0Normalized net stress at footing base qb,net/su
PI=60PI=50PI=40PI=30
2.4
3
3.6
Settl
emen
t inf
luen
ce fa
ctor
I q
47
immediate settlement (1%B, 2%B, 3%B and 4%B). For PI =56 (corresponding
G0=2.5MPa) and su=50kPa (i.e, G0/su=50), optimal top layer spacing d0 is found to be
around 0.5B (Figure 4-6).
Figure 4-6 Variations of BCR with depth d0 (measured from the footing base) of the
top reinforcement layer; based on FEAs with PI =56 (i.e., G0=2.5MPa) and su=50kPa
4.6. Optimal Reinforcement Width LR for a Single Layer of Reinforcement
FEAs are also performed with different values of reinforcement width (measured
parallel to the footing width) while keeping the top layer spacing d0 (=0.5B) and other
input parameters (PI = 40, G0=5MPa and su=50kPa) constant. Figure 4-7 shows that
for different levels of immediate settlement change in BCR is insignificant beyond LR
= 2B for both clay-reinforcement interface friction angle=30° [Figure 4-7 (a)] and 20°
[Figure 4-7 (b)]. Note that very low values (less than 4%) of increase in BCR are
0 1 2 3 4 5Normalized depth of top reinforcement layer d0/B
1
1.01
1.02
1.03
1.04
Bea
ring
capa
city
ratio
(BC
R)
s/B=4%s/B=3%s/B=2%s/B=1%
48
observed when a single layer of reinforcement is used, and thus, for all practical
purposes it is important to explore the load-settlement response of RSF with multiple
layers of reinforcement.
Figure 4-7 (a)
0 1 2 3 4 5 6Normalized reinforcement width LR/B
1
1.02
1.04
Bea
ring
capa
city
ratio
(BC
R)
s/B=3%s/B=2%s/B=1%
49
(b)
Figure 4-7 Variations of BCR (at different levels of footing settlement) with normalized reinforcement width LR/B for a single layer of reinforcement; based on
FEAS with PI = 40 (i.e., G0=5MPa) and su=50kPa: a) interface angle=30°; b) interface angle=20°.
4.7. Optimal Vertical Spacing between Two Reinforcement Layers
In order to evaluate an optimal spacing between reinforcement layers, FEAs are
performed for footings on reinforced clay with two layers of reinforcement. Different
values of vertical spacing h (=0.1B, 0.2B, 0.3B, 0.5B, 1B) are used for these FEAs and
for all analyses the top layer spacing d0 and width of reinforcement LR are kept at equal
to 0.5B and 2B, respectively. Initial shear modulus G0 (calculated from PI = 60) and
undrained shear strength su values used in these FEAs are 2.2MPa and 30kPa
(G0/Su=73), respectively. Optimal vertical spacing (for which BCR is the maximum) is
observed to be around 0.3-0.5B for settlement levels ranging from 1 to 4% of footing
0 1 2 3 4 5 6Normalized reinforcement width LR/B
1
1.02
1.04B
earin
g ca
paci
ty ra
tio (B
CR
)
s/B=3%s/B=2%s/B=1%
50
width B (Figure 4-8).
Figure 4-8 Variation of BCR (for different settlement levels) with normalized vertical
spacing h/B between reinforcement layers; based on FEAs with PI = 60 (i.e., G0=2.2MPa) and su=30kPa.
4.8. Effective Total Reinforcement Depth de
Performance of multi-layer (with N≥2) reinforced soil-foundation system is examined
by increasing the number of reinforcement N while keeping the other input parameters
constant (d0=0.5B, h=0.3B, PI = 60, G0 = 2.2 MPa, su = 22kPa). Optimal number of
reinforcement is 9, which means that the optimal total depth of reinforcement de below
of E; the minimum value of Iq is achieved when the value of E approaches to that of
steel and more than 20% reduction in the settlement influence factor Iq could be
achieved with a 7 times increase in the bending stiffness of the reinforcement (E to 8E).
Figure 4-12 Influence factors for different reinforcement stiffness; based on FEAs with PI =30 (i.e., G0=6.9MPa), su=34.5kPa, N=4, and E=1.2GPa.
4.12. Effect of Clay Layer Thickness on Settlement Influence Factor Iq
The clay layer thickness H affects immediate settlement of footing supported on it for
both unreinforced (as shown in the “Convergence Study” section in Chapter 3) and
reinforced cases. To study the influence of clay layer thickness on Iq for the reinforced
case, FEAs are performed with three values of H/B = 5, 10 and 20 (PI=60, G0=2.2MPa,
su=22kPa, N=4, d0=0.5B and h=0.3B. Figure 4-13 demonstrates that beyond H = 10B,
the thickness of the underlying clay layer does not affect immediate settlement of the
strip footing.
0 1 2 3 4 5Normalized net stress at footing base qb,net/su
1.6
2
2.4
2.8
3.2
3.6
4
Settl
emen
t inf
luen
ce fa
ctor
I q
0.25E0.5EE2E4E8ESteel
57
Figure 4-13 Influence factor for different clay thickness (N=4)
0 1 2 3 4Normalized net stress at footing base qb,net/su
1.2
1.6
2
2.4
2.8
3.2
3.6
Settl
emen
t inf
luen
ce fa
ctor
I q
H=20BH=10BH=5B
58
Chapter 5 Discussion and Conclusions
Key findings from the present research are compared to and discussed in light of past
related studies reported in literature. Important conclusions drawn from this study are
summarized.
5.1. Comparison with Results Reported in Previous Numerical Studies on Footings on Reinforced Clay
Comparisons are made for several reinforcement arrangement factors (e.g., top layer
spacing d0, vertical spacing between adjacent two reinforcement layers h, width of the
reinforcement layer LR) reported in literature. While Maharaj (2003) reported an
optimal top layer spacing d0 = 0.125B, this ratio falls in the range of 0.3-0.6B according
to Jie (2011). Based on limit analysis Chakraborty and Kumar (2012) reported the
upper and lower bound solutions for d0 to be equal to 0.22B and 0.64B. The present
research finds the optimal value of d0 to be approximately around 0.5, which is in
general agreement with values reported in literature.
The optimal ratio of interlayer spacing h to B is reported to be equal to 0.25 for
multi-layer within the effective total reinforcement depth (Jie 2011) and in the range of
0.22 to 0.64 for 2-layer case analyzed by Chakraborty and Kumar (2012). Based on
FEA results obtained as part of the present study, the optimal h/B value is in the range
of 0.3-0.5 for 2-layer and 0.2-0.25 for multi-layer system.
As for the optimum reinforcement width LR, the ideal ratio of LR to footing
width B was found to be about 4 according to Jie (2011). The same value obtained from
the present study is equal to 2; this discrepancy might have been caused due to several
59
reasons which may include the difference in the soil constitutive model, the difference
in element type used to model the reinforcement layer, difference in interface model
and finally the difference in settlement level s/B at which BCR was evaluated (while
s/B=10% in Jie 2011, s/B is less than 5% in the present study).
For the effective influence depth of reinforcement d, the critical value of d/B
was reported to be around 1.5 by Jie (2011), however, this value is around 2 to 3 based
on the present study. A brief comparison of results from different numerical studies is
given in Table 5-1.
Table 5-1 Summary of optimal parameters as reported in different numerical studies
References Maharaj (2003)
Jie (2011) Chakraborty and Kumar (2012)
Present study (2015)
Analysis type
Parameters
Limit analysis of strip
footings on reinforced
clay
FEA of strip footings on reinforced
clay
Limit analysis of strip footings on reinforced clay
FEA of strip footings on
reinforced clay
d0/B 0.125 0.3-0.6 0.22-0.64 0.5 h/B
N/A
0.25 0.22-0.64 0.2-0.5 L/B 4 2 2 d/B 1.5 N/A 2-3
BCR 1.1-2 1.13-1.84 1.03-1.3
60
5.2. Comparison with Previous Experimental Studies
Results from past experimental studies on footings bearing on reinforced clay are also
compared with results from the present study in terms of reinforcement arrangement
factors. A summary of such comparison is shown in Table 5-2.
Table 5-2 Comparison of optimal parameters reported in past experimental studies with those obtained from the present research
References Parameters
Mandal and Sah (1992)
Das et al. (1994)
Shin and Das (1998)
Chen et al. (2007)
Present study (2015)
Footing Type Square Strip
Strip with slope
Square Strip
d0/B 0.175 0.3-0.4 0.4 0.33 0.5 h/B
N/A N/A
N/A N/A 0.2-0.5
L/B 5 6 2 d/B 1.75 1.72 1.5 2-3
BCR 1.36 (max) 1.1-1.5 1.4-1.7 1.02-1.6 1.03-1.3
61
5.3. Conclusions
Specific conclusions drawn from the present study are:
(1) An increase in the number of reinforcement layers N below the footing would result
in immediate settlement reduction. More than 10% reduction in immediate
settlement influence factor Iq is observed, compared to that for unreinforced case,
when four layers of reinforcement are used (N = 4, h = 0.3B, d0 = 0.5B) below the
footing. The exact amount of such reduction in Iq with increase in N also depends
on soil input parameters.
(2) The settlement influence factor Iq decreases as the undrained shear strength su
increases, approximately 50% decrease is observed when su increases from 16kPa
to 45kPa, indicating lower immediate settlement levels for footings on clays with
higher undrained shear strengths.
(3) The settlement influence factor Iq increases with decrease in plasticity index PI
when initial shear modulus G0 decreases with PI following Viggiani and Atkinson
(1995) relation. Nonetheless, absolute value of immediate settlement of footing
increases with increase in PI.
(4) The optimal depth d0 (below the footing base) of top layer placement is about 0.5B.
(5) The optimal reinforcement width LR is around 2B for soil-reinforcement interface
friction angle equaling 30° and 20°.
(6) The critical value of vertical spacing h between reinforcement layers is in the range
of 0.2B to 0.5B.
62
(7) The effective total depth of reinforcement d below the footing base is about 3B.
(8) The stress influence depth below the footing base (at which the increment in
vertical effective stress is same for reinforced and unreinforced cases) is
approximately equal to 3B.
(9) Bending stiffness of reinforcement layers plays an important role in the
performance of strip footings on geogrid-reinforced clay. According to the results
presented in this thesis, more than 20% reduction in the settlement influence factor
Iq could be achieved with a 7 times increase in the bending stiffness of the
reinforcement.
(10) The clay thickness does affect the influence factor Iq; the impact becomes
insignificant when the ratio of clay thickness to the footing width H/B is higher
than 10.
63
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