a parametric study of seismic response analysis of reinforced soil retaining structures with plaxis...
TRANSCRIPT
INFLUENCE OF A PARAMETRIC STUDY OF SEISMIC RESPONSE ANALYSIS OF
REINFORCED SOIL RETAINING STRUCTURES
WITH PLAXIS
by
Tahir Erdem Öztürk
B.S., Civil Engineering, Boğaziçi University, 2003
Submitted to the Institute for Graduate Studies in
Science and Engineering in partial fulfillment of
the requirements for the degree of
Master of Science
Graduate Program in Civil Engineering
Boğaziçi University
2005
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INFLUENCE OF A PARAMETRIC STUDY OF SEISMIC RESPONSE ANALYSIS OF
REINFORCED SOIL RETAINING STRUCTURES
WITH PLAXIS
APPROVED BY:
Prof. Erol Güler .........................
(Thesis Supervisor)
Prof. Cem Avcı .........................
Prof. Sabri Altıntaş .........................
DATE OF APPROVAL: .........................
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ACKNOWLEDGEMENTS
I owe special thanks to Prof. Dr. Erol Güler for his helpful guidance through out this
thesis.
I have very much benefited from the discussions with my dear friends in the Soil
Mechanics laboratory, among whom I would like to mention especially Öznur Selek,
Semih Büyüktunçer , Yavuz Tokmak and Mustafa Kalafat. I thank them all.
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ABSTRACT
A PARAMETRIC STUDY OF SEISMIC RESPONSE ANALYSIS OF
REINFORCED SOIL RETAINING STRUCTURES
WITH PLAXIS
In Turkey, the attention on the seismic performance of reinforced soil structures has
dramatically increased after 1999 Adapazarı Earthquake. This increase has led to the use of
dry-stacked concrete blocks in geosynthetic reinforced soil retaining wall construction.
Because of its ease of construction and the satisfactory performance under seismic loading
it is becoming widely used in Turkey. In addition, its aesthetically pleasing appearance and
cost-efficiency is increasing its popularity.
In this study, a parametric study of seismic response analysis of reinforced soil
retaining structures was performed using a finite element analysis with a commercial
computer program, Plaxis. It is aimed to determine the influence of reinforcement length,
reinforcement spacing, wall height and block width on seismic-induced permanent
displacements. Permanent displacements under earthquake loading conditions associated
with different L/H ratios and reinforcement spacing for different wall heights varying
between 2 m to 10 m are investigated. 20 seconds of Adapazarı earthquake was applied in
dynamic analysis to understand the response of the reinforced soil retaining walls subjected
to an earthquake.
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ÖZET
PLAXIS PROGRAMI İLE DONATILI İSTİNAT YAPILARININ SİSMİK
TEPKİLERİNİN PARAMETRİK ANALİZİ
Türkiye’de, donatılı zemin yapılarının sismik performansına olan ilgi 1999
Adapazarı depreminden sonra önemli ölçüde artmıştır. Bu ilgi artışı geosentetik donatılı
istinat duvarlarında harçsız örülmüş beton blokların kullanımına yol açmıştır. İnşaa
kolaylığı ve deprem yükü altındaki tatmin edici performansından dolayı bu tür yapılar
Türkiye’de çokça kullanılmaya başlamıştır. Ayrıca estetik görünümü ve düşük
maliyetinden dolayı popülerliği günden güne artmaktadır.
Bu çalışmada donatılı zemin istinad yapılarının sismik tepki analizleri, sonlu
elemanlar yöntemi ile hesap yapan Plaxis programı kullanılarak yapılmıştır. Donatı
uzunluğu, donatı aralığı, duvar yüksekliği ve blok genişliği gibi parametrelerin depremde
oluşan kalıcı yer değiştirmelere olan etkilerinin incelenmesi amaçlanmıştır. Farklı L/H
oranları ve donatı aralıklarının deprem yüklemesi durumundaki kalıcı yer değiştimelere
olan etkisi, 2 m - 10 m arasında değişen farklı duvar yükseklikleri için araştırılmıştır.
Donatılı zemin istinad duvarının gerçek deprem yükü altındaki tepkisinin anlaşılması
amacıyla Adapazarı depreminin 20 saniyesi modele uygulanmıştır.
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TABLE OF CONTENTS
ACKNOWLEDGMENTS ....................................................................................................iii
ABSTRACT.......................................................................................................................... iv
ÖZET ..................................................................................................................................... v
LIST OF FIGURES .............................................................................................................. ix
LIST OF TABLES..............................................................................................................xiii
LIST OF SYMBOLS..........................................................................................................xiv
1. INTRODUCTION ............................................................................................................ 1
2. LITERATURE REVIEW ................................................................................................. 5
2.1. Reinforced Soil Structures ......................................................................................... 5
2.1.1. Description of Reinforced Soil Principles ...................................................... 5
2.1.2. The Elements of Reinforced Soil Structures................................................... 7
2.1.2.1. The Backfill Soil ............................................................................... 7
2.1.2.2. Reinforcement................................................................................... 8
2.1.2.3. Facing Unit ....................................................................................... 9
2.1.2.4. Foundation Soil............................................................................... 12
2.1.3. Historical Development of Reinforced Soil Structures ................................ 12
2.1.4. Advantages and Disadvantages of Reinforced Soil Retaining Walls ........... 14
2.1.5. Performance of reinforced Soil Structures During Recent Earthquakes ...... 15
3. DESIGN OF GEOSYNTHETIC REINFORCED SEGMENTAL RETAINING
WALLS............................................................................................................................ 19
3.1. Modes of Failure...................................................................................................... 19
3.2 External Stability ..................................................................................................... 21
3.2.1. Base Sliding .................................................................................................. 25
3.2.2. Base overturning ........................................................................................... 26
3.2.3. Bearing Capacity........................................................................................... 27
3.3. Internal Stability ...................................................................................................... 30
3.3.1. Reinforcement Loads.................................................................................... 30
3.3.2. Over-stressing of Reinforcement .................................................................. 31
3.3.3. Reinforcement Anchorage ............................................................................ 31
3.3.4. Internal Sliding ............................................................................................. 33
3.4. Facing Stability ........................................................................................................ 36
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3.4.1.Interface Shear ............................................................................................... 36
3.4.2.Connection Failure......................................................................................... 37
3.4.3.Local Overturning.......................................................................................... 38
3.4.4.Crest Toppling ............................................................................................... 39
4. SEISMIC ANALYSIS APPROACH.............................................................................. 40
4.1. Pseudo-static Methods ............................................................................................. 40
4.1.1. Mononobe-Okabe Earth Pressure Theory..................................................... 40
4.1.1.1. Calculation of Earth Dynamic Force .............................................. 40
4.1.1.2. Distribution of Dynamic Lateral Earth Pressure and Point
of Application ................................................................................. 42
4.1.1.3. Orientation of Active Failure Plane ................................................ 43
4.1.2. External Stability Calculations for Walls ..................................................... 45
4.1.3. Internal Stability Calculations for Walls and Slopes .................................... 46
4.1.4. Two-part Wedge Failure Mechanism ........................................................... 48
4.1.5. Log Spiral Failure Mechanism ..................................................................... 51
4.1.6. Circular Slip Failure Mechanism.................................................................. 53
4.1.7. Selection of Seismic Coefficients ................................................................. 55
4.1.8. Comparisons between Selected Pseudo-Static Methods .............................. 59
4.1.9. Pseudo-dynamic Methods............................................................................. 61
4.2. Displacement Calculations ...................................................................................... 63
4.2.1. Newmark’s Method and Variations.............................................................. 63
4.2.2. Empirical Approaches................................................................................... 64
4.3. The Finite Element Method of Analysis of Reinforced Soil Retaining Walls ........ 66
4.3.1. The Finite Element Method .......................................................................... 66
4.3.2. Previous Studies on Seismic Analysis of Reinforced Soil Retaining Walls
with FEM and Finite Difference Method ..................................................... 70
4.4. The Plaxis Program.................................................................................................. 73
5. MODELING OF REINFORCED SOIL RETAINING WALLS WITH PLAXIS ......... 76
5.1. Material Modeling ................................................................................................... 77
5.1.1. Modeling of the Soils.................................................................................... 77
5.1.2. Modeling of Reinforcement.......................................................................... 78
5.1.3. Modular Block Facing Modeling.................................................................. 79
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5.1.4. Modeling of Interfaces.................................................................................. 81
5.2. Boundary Modeling ................................................................................................. 81
5.3. Mesh Generation...................................................................................................... 82
5.4. Determining the Initial Conditions .......................................................................... 82
6. CALCULATIONS........................................................................................................... 84
6.1. Stage Construction................................................................................................... 84
6.2. Dynamic Analysis.................................................................................................... 84
6.2.1. Seismic Loading ........................................................................................... 84
6.2.1.1. Earthquake Input Record ................................................................ 84
6.2.2. Damping........................................................................................................ 85
7. RESULTS ........................................................................................................................ 87
8. CONCLUSIONS AND REMARKS ............................................................................... 98
REFERENCES .................................................................................................................. 100
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LIST OF FIGURES
Figure 1.1. Typical geosynthetic-reinforced soil segmental retaining wall cross-section….2
Figure 1.2. Modes of failure for reinforced SRW structures: external; internal …………...3
Figure 2.1. The components of the reinforced soil retaining wall………………………….5
Figure 2.2. Stress transfer mechanism of soil reinforcement…………………...…………..6
Figure 2.3. Soil passive resistance in reinforcements……...……………………………....7
Figure 2.4. Modular block facing with geogrid reinforcement………………………..…..11
Figure 2.5. The west end of Grand Wall Built of soil and reeds in China……………..….13
Figure 2.6. The photo of Zigurat Wall in 60 high with two directional spacing in India…15
Figure 2.7. Tanata Wall and the around structures after Kobe Earthquake ……................18
Figure 3.1. A fail reinforced soil gabion wall…...….……………………………………..20
Figure 3.2. Geometry and forces in external stability calculations for reinforced SRW
structures…………………………………...………………...………….……22
Figure 3.3. Resisting moments for base overturning in external stability calculations for
reinforced SRW structures……………………...……………………….……26
Figure 3.4. Geometry and forces used to calculate reinforcement loads for reinforced
SRW structures…………………………………………….…………………32
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Figure 3.5. Geometry and forces used to calculate anchorage capacity of reinforcement
layers in SRW structures……………………………………………………...32
Figure 3.6. Geometry and forces used to calculate internal sliding of reinforcement layers
in reinforced SRW structures………………….……...…....…………...…….34
Figure 3.7. Geometry and forces used to calculate interface shear and overturning of the
facing column for reinforced SRW structures……………..…………….…...37
Figure 4.1. Forces and geometry used in pseudo-static seismic analysis……..……….…41
Figure 4.2. Earth pressure distributions due to soil self-weight………………..…………44
Figure 4.3. Forces and geometry for external stability calculations for base sliding and
overturning…………...…………………………………...……………..…....45
Figure 4.4. Calculations of tensile load, Ti, in a reinforcement layer due to dynamic earth
pressure and wall inertia for segmental retaining walls …………….……….49
Figure 4.5. Calculations of tensile load, Ti, in a reinforcement layer for reinforced soil
walls with extensible reinforcement using the FHWA (1996) method ...........49
Figure 4.6. Two-part wedge analysis: free-body diagram; with reinforcement forces ......50
Figure 4.7. Log spiral analysis :(a) free-body diagram; (b) with reinforcement forces…..52
Figure 4.8. Circular slip analysis: (a) circular slip geometry; and (b) method of slices.…55
Figure 4.9. Influence of seismic coefficients, kh and kv and wall inclination angle, ω, on
dynamic earth force, PAE…………………….……………………………….58
Figure 4.10. Comparison of wedge and log spiral pseudo-static methods)……….………60
Figure 4.11. Pseudo-dynamic method………………………………………..….………..62
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Figure 4.12. Point of application of dynamic force increment……………………..…..…63
Figure 4.13. Calculation of permanent displacements using Newmark’s method……......65
Figure 4.14. Nondimensionalized displacement in terms of d/(vm2/kmg) versus ac ratio
kc/km (after Cai and Bathurst 1996)………………..………………………..66
Figure 4.15. Typical finite element meshes………………………………..…...…......…..67
Figure 4.16. The finite difference model of reinforced soil retaining wall…..…................74
Figure 4.17. Position of nodes and stress points on the element………………………......75
Figure 5.1. Plaxis window and numerical model of reinforced soil wall………………….76
Figure 5.2. The geometry of model wall…………………………………………………..77
Figure 5.3. Modular block Facing………………………………………………….……..80
Figure 5.4. A-A detail of modular block in the model…………………………………....80
Figure 5.5. The finite element mesh of reinforced soil wall in current analysis……….….83
Figure 6.1. The acceleration time history of Sakarya Earthquake ……………………..…86
Figure 7.1. Acceleration measurements points ………………………………………...…90
Figure 7.2. The acceleration time history at point B for H=2m, H=6m, H=10m………….90
Figure 7.3. The acceleration time history at point A for H=2m…………………………...91
Figure 7.4. The acceleration time history at point A for H=6m……………….…………..91
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Figure 7.5. The acceleration time history at point A for H=10m………………………….92
Figure 7.6. Measured Peak Accelerations on upper layers at point A………………….…92
Figure 7.7. Total Displacement Change According to H, Lw = 0.2 and γ=23kN/m3 …….93
Figure 7.8. Total Displacement Change According to H, Lw = 0.4 and γ=23kN/m3 …….93
Figure 7.9. Total Displacement Change According to H, Lw = 0.2 and γ=13kN/m3……..94
Figure 7.10. Total Displacement Change According to H, Lw = 0.4 and γ=13kN/m3…....94
Figure 7.11. Per cent Change in Total Displacement with Respect to Change in L /H
from 0.7 to 1, Spacing=0.2……………………………………………..……95
Figure 7.12. Per cent Change in Total Displacement with Respect to Change in L /H
from 0.7 to 1, Spacing=0.4…………………..………………………………95
Figure 7.13. Total Displacement according to H, L/H=0.7, S=0.2m, γ= 23kN/m3 …......96
Figure 7.14. Total Displacement according to H, L/H=0.7, S=0.4m, γ= 23kN/m3 ……...96
Figure 7.15. Per cent Change in Total Displacement with Respect to Unit Weight of
Modular Block from 13kN/m3 to 23kN/m3, L/H =0.7, Block Width=0.2…..97
Figure 7.16. Per cent Change in Total Displacement with Respect to Unit Weight of
Modular Block from 13kN/m3 to 23kN/m3, L/H=1, Block Width=0.2m…..97
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LIST OF TABLES
Table 2.1. Approximate soil design parameters ranges………...………………………....9
Table 3.1. Recommended minimum Factors of Safety for Design of Geosynthtic
Reinforced SRW Structures…………………………………….………….…..20
Table 3.2. Bearing capacity factors………………………….……………………...……..29
Table 5.1. Material Properties of Soil Layers……………….………………………….…79
Table 5.1. Material Properties of Modular Block Facing……………………………....…80
Table 7.1. Summary of Displacement Values (cm).............................................................88
Table 7.2. Summary of Displacement Values (cm) for Newmark and Bathurts Method....89
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LIST OF SYMBOLS/ ABBREVIATIONS
a(t) ground acceleration with time t (m/s2)
acs minimum peak connection strength (N/m)
au minimum peak interface shear strength (N/m)
Bf footing width (m)
B’f equivalent footing width (m)
c soil cohesion (N/m2)
cf foundation soil cohesion (N/m2)) capacity design (dimensionless)
Cds coefficient of direct sliding (dimesionless)
Ci coefficient of interaction of anchorage (pullout) capacity design
(dimensionless)
e eccentricity (m)
fg ground motion predominant frequency
fl wall fundamental frequency
Fdtyn i dynamic reinforcement load (component) in reinforcement layer i (N/m)
F i total reinforcement load in reinforcement layer i (N/m)
Fsta i static reinforcement load (component) in reinforcement layer i (N/m)
FSbc factor of safety against bearing capacity failure (dimensionless)
FScs factor of safety against connection failure (dimensionless)
FSgl factor of safety against global stability failure (dimensionless)
FSos factor of safety against reinforcement tensile over-stress (dimensionless)
FSot factor of safety against base overturning (dimensionless)
FSotc factor of safety against crest toppling (dimensionless)
FSoti factor of safety against internal overturning for conventional SRW structures
(dimensionless)
FSotl factor of safety against local overtuning for reinforced SRW structures
(dimensionless)
FSpo factor of safety against pullout (dimensionless)
FSsc factor of safety against interface shear failure (dimensionless)
FSsl factor of safety against base sliding (dimensionless)
FSsli factor of safety against internal sliding (dimensionless)
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g gravitational constant (m/s2)
h height at back of reinforcement soil zone used in external stability
calculations (m)
hIR height from toe of wall to line of action of inertial force PIR (m)
hzi height of soil at back of reinforced soil zone used in internal sliding
calculations (dimensionless)
hβ height from base of wall to center of gravity of wedge of soil above
reinforced soil zone (m)
H vertical wall height measured at face of wall (m)
Hemb embedment depth of wall (m)
Hf leveling pad thickness (m)
Hh hinge height of facing column (m)
Hw height of facing unit (m)
kh horizontal seismic coefficient (dimensionless)
kh (ext) value of kh used for all external stability calculations and internal sliding
calculations for reinforced SRW structures (dimensionless)
kh (int) value of kh used for all internal and facing stability calculations for reinforced
SRW structures (dimensionless)
kv vertical seismic coefficient (dimensionless)
KA static earth pressure coefficient calculated using Coulomb earth pressure
theory (dimensionless)
KAH horizontal component of static earth pressure coefficient calculated using
Coulomb earth pressure theory (dimensionless)
KAE dynamic earth pressure coefficient calculated using Mononbe-Okabe (M-O)
method (dimensionless)
KAEH horizontal component of dynamic earth pressure coefficient calculated using
Mononbe-Okabe method (dimensionless)
LAi anchorage length of reinforcement layer i (m)
Lg distance from the toe of a SRW unit to the center of gravity of theunit
(including contribution of granular soil infill volumes if applicable)
Li total length of reinforcement layer i beginning at face of wall (m)
Lmin base width of reinforced soil zone plus facing column ≤ H (m)
Lw width of facing column (toe to heel dimension of SRW unit) (m)
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Mo driving moment taken about toe of wall (N-m/m)
Mo (z) driving moment over depth z (N-m/m)
Mr resisting moment taken about toe of wall (N-m/m)
Mr (z) resisting moment due to weight of facing column over depth z (N-m/m)
m ratio of moment arm of dynamic active earth force to wall height
(dimensionless)
N number of reinforcement layers (dimensionless)
Nc, Nγ, Nq bearing capacity coefficients (dimensionless)
Nh integer number of standard SRW units comprising hinge height of facing
column (dimensionless)
Nw total number of standard SRW units in facing column (dimensionless)
Nz integer number of facing units above the target point of rotation at depth z
(dimensionless)
PA static active earth force (N/m)
PAH horizontal component of static active earth force (N/m)
PAE (total) dynamic earth force (N/m)
PAEH horizontal component of (total) dynamic active earth force (N/m)
PAEH (z) horizontal component of (total) dynamic active earth force acting over depth z
(N/m)
PIR horizontal inertial force due to the reinforced soil mass used in external
stability factor of safety calculations (N/m)
qult ultimate bearing capacity of the foundation soil (N/m2)
RFCR creep reduction factor (dimensionless)
RS base sliding resistance at bottom of reinforced soil zone including facing
column for reinforced SRW structures (N/m)
RSW base sliding resistance at bottom of facing column for conventional SRW
structures (N/m)
RS (z) internal sliding resistance at depth z below the crest of the wall (N/m)
Svi contributory area corresponding to reinforcement layer i (m2/m)
Ta (dyn) allowable tensile load for the reinforcement under seismic loading (N/m)
Tci peak connection capacity corresponding to reinforcement layer i
Tpull i peak anchorage (pullout) capacity corresponding to reinforcement layer i
(N/m)
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Vu (z) peak interface shear capacity at interface located at depth z below crest of
wall (N/m)
W weight of active earth wedge behind retaining wall weight of
WA weight of static internal failure wedge (AASHTO/FHWA method) (N/m)
Wh weight of facing column at base of wall using hinge height (N/m)
Wi total weight of the reinforced soil zone extending from the back weight ofof
the facing column to length Lmin beyond the face of the wall and having
constant height H (N/m)
W’i reduced weight of the reinforced zone extending from the back of the facing
column to length 0,5H beyond the face of the wall and having constant height
H used to calculate inertial force PIR or PIR (z) (N/m)
Ww total weight of facing column (N/m)
Wr total weight of reinforced sol zone ( = Ww + Wi + Wβ) (N/m)
Wβ weight of the wedge of soil in the slope above the crest of the wall wall at
height H (N/m)
W’β reduced weight of the wedge of soil in the slope above the crest of the wall at
height H used to calculate inertial force PIR or PIR (z) (N/m)
Xh horizontal distance from the toe of the facing column to the center of gravity
of the facing column corresponding to the hinge height weight Wh (m)
Xi horizontal distance from the toe of the facing column to the center of gravity
of the reinforced soil zone corresponding to the weight Wi (m)
Xw horizontal distance from the toe of the facing column to the center of gravity
of the facing column corresponding to the weight Ww (m)
Xβ horizontal distance from the toe of the facing column to the center of gravity
of the wedge of soil corresponding to the weight Wβ (m)
yi vertical distance from point of rotation on wall face to reinforcement layer I
(m)
ydyn (z) moment arm between the point of rotation at depth z and the centroid of the
dynamic earth pressure distribution (m)
zi depth from crest of wall to reinforcement layer i (m)
zidyn moment arm between the point of rotation at depth z and the line of action of
the dynamic earth force increment (m)
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zvi distance from the crest of the wall to the middle of the contributory area Svi
(m)
αAE orientation of failure plane from horizontal using M-O method (°)
β backslope angle(°)
δ mobilized interface friction angle (°)
δw mobilized interface friction angle at the back of wall facing column (°)
ф peak friction angle of soil (°)
фb peak friction angle of retained (backfill) soil (°)
фcv residual (constant volume) friction angle of soil (°)
фd peak friction angle of drainage (leveling pad) soil (°)
фf peak friction angle of foundation soil (°)
фr peak friction angle of reinforced (infill) soil (°)
γ unit weight of soil (N/m3)
γb unit weight of retained (backfill) soil (N/m3)
γf unit weight of foundation soil (N/m3)
γr unit weight of reinforced (infill) soil (N/m3)
γw unit weight of SRW units (N/m3)
λcs slope of peak connection strength failure envelope (°)
λu slope of peak interface shear strength failure envelope for SRW units(°)
µb masonry friction reduction factor (dimensionless)
σvi average overburden pressure acting over anchorage length LAi (N/m2)
θ seismic inertia angle (°)
ω wall inclination angle (positive in a clockwise direction from the vertical) (°)
AASHTO American Association of State Highway and Transportation Officials
DMSRW Design Manual for Segmental Retaining Walls (Second Edition 1997)
FEM Finite Element Method
FHWA Federal Highway Administration
NCMA National Concrete Masonry Association
MSE Mechanically Stabilized Earth
MBW Modular Block Wall
M-O Mononbe-Okabe (pseudo-static earth pressure theory)
SRW Segmental Retaining Wall
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1. INTRODUCTION
Due to their cost effectiveness and increasing acceptance, large number of reinforced soil retaining structures is being designed and constructed throughout the world and also in Turkey. In order to gain better insight into mechanism affecting the behavior of such structures, engineers are turning to numerical experimental (simulation) analysis. For both under the static loading conditions and dynamic loading conditions, currently the most popular numerical analysis technique in use is the finite element method. This powerful analytical tool holds much promise for simulating the behavior of reinforced soil retaining structures, especially under dynamic stress conditions which are accepted as a very sophistical manner. Current conceived and executed numerical experiments offer the possibility to improve the understanding of the effects of dynamic loading on reinforced soil retaining structures and to demonstrate the influence of the component properties such as reinforcement stiffness, vertical spacing of the reinforcement along the wall, facing type and backfill material of the reinforced soil zone, on the system response to an earthquake. Numerical simulations were carried out to investigate the influence of reinforcement stiffness, backfill material type and vertical spacing of the reinforcement on the seismic response of 2-10m high reinforced soil retaining wall with modular block facing. The wall height, number of reinforcement layers and reinforced soil volume are typical of actual structures in the field. The Plaxis program which was used in the analysis of seismic response of reinforced soil walls, is a finite element package specifically intended for analysis of deformation and stability in geotechnical engineering projects. Geotechnical applications require advanced constitutive modals for the simulation of the nonlinear and time dependent behaviour of soils. The modeling of the soil itself is an important issue; many geotechnical engineering projects involve the modeling of the structures and the interaction between the structures and the soil. In this finite element program a two-dimensional plain strain model is used for structures with a (more or less) uniform cross-sections and corresponding stress-state and loading scheme over a certain length perpendicular to the cross section. The use of segmental retaining walls that include dry-stacked concrete block units as the facia system together with extensible sheets of polymeric materials (geosynthetics) that internally reinforce the retained soils and anchor the facia has gained wide popularity in North America (Bathurst and Simac 1994). These structures have also been reported in Europe, Scandinavia and Australia in recent years (Cazzuffi and Rimaldi, 1994; Gourc et al., 1990; Knutson, 1990; Won, 1994). An example of a reinforced segmental retaining wall structure is illustrated in Figure 1.1. The distinguishing feature of these structures is the facing column that is constructed using mortarless modular concrete block units that are stacked to form a wall batter into the retained soils (typically 3° to 15° from vertical). The economic benefits of these systems over conventional reinforced concrete gravity wall structures and mechanically stabilized soil retaining walk that use inextensible (steel) reinforcement) and select backfills have been demonstrated in several of the references cited in an earlier paper by Bathurst and Simac (1994).
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Figure 1.1. Typical geosynthetic-reinforced soil segmental retaining wall cross-section
(after Simac et al., 1991)
Stability analyses for geosynthetic-reinforced soil walls under static loading conditions (including segmental retaining wall systems) involve separate calculations to establish factors of safely against external modes of failure and internal modes of failure (Figure 1.2). External stability calculations consider the reinforced soil zone and the facing column as a monolithic gravity structure. The evaluation of factors of safety against base sliding, overturning about the toe and foundation bearing capacity is analytically identical to that used for conventional gravity structures. Internal stability analyses for geosynthetic-reinforced soil walls are carried out to ensure that the structural integrity of the geosynthetic-reinforced soil mass is preserved with respect to reinforcement over-stressing and pullout of geosynthetic reinforcement layers from the anchorage zone.
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Figure 1.2. Modes of failure for reinforced SRW structures: external (a,b,c); internal
(d,e,f); and facing (g,h,i,j) (after Bathurst and Cai 1995)
A comprehensive design methodology has been proposed by the National Concrete Masonry Association (NCMA) for the static analysis of segmental retaining walls (Simac et al., 1993; Bathurst et al., 1993). The NCMA guidelines address potential failure mechanisms not found in other geosynthetic-reinforced soil wall systems as illustrated in Figure 1.2 (f,g,h,i). The dry-stacked (without mortar) concrete blocks are discrete units that transmit shear through concrete keys, interface friction, mechanical connectors, or a combination of these methods. The stacked facing units result in potential failure plants through the facing column and this requires that additional stability calculations be carried out to estimate interface shear forces and to compare these forces with available shear capacity. In addition, the connection between the reinforcement layers and the facia is typically formed by extending the reinforcing layers along the interface between facing units to the front of the wall.
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LITERATURE REVIEW
Reinforced Soil Structures
Description of Reinforced Soil Principles
Reinforced Soil Retaining Structures are composite construction materials in which the strength of engineering fill is enhanced by the addition of tensile reinforcement in the form of both steel strips and geosynthetic fabrics or grids. The basic mechanism of Reinforced Soil Structures involves the generation of frictional forces between the soil and the reinforcement. These forces are manifested in the soil in a form of analogous to an increased confining pressure which enhances the strength of composite. Additionally the reinforcement has ability to unify a mass of soil that would otherwise part along the failure surface. The beneficial effects of soil reinforcement derive from:
• The soils increased tensile strength.
• The shear resistance developed from the friction at the soil-reinforcement interfaces
(Das, 1994).
Figure 2.1. The components of reinforced soil retaining wall
A reinforced soil mass is somewhat analogous to reinforced concrete in that the mechanical properties of the mass are improved by reinforcement placed parallel to the principle strain direction to composite for soils lack of tensile resistance. The composite material has the following characteristics:
• Stress transfer between the soil and reinforcement takes place continuously along the
reinforcement.
Compacted Backfill
Reinforcement
Facing Element
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• Reinforcements are distributed throughout the soil mass with a degree of regularity
and must not be localized.
Stresses are transferred between soil and reinforcement by friction (Figure 2.2) and/or passive resistance (Figure 2.3) depending on reinforcement geometry. Friction develops at locations where there is a relative shear displacement and
corresponding shear stress between soil and reinforcement surface. Reinforcing elements where friction is important should be aligned with the direction of soil reinforcement relative movement. Examples of such reinforcing elements are steel strips, longitudinal bars in grids, geotextile and some geogrid layers.
Figure 2.2. Stress transfer mechanism of soil reinforcement
Figure 2.3. Soil passive resistance in reinforcements
Passive resistance occurs through the development of bearing type stresses on "transverse" reinforcement surfaces normal to the direction of soil reinforcement relative movement. Passive resistance is generally considered to be the primary interaction for rigid geogrids, bar mat, and wire mesh reinforcements. The transverse ridges on "ribbed" strip reinforcement also provide some passive resistance.
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The contribution of each transfer mechanism for a particular reinforcement will depend on the roughness of the surface (skin friction), normal effective stress, grid opening dimensions, thickness of transverse members, and elongation characteristics of the reinforcement. Equally important for interaction development are soil characteristics, including grain size, grain size distribution, particle shape, density, water content, cohesion, and stiffness (FHWA, 1996). The Elements of Reinforced Soil Structures
The major components comprising a reinforced soil wall are ; the backfill soil, the reinforcement, the facing units and foundation soil. In the above these components are examined briefly. The Backfill Soil: Reinforced Soil Walls require high quality backfill for durability,
good drainage, constructability, and good soil reinforcement interaction which can be
obtained from well graded, granular materials. Many reinforced soil systems depend
on friction between the reinforcing elements and the soil. In such cases, a material
with high friction characteristics is specified and required. Some systems rely on
passive pressure on reinforcing elements, and, in those cases, the quality of backfill is
still critical. These performance requirements generally eliminate soils with high clay
contents.
From a reinforcement capacity point of view, lower quality backfills could be used for Reinforced Soil structures; however, a high quality granular backfill has the advantages of being free draining, providing better durability for metallic reinforcement, and requiring less reinforcement. There are also significant handling, placement and compaction advantages in using granular soils. These include an increased rate of wall erection and improved maintenance of wall alignment tolerances. The selection criteria of reinforced backfill should consider long-term performance of the completed structures, construction phase stability and the degradation environment created for the reinforcements. Much of our knowledge and experience with Reinforced Soil Structures today has been with select, cohesionless backfill. But researches are being carried out into the possibility of using cohesive soils as a backfill material. As clay is probably the most common soil encountered in the United Kingdom and also in Taiwan, encouraging results from such research would be of interest (Smith and Pole, 1980). In his research Simons pointed out that the tests were conducted at a very high rate of shear with failure resulting in less than 10 minutes under undrained conditions at the higher clay contents. It was argued that in the field the generation of pore water pressures could be controlled by construction rate and provision of suitable drainage layers. Combining this with an effective stress analysis, rather than somewhat conservative total stress analysis, Simon saw no reason why cohesive fill should not be used successfully (Ingold, 1982).
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Reinforcement: We can distinguish the reinforcement element into two main types:
• Metallic reinforcements: Typically it is made of mild steel. The steel is usually
galvanized or may be epoxy coated. The steel behaves as inextensible
reinforcement; deformation of the reinforcement at failure is much less than the
deformability of the soil. The geometry of the steel reinforcement is linear
unidirectional.
Table 2.1 Approximate soil design parameters ranges
• Nonmetallic (geosynthetic) reinforcements: Generally polymeric materials
consisting of polypropylene, polyethylene, or polyester are used. The deformation of
the reinforcement at failure is comparable to or even greater than the deformability of
the soil (FHWA, 1996).
Facing Unit: At a free boundary of reinforced soil structures, it is necessary to
provide some form of barrier so that the soil is contained. This skin can be either
flexible or stiff but it must be strong enough to hold back the local soil and to allow
attachment of the reinforcement. The types of facing elements used in the different
Reinforced Soil Walls systems control their aesthetics because they are the only
visible parts of the completed structure. A wide range of finishes and colors can be
provided in the facing. In addition, the facing provides protection against backfill
sloughing and erosion, and provides in certain cases drainage paths. The facing type
influences settlement tolerances. Major facing types are:
• Segmental precast concrete panels: The precast concrete panels have a minimum
thickness of 140mm and are of a cruciform, square, rectangular, diamond, or
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hexagonal geometry. Temperature and tensile reinforcement are required but will
vary with the size of the panel. Vertically adjacent units are usually connected with
shear pins. Precast elements can be cast in several shapes and provided with facing
textures to match environmental requirements and blend aesthetically into the
environment. Retaining structures using precast concrete elements as the facings can
have surface finishes similar to any reinforced concrete structure.
• Dry cast modular block wall (MBW) units: These are relatively small, squat concrete
units that have been specially designed and manufactured for retaining wall
applications. The mass of these units commonly ranges from 15 to 50 kg, with units
of 35 to 50 kg routinely used for highway projects. Unit heights typically range from
100 to 200mm for the various manufacturers. Exposed face length usually varies
from 200 to 450mm. Nominal width (dimension perpendicular to the wall face) of
units typically ranges between 200 and 600mm. Units may be manufactured solid or
with cores. Full height cores are filled with aggregate during erection. Units are
normally dry-stacked (i.e., without mortar) and in a running bond configuration.
Vertically adjacent units may be connected with shear pins, lips, or keys. Recently
introduced dry cast segmental block MBW facings raise some concerns as to their
durability in aggressive freeze-thaw environments because their water absorption
capacity can be significantly higher than that of wet-cast concrete. Historical data
provide little insight as their usage history is less than a decade. Further, because the
cement is not completely hydrated during the dry cast process, (as is often evidenced
by efflorescence on the surface of units), a highly alkaline regime may establish itself
at or near the face area, and may become an aggressive aging media for some
geosynthetic products potentially used as reinforcements. Freeze-thaw durability is
enhanced for products produced at higher compressive strengths and/or sprayed with
a posterection sealant.
• Metallic Facings: The original Reinforced Earth system had facing elements of
galvanized steel sheet formed into half cylinders. Although precast concrete panels
are now usually used in Reinforced Earth walls, metallic facings may be appropriate
in structures where difficult access or difficult handling requires lighter facing
elements.
• Geosynthetic Facing: Various types of geotextile reinforcement are looped around at
the facing to form the exposed face of the retaining wall. These faces are susceptible
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to ultraviolet light degradation, vandalism (e.g. target practice) and damage due to
fire. Alternately, a geosynthetic grid used for soil reinforcement can be looped
around to form the face of the completed retaining structure in a similar manner to
welded wire mesh and fabric facing. Vegetation can grow through the grid structure
and can provide both ultraviolet light protection for the geogrid and a pleasing
appearance.
Figure 2.4 Modular block facing with geogrid reinforcement
• Gabion facing: Gabions (rock-filled wire baskets) can be used as facing with
reinforcing elements consisting of welded wire mesh, welded bar-mats, geogrids,
geotextiles or the double-twisted woven mesh placed between or connected to the
gabion baskets. Facings using welded wire or gabions have the disadvantages of an
uneven surface, exposed backfill material, more tendencies for erosion of the
retained soil, possible shorter life from corrosion of the wires, and more
susceptibility to vandalism. These disadvantages can, of course, be countered by
providing shotcrete or by hanging facing panels on the exposed face and
compensating for possible corrosion. The greatest advantages of such facings are
low cost, ease of installation, design flexibility, good drainage (depending on the
type of backfill) that provides increased stability, and possible treatment of the face
for vegetative and other architectural effects. The facing can easily be adapted and
well-blended with natural country environment. These facings, as well as
geosynthetic wrapped facings, arc especially advantageous for construction of
temporary or other structures with a short-term design life.
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• Postconstruction facing: For wrapped faced walls, the facing - whether geotextile,
geogrid, or wire mesh can be attached after construction of the wall by shotcreting,
guniting, cast-in-place concrete or attaching prefabricated facing panels made of
concrete, wood, or other materials. This approach adds cost but is advantageous
where significant settlement is anticipated.
Foundation Soil: To determine the characteristics of foundation soils, boring may have to
be conducted to understand better the geological conditions of the foundation. The
standard penetration test is used to obtain the strength of the foundation. The depth of
investigation should be extended up to a firm soil layer that does not exhibit sign of
instability, settlement and liquefaction. For the sites where potential problems have been
revealed during pre-investigation, sounding, sampling and soil testing are required to
obtain additional information (Rimoldi, 2002).
The determination of engineering properties for foundation soils should be focused on establishment of bearing capacity, settlement potential, and position of ground water levels. Major foundation weakness and compressibility may require the consideration of ground improvement techniques to achieve the adequate bearing capacity, or limiting total or differential settlement (FHWA, 1996). Historical Development of Reinforced Soil Structures
As earth reinforcement instruments, inclusions have been used since prehistoric times to improve soil. Ancient historical relics are explored to study where natural materials have been employed as earth reinforcement over a period of 4000 years in China and Middle East countries. The use of straw to improve the quality of adobe, many primitive people used sticks and branches to reinforce mud dwellings. The construction of embankments, dykes, city-castle wall are performed by reinforcing of soil with some interesting methods. For example the embankments and castle wall construction that have originally practiced in China, was carried out adding some water and using tampers on soil with layer thickness of 10 cm. This method construction is the most suitable to the yellow earth and it was dated back to B.C 4000 and finding these structures over last several hundred years are quite amazing (Yamanouchi, 1993).
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Figure 2.5. The west end of Grand Wall, built of soil and reeds in China
During the 17th and 18th centuries, French settlers along the Buy of Fundy in Canada used sticks to reinforce mud dikes. Also examples include wooden pegs used for erosion control in England, and bamboo and wire mesh, used universally for revetment erosion control. The modern methods of soil reinforcement for retaining wall construction were pioneered by the French architect and engineer Henry Vidal in the early 1960s. His research led to invention and development of Reinforced Earth, a system in which steel strip reinforcement is used. The use of geotextile in retaining walls and slopes after the beneficial effect of reinforcement with geotextile was noticed in highway embankments over weak sub grade. The first geotextile-reinforced wall was constructed in France in 1971, and first structure of this type in United States was constructed in 1974. Since about 1980, the use of geotextil in reinforced soil has increased significantly. Geogrids for soil reinforcement were developed in 1980. The first use of geogrid in earth reinforcement was in 1981. Extensive use of geogrid products in the United States started in about 1983, and they now comprise a growing portion of the market. Recently, modular block dry cast facing units have gained acceptance due to their lower cost and nationwide availability, these small concrete units are generally mated with grid reinforcement, and the wall system is referred to as modular block wall (MBW). It has been reported that more than 200 such structures have been constructed in the United States, for highway applications to date. The current yearly usage for transportation- related applications is estimated at about 25 projects per year (FHWA, 1996). Advantages ad Disadvantages of Reinforced Soil Retaining Wall
Reinforced soil retaining walls have many advantages compared with conventional reinforced concrete and concrete gravity retaining walls:
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• Use simple and rapid construction procedures and do not require large construction
equipment. Do not require experienced craftsmen with special skills for
construction.
• Require less site preparation than other alternatives.
• Need less space in front of the structure for construction operations.
• Reduce right of way acquisition.
• Do not need rigid, unyielding foundation support because reinforced soil retaining
structures are tolerant to deformations.
• Are cost effective.
• Are technically feasible to heights in excess of 25m.
The relatively small quantities of manufactured materials required, rapid construction, and, competition among the developers of different proprietary systems has resulted in a cost reduction relative to traditional types of retaining walls. Mechanically stabilized earth (MSE) walls are likely to be more economical than other wall systems for walls higher than about 3m or where special foundations would be required for a conventional wall. One of the greatest advantages of MSE walls is their flexibility and capability to absorb deformations due to poor subsoil conditions in the foundations. Also, based on observations in seismically active zones, these structures have demonstrated a higher resistance to seismic loading than have rigid concrete structures. Precast concrete facing elements for MSE walls can be made with various shapes and textures (with little extra cost) for aesthetic considerations. Masonry units, timber, and gabions also can be used with advantage to blend in the environment.
Figure 2.6. The photo of Zigurat Wall, 60m high with two directional spacing in India
The following general disadvantages may be associated with all reinforced soil structures:
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• Require a relatively large space behind the wall or outward face to obtain enough
wall width for internal and external stability.
• Since design and construction practice of all reinforced systems are still evolving,
and contracting practices have not been fully standardized.
Performance of Reinforced Soil Structures During Recent Earthquakes
Largely qualitative observations of the performance of reinforced slopes and walls in
both USA, Japan and Turkey suggest that those structures perform well during seismic
events when located on competent foundation soils and above water table. The relatively
flexible nature of reinforced soil walls constructed with extensible and inextensible
reinforcement is routinely cited as the reason for good performance of those structures
during seismic event (Bathurst and Alfero, 1997).
In the below paragraphs the performance of the reinforced soil structures during 1989 Loma Prieta, USA, 1994 Northridge, USA, 1995 Grant Hanshin (Kobe), Japan, 1999 Ji-Ji, Taiwan, 1999 Sakarya, Turkey earthquakes will reviewed from the observations of the researchers. The performance of five reinforced slopes and walls that experienced the Loma Prieta earthquake of 1989 was evaluated by Collin in 1992. Two of these slopes were summarized as: A 3m high geogrid wrap face wall with 4H:1V sloping backfill above the top of the wall located 11 km from the epicenter and estimated horizontal acceleration at the site was 0.4 g . Although their originals design in corporated a maximum horizontal acceleration of 0.1-0.2g, no cracks were observed on top of wall. Nearby this a 15m high geogrid reinforced slope with a slope angle of 1H:1V was located 26 km from the epicenter and estimated horizontal acceleration of the site was 0.4 g. The face of the slope showed no sign of sloughing or damage. The performance of five reinforced soil slopes subjected to the Loma Prieta earthquake has shown that these structures can withstand severe ground motions (Collin et al., 1992). White and Holtz, (1997) reported the performance of seven geosynthetic reinforced slopes and wall allow which experienced significant to moderate shaking during 1994 Northridge, California earthquake. The performance of the seven geosynthetic reinforced slopes and wall shaken in the Northridge earthquake was adequate particularly when compared to the performance of other structures in the immediate vicinity (White and Holtz, 1997). Similar performances were observed in Northridge earthquake with extensible reinforced walls (Reinforced Earth) as reported by Frankenberger et al., (1996). The structures include 21 Reinforced Earth walls supporting rail line, highways, freeways an on/off ramps, city street, refinery oil storage tanks, housing development and bridge abutments. The distance of the structures were from earthquake epicenter, range from 13 to 83 km. In this area, ground accelerations ranged from 0.46 to 0.66 g horizontal and 0.1 to 0.29 g vertical.
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Regardless of the wall locations relative to the epicenter, all structures have remained fully intact and structurally sound well (Frankenberger et al., 1996). The performance of geogrid reinforced soil walls during the Great Hanshin (Kobe) earthquake in 1995 was reviewed by Tatsuoka, Koseki and Tateyama. In compression with other reinforced retaining structures as masonary leaning type and gravity type unreinforced concrete retaining walls showed very low stability against the strong seismic shaking. A number of geogrid reinforced soil retaining walls with full height rigid facing that are constructed in 1992 at Tanata, did not collapse despite the fact that the site was located in the one of the most severely shaken and seriously damaged areas. Tanata wall was located on the south slope of the existing embankment of JR Tohkaido railway line and was constructed to increase the number of railway trucks from four to five. The wall was 305m in total length with a maximum height of 6 m. In the area surrounding Tanata side where seismic intensity of 7 was estimated that this wall experienced the highest seismic load among other modern retaining walls (Tatsuoka and Tateyama, 1995; Tatsuoka et al., 1997). Also researchers Nishimura and his colleagues report the findings of the onsite investigation of geogrid reinforced soil walls stricken by Kobe earthquake. They investigated ten geogrid Reinforced soil retaining walls, nearby the hypocenter where a seismic intensity of 6 to 7 was recorded. They found that although the earthquake caused some settlement and cracks in the foundation, the wall themselves were almost free of deformation (Nishimura et al., 1996). The observations of steel reinforced earth structures such as reinforced retaining wall and reinforced natural ground structures did not suffer any catastrophic damage fulfilling their structural functions, despite their subjection of a strong seismic motion by maximum scale inland type earthquake as the 1995 Hyogoken Nambu earthquake , was made by the writers Otani and his collogues (Otani et al., 1996). The performance of several modular block reinforced soil retaining walls a on reinforced slopes at the vicinity of the fault of Ji-Ji earthquake of Taiwan in 1999 was evaluated by Ling, Leschinsky and Chou. Reinforced soil retaining walls and reinforced slopes have gained wide popularity in Taiwan over recent years because many of large scale housing and industrial development sites located on the slopes and hillsides. Taiwan has a geotechnical conditions that rendered a less conservative and more challenging design comparing to North America, Europe and Japan. The Ji-Ji earthquake caused some damages to reinforced soil retaining walls in Taiwan. The writers gave attention on the cracks behind the wall indicated that few of the structures suffered compound failure or did not have adequate global stability. The lack of seismic design consideration could be a major cause of failures in the earthquake (Ling et al., 2001).
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Figure 2.7. Tanata Wall and the around structures after Kobe Earthquake
And also following the August 1999 Sakarya Earthquake ( wM 7.4= ) the authors Martin and Olgun performed field investigation in the affected area to document the performance of improved soil sites and mechanically stabilized embankments. The reinforced Earth system at Arifiye Bridge Overpass was constructed of steel strips and compacted select backfill, performed well despite being shaken with ground acceleration more than 0.3 g and being subjected to fault related ground displacement of 350cm that occurred almost adjacent to the wall. An unreinforced earth embankment about 250m from the wall suffered heavy damage, settling more than 1m. The maximum permanent lateral movement of the wall facing panels was about 10cm and this occurred at about one third of the wall height above the base. The settlement along the centerline of the double wall system was estimated at 25-30cm primarily to lateral bugling of the system. The results suggested that well-designed conventionally constructed walls and with good foundation, tend to perform well under strong ground shaking (Olgun and Martin, 2002).
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DESIGN OF GEOSYNTHETIC REINFORCED SEGMENTAL RETAINING WALLS
Modes of Failure
Stability analyses for geosynthetic reinforced segmental retaining wall systems under static and seismic loading conditions involve separate calculations to establish factors of safety against external, internal and facing modes of failure (Figure 3.1). External stability calculations consider the reinforced soil zone and the facing column as a monolithic gravity structure. The evaluation of factors of safety against base sliding, overturning about the toe, and foundation bearing capacity is similar to that used for conventional reinforced concrete gravity structures. Internal stability analyses for geosynthetic reinforced soil walls are carried out to ensure that the structural integrity of the reinforced zone is preserved with respect to reinforcement over-stressing within the reinforced zone, pullout of geosynthetic reinforcement layers from the anchorage zone and internal sliding along a reinforcement layer. Facing stability analyses are carried out to ensure that the facing column is stable at all elevations above the toe of the wall and connections between the facing units and reinforcement layers are not over-stressed. Minimum recommended factors of safety for static and seismic design of geosynthetic reinforced SRW structures are given in Table 3.1. In general, minimum recommended factors of safety for seismic design are taken as 75 per cent of the values recommended for statically loaded structures following AASHTO/ FHWA practice.
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Figure 3.1. A failed reinforced soil gabion wall
Table 3.1. Recommended Minimum Factors of Safety for Design of Geosynthtic
Reinforced SRW Structures
External Stability
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External stability calculations are similar to those carried out for conventional (gravity) SRW structures with the gravity mass now taken as the composite mass formed by the reinforced soil zone and the facing column. The facing column may comprise a significant part of the gravity mass, particularly for low height structures (and hence generate additional inertial forces during a seismic event). For brevity, this gravity mass is called the reinforced mass or reinforced zone in this document The dynamic earth pressure distribution shown in Figure 3.2 (f) is used to calculate the destabilizing forces in otherwise conventional expressions for the factor of safety against sliding along the foundation surface, overturning about the toe of the structure and bearing capacity failure of the foundation soils. h ck a 2g= is used to calculate the magnitude of the uniformly applied horizontal seismic coefficient value kh, in all external stability calculations (i.e. ( )h hk k ext= ). The peak friction angle is taken as bφ = φ in earth pressure and force calculations. The calculation of force components AHP and dynHP∆ assumes full mobilization of inter face friction between the reinforced soil zone and the retained soil (i.e. δ = φ with φ equal to lesser of rφ and bφ values). The simplified geometry and body forces illustrated in Figure 3.2 are used in the external stability calculations to follow. Here; Wi is total weight of the reinforced zone extending from the back of the facing column to length Lmin beyond the face of the wall and having constant height H; Wβ represents contribution of the wedge of soil in the slope above the crest of the wall at height H; Ww defined as total weight of the facing column. w w w w w w wW N L H L H= γ = γ (3.1)
The results of parametric analyses reported by Bathurst and Cai (1995) have illustrated that as the backslope angle β for the infinite slope case increases, the factors of safety against external stability modes of failure diminish rapidly and reasonable solutions even for modest values of ground acceleration are not possible. This result is due in part to the formulation of earth forces calculated using the M-O method and the conservative estimates of soil strength parameters that are routinely used for the design and analysis of geosynthetic reinforced wall systems. In order to prevent this problem from developing the following empirical rule is proposed in this design guideline: Regardless of the wall geometry and reinforcement lengths the maximum value of the reinforced zone width Lmin (Figure3.2) is restricted to the height of the wall H. Hence Lmin ≤ H this approach has been adopted by the Reinforced Earth Company (RECO 1990) for the design of steel strip reinforced soil wails for the same reasons given above. The total weight of the reinforced soil zone is: r w iW W W Wβ= + + (3.2)
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