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1 INTRODUCTION
Slope stability is one of the important geotechnical engineering
applications. Geotechnical engineers aim is to achieve optimum design
with minimum cost using the readily available material. This research was
performed to find alternative solutions for soil slope stability application,
specifically slope of soil embankment. Various options for reinforcement
of retaining structure will be studied. Specifically reinforced earthen
retaining walls will be considered. The suitability of using Geosynthetics
products in retaining structure application will be studied in detailed.
2 BACKGROUND AND PREVIOUS WORK
Since most of the different constructions and structures are deal with soil,
soil must be controlled and perform to be provided to service that
constructions. Since most of these constructions are required to attend to
construct with earth retaining structure. This is which known soil stability.
2.1 METHODS OF SOIL STABILITY
Soil stability is a term used widely in civil engineering applications.
Stability could be gained simply by using a steeled mesh known as gabion
mesh. Another common method is widely used which work to provide
lateral support is known as conventional retaining wall. But most of field
applications now required a more effective stability. This could be applied
by using a specific manufactured material to reinforce the soil. This will
provide a mechanical process known as soil reinforcement. This
mechanical process helps the instability soil to against itself. Soil is
reinforced with polymer materials known as Geosynthetics. This study
evaluates the alternative of the conventional retaining wall structures by
using Geosynthetics reinforced structures known as the Mechanically
Stabilized Earth walls (MSEW).
2
2.2 SOIL REINFORCEMENT WITH GEOSYNTHETICS
Reinforced soil technique for reinstatement of failed slop using
Geosynthetics product is used as alternative of methods stated above.
Soil reinforcement based on controlling the load applied occurs due to soil
weight and other external loads may be considered. Reinforcement with
Geosynthetics material transfers the vertical load to tensile load applied
for a calculated natural compacted soil layer thickness to a specific
Geosynthetics material which fabricated for that suppose. This process
Lead that Load to developed at very low strains by the soil.
2.3 Geosynthetics
Geosynthetics is the term used to describe a range of generally polymeric
products used to solve civil engineering problems. Geosynthetics provide
long-lasting reinforcement, and to increase soil stability. When placed in
the direction of soil deformation, Reinforcement Geosynthetics generate
tensile forces to carry tensile stress. The high stiffness of the
Reinforcement Geosynthetics prevents excessive deformation in the soil.
Bonds develop between the soil and Reinforcement Geosynthetics
efficiently transferring stress into the surrounding soil through
interlocking, friction, and end bearing resistance.
The term is generally regarded to encompass seven main product
categories: Geotextile, Geogrid, Geonet, Geomembrane, Geosynthetics
clay liners, Geofoam and Geocomposite. The polymeric nature of the
products makes them suitable for use in the ground where high levels of
durability are required. Properly formulated, however, they can also be
used in exposed applications. Geosynthetics are available in a wide range
of forms and materials, each to suit a slightly different end use. These
products have a wide range of applications and are currently used in many
civil engineering problems. The following paragraphs describe each type
of Geosynthetics material and typical use in engineering applications.
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2.3.1 Geotextile
Geotextile is a permeable Geosynthetics made of textile materials. When
used in association with soil, have the ability to separate, filter, reinforce,
protect, or drain Geotextile are made from polypropylene or polyester
material.
2.3.2 Geogrid
Geogrid are synthetics planar structure primarily used for reinforcement
applications. Geogrid used as reinforcement material to add tensile
strength to soil matrix, so providing more stability structure. It's also used
as separated material when it used to separate fine-grained sub grade in
road way. Geogrid formed by a regular network of tensile elements with
apertures of sufficient size to interlock with surrounding fill material. It's
important to note that most Geogrids are manufactured to function
uniaxially although the present of the biaxial Geogrids and that well affect
the method manufactory. Geogrids have higher stiffness and strength than
most Geotextiles. Geogrid also used to tensile reinforce steep slopes,
retaining structures, and embankments constructed over soft foundation.
2.3.3 Geonet
Genets are formed by continuous extrusion of parallel sets of polymeric
ribs at acute angles to one another. When the ribs are opened, relatively
large apertures are formed into a netlike configuration. Their design
function is completely within the in-plane drainage area where they are
used to convey all types of liquids.
2.3.4 Geomembrance
Geomembranes are low permeability Geosynthetics used as fluid barriers.
Geomembranes are a good material used in landfill sites for the
containment of hazardous or municipal wastes and their leachates. In
many of these applications Geomembranes are employed with Geotextile
or mesh underlines which reinforce or protect the more flexible
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Geomembranes whilst also acting as an escape route for gases and
leachates generated in certain wastes.
2.3.5 Geosynthetics clay liners
Geosynthetic clay liner (GCL) is a woven fabric like material primarily
used for the lining of landfills. It is a kind of Geomembranes and which
Geosynthetics incorporates a betonies or other clay, which has a very low
hydraulic conductivity. The resulting lower permeability slows the rate of
seepage out of the landfill.
2.3.6 Geofoam
Geofoam is made of expended polystyrene (PES). Itβs used as a light
weight fill under a road sub-grid. Belt over a low load bearing soil.
Geofoam also has also found application for vibration damping, gas
venting and soil stabilization.
2.3.7 Geocomposite
Geocomposites is a combination made from two or more Geosynthetics
by bonding together (mostly Geomembranes/Geonet and Geotextile) for
specie applications in drainage, filtration, fluid transmission, erosion
control.
Geotextile and related products can combined with Geomembranes
material and other synthetics, to complement the best attributes of each
material. The most attributes should consider is drainage with a specific
volumetric flow. The hydraulic properties are a major consideration in
design. The flow rate obtained from the tests is reduced using reduction
factors considering soil clogging and blinding, creep reduction of void
space, intrusion of adjacent materials into Geotextile voids, chemical
clogging, and biological clogging. But sometime large capacity is
required for design.
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In this research we will spot light on georgic and Geocomposites
Geosynthetics materials to be consider for our studying.
3 Basic performance properties of Geogrid, Geotextile and Geonet
Geogrid:
Geogrid used in past in first appearance which was made of high density
of polyethylene (HDPE) and sometime made of PET which designed to
carry a load not exceed 250 kN per unit length and which widely used in
side slope reinforcement. Now, Geogrid is manufactured to be stronger
.Geogrid classified related to variety of stiffness which includes:
1. Stiff Geogrid, mostly HDPE with a monolithic mesh structure
2. Flexible Geogrid, mostly PET with PVC or acrylic coating with
mechanically connected longitudinal and transverse elements.
Geogrid fabrics on two functions related to suppose used uniaxially and
biaxial. In manufacturing uniaxial Geogrids, circular holes are punched on
the polymer sheet, which is subsequently drawn to improve the
mechanical properties. For biaxial Geogrids, square holes are made on the
polymer sheet, which is then drawn longitudinally and transversely.
Uniaxial Geogrid Biaxial Geogrid
Figure 1 Uniaxial and biaxial Geogrids
6
Geonet:
All Geonets are made of polyethylene. Geonet are made b Extrusion
corresponding sets of polymeric ribs at acute angles to one another. The
ribs are opened, relatively large apertures are shaped into a netlike pattern.
The only other materials in Geonets are carbon black and a processing
package. The specific gravity of most Geonets is in the range of 0.935 to
0.942.
Geotextile:
Geotextile are made primly of fibers or yarns. Thus these product could
be indentify by polymer were used .high strength polymer grids are made
from extruded sheet of polymer (polypropheline or polyethylene) where
first punched with a regular patterns of holes. Then sheet is stretched in
controlled temperature. Also Geotextile can make by strand, ribs, and
coated ribs.
Geotextile verify in filaments. Filaments are type of fibers which are
produced by extruding molten polymer through dies or spinnerets, which
can have holes of a required diameter.
Bonding mechanism (bonding is a process confirmed during rearrange
fibers (filaments/staple fiber) over conveyor belt in continuous fashion
(lapping) to form a loose web in a nonwoven Geotextile/Geogrid fabrics.
Thus it compressed and bonded by using one or combination of the
following processes:
1. Mechanical process (needle pouching).
2. Thermal bonding (under heat and pressure).
3. Chemical bonding (using bonding agents).
Geotextile material also different in woven or non-woven patterns,
thicknesses, masses per unit area (areal density). Specific properties were
defined by ASTM and GRI.
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4 FUNCTION AND APPLICATIONS
Geogrid can perform the separation, protection, and reinforcement.
Geocomposites (Geotextile/Geonet) are design to play a specific role
(mostly provide high capacity flow for drainage application).table 1 show
different functions related to their applications according to IFAI (modified
after IFAI, 1989).
5 TESTING STANDARDS FOR GEOGRID AND GEOCOMPOSITES
GEOSYNTHETICS BY ASTM AND GRI
Different type of Testing was developed relevant to their applications.
Several testing was provided use to serve industrial needs. On other hand
most civil engineering designs and applications require the Geosynthetics
materials to be tested with site-specific soils, with the testing conditions
representing those in the field. These kinds of tests are known as
performance tests. ASTM has developed standardized testing procedures
for Geogrid and Geocomposites Geosynthetics under Committee D35 for
could be listed as (related for their composite and suppose).The properties
should be tested for a specific Geosynthetics type:
1. Terminology
2. Mechanical Properties
3. Endurance Properties
4. Permeability and Filtration
5. Geosynthetics Erosion Control
6. Standards for the above listed properties are included in Appendix A
8
Table 1 functions related to their applications according to IFAI (modified after IFAI, 1989).
application Primary function products
Subgrade
stabilization
Separation/
Reinforcement/
Filtration
Geotextile/Geogrid
Railroad tracked
stabilization
Drainage/
Separation/
Filtration
Geotextile/Geogrid
Sedimentation
Control silt fence
Sediment retention/
Filtration/ Geotextile/Geogrid
Asphalt overlay Stress relieving layer/
Water proofing Geotextile/Geogrid
Soil reinforcement
Embankments
Steep slops
Vertical walls
Reinforcement
Reinforcement
Reinforcement
Geotextile/Geogrid
Geotextile/Geogrid
Geotextile/Geogrid
Erosion control filter Filtration/ Geotextile/Geogrid
Subsurface drainage
filter Filtration Geotextile/Geogrid
Geomembrance
protection
Protection
/cushion Geotextile/Geogrid
Subsurface drainage
Filtration/fluid
transmission
Prefabricated
Drainage composites
Surficial erosion
control
Turf Reinforcement
Erosion control mats
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6 MECHANICALLY STABILIZED EARTH WALL
Mechanically Stabilized Earth Wall (MSEW) is a generic term that
includes reinforced soil (a term used when multiple layers of inclusions
act as reinforcement in soils placed as fill). Reinforced Earth is a
trademark for a specific reinforced soil system.
6.1 APPLICATIONS
Mechanically Stabilized Earth Walls (MSEW) is cost-effective soil-
retaining structure that can tolerate much larger settlements than
conventional reinforced concrete walls. The MSEW structures are cost-
effective alternatives for most applications where reinforced concrete or
gravity type walls have traditionally been used to retain soil. These
include bridge abutments and wing walls as well as areas where the right-
of-way (R-O-W) is restricted, such that an embankment or excavation
with stable side slopes cannot be constructed. They are particularly suited
to economical construction in steep-sided terrain, in ground subject to
slope instability, or in areas where foundation soils are poor.
There are two primary purposes for using reinforcement in engineered
slopes:
1. To increase the stability of the slope, particularly if a steeper than safe
unreinforced slope is desirable or after a failure has occurred.
2. To provide improved compaction at the edges of a slope, thus decreasing
the tendency for surface sloughing.
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6.2 Advantages and Disadvantages
6.2.1 Advantages of Mechanically Stabilized Earth (MSE) Walls
MSE walls have many advantages compared with conventional reinforced
concrete and concrete gravity retaining walls. The following are the
advantages of using MSE walls:
1. Use simple and rapid construction procedures and do not require large and
heavy construction equipment.
2. Do not require experienced craftsmen with special skills for construction.
3. Require less site preparation than other alternatives.
4. Need less space in front of the structure for construction operations.
5. Reduce right-of-way acquisition.
6. Do not need rigid, unyielding foundation support because MSE structures
are tolerant to deformations.
7. Are relatively cost effective:
MSE walls are likely to be more economical than other wall systems for
walls higher than about 3 m (10 ft) or where special foundations would be
required for a conventional wall.
8. Are technically feasible to heights in excess of 25 m (80 ft).
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6.2.1 The Following General Disadvantages May Be Associated With
the Soil Reinforced Structures:
1. Require a relatively large space behind the wall or outward face to obtain
enough wall width for internal and external stability.
2. MSEW require select granular fill. (At sites where there is a lack of
granular soils, the cost of importing suitable fill material may render the
system uneconomical). Requirements for RSS are typically less
restrictive.
3. Suitable design criteria are required to address corrosion of steel
reinforcing elements, deterioration of certain types of exposed facing
elements such as Geosynthetics by ultra violet rays, and potential
degradation of polymer reinforcement in the ground.
4. Since design and construction practice of all reinforced systems are still
evolving, specifications and contracting practices have not been fully
standardized, in comparison with the RSS.
5. The design of soil-reinforced systems often requires a shared design
responsibility between material suppliers and owners and greater input
from agencies geotechnical specialists in a domain often dominated by
structural engineers.
6.3 MODULAR BLOCK WALL USING FLEXIBLE GEOGRID
REINFORCEMENT
Modular block, or segmental, retaining walls employ interlocking
concrete units serve as facial material that tie-back into the earth using
Geogrid material for reinforcement. Note that the Geogrid is the structural
material for the MSE wall. These pre-engineered modular systems are an
attractive, economical, and durable alternative to stone or poured concrete
12
retaining walls. The inherent design flexibility can accommodate a wide
variety of site constraints, project sizes, and aesthetic preferences.
Modular block wall with low extension Geogrid is designed to provide a
required flexibility and ability to absorb deformations due to poor subsoil
conditions in the foundations. Also, based on observations in seismically
active zones, this structure has demonstrated a higher resistance to seismic
loading than have rigid concrete structures.
Modular block MSE wall will be considered as a design alternative for the
proposed project. The other design alternative is a conventional cantilever
concrete retaining wall.
Flexible Geogrid Unit block
Figure 2 Modular block wall with flexible material.
13
6.3.1 MSE MODULAR BLOCK WALL DESIGN FOR A RAMP
OF A BRIDGE INSTABILITY SOIL
Geotechnical evaluation of the site soils where used along with proposed
wall heights and surcharge loading to determine the extent of the
reinforcement required to construct the Modular Block retaining Wall in
addition, water table and one hundred year flood elevations were
considered during design process.
6.3.1.1 Method Statement for Construction Modular Block Wall
System with Flexible Geogrid Reinforcement
The proposed system consists machine produced concrete modular blocks
and layer of Geogrid reinforcement embedded and anchored within the
retained soil fill which will interact with surrounding soil resulting in
stabilizing the soil mass and reducing the potential for movement of the
wall in response to the vertical load being transferred horizontally as
pressure against the back of the wall. It is also required to include a
drainage system immediately behind the modular blocks in form of ΒΎ"
single size aggregate separated from the soil fill by an adequate nonwoven
Geotextile filter.
The modular block wall system, schematically shown in figure (3)
consists of the following:
1- Leveling pad:
The leveling pad is placed under the wall facing elements to facilitate
proper alignment of facing blocks. It is commonly composed of crushed
stone (base course) or unreinforced concrete blinding.
14
In the event the foundation soil is weak, layer of Geogrid material could
be placed below and within the crushed soil layer.
2- Facing elements:
Is a component of the reinforced soil system used to prevent the soil from
raveling out between the rows of reinforcement. Common facings include
precast concrete panels; dry cast modular blocks, metal sheets and plates,
gabions, welded wire mesh, shotcrete, wood lagging and panels, and
wrapped sheets of Geosynthetics. The facing also plays a minor structural
role in the stability of the structure.
For this project the facing elements will compose of modular blocks (type
MB-H-20). The shape, size and the specifications for this standard block
are provided below in table 2.
Table 2 specifications for standard block
Specification Information
Size ( w x d x h ) 40 x 30 x 20 cm
Setback 10 mm per 200 mm
Weight approximate 32 kg
Cement Type used OPC
Strength 25 MPa concrete
Area 0.08 mΒ² per block
Maximum absorption % 5
15
30
0
Figure 4 Block unit
3- Drainage layer:
The drainage layer is approximately 30 cm (Β±5 cm) wide, placed behind
the wall facing blocks. The drainage layer is separated from the reinforced
fill by a nonwoven Geotextile fabric. The drainage layer shall be
composed of ΒΎ" single size aggregate.
Placement of well graded gravel immediately adjacent to modular blocks
is recommended for several reasons. Gravel has a high permeability that
will not impede water flow out of the reinforced mass and through the dry
stacked modular blocks. Gravel is not prone to piping through joints
between modular blocks. Gravel is also easily placed and compacted,
especially adjacent to elements such as modular blocks.
4- Reinforced fill:
Selected fill material which placed behind the wall in which the Geogrid
reinforcements layers are placed. MSE block walls require high quality
16
backfill for durability, good drainage, constructability, and good soil
reinforcement interaction which can be obtained from well graded and
single size granular materials. MSE systems depend on interface 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. When drainage layer is
placed behind the wall, granular fill material could be placed in reinforced
fill.
Reinforced fill proposed for this project has the following gradation:
Table 3 Reinforced fill gradation
Size
(mm) % passing PI
< 75 mm 100 %
Max. PI = 15% Sand Fraction
(0.075 β 4.75 mm) 40 β 60%
Silt and clay
< 0.075 mm < 20%
The reinforced fill shall be placed in not exceeding 20-cm (+5cm) in
compacted thickness with a minimum relative compaction of 95% of the
maximum density obtained from laboratory measurements using standard
effort or 90% of the maximum density obtained from modified proctor.
5- Reinforcement material:
The structural reinforcements where used for this project is Flexible-
Geogrid. Flexible-Geogrid is ideal for reinforcing earth retaining support
structures. Flexible Geogrid is a woven process manufactured grid from
high-modulus, low-creep synthetic yarns and have a protective PET
17
polymer PVC coating. Flexible reinforcement can be supplied in various
mesh sizes and standard ultimate strength of 35 kN/m. Geogrid has a 170
kN/mΒ² and 20 mm x 20 mm opining size.
Flexible-Geogrid is consider ideal for reinforcing earth retaining support
structures because flexible one exhibits considerably lower deformation
under permanent loading than many grids of equivalent nominal strength
from other manufactured and Transmits high tensile forces with low
elongation. Also has lower stress-strain elasticity behavior which provides
a high flexible earthen stability system resist the backfill and foundation
soil settlement.
The Geogrid and locations are to be in accordance with the designs and
finalized plans.
Figure 5 Flexible low-extension Geogrid
6- Geotextile filter:
Nonwoven Geotextile filter fabric are placed between the reinforced soil
and the drainage layer (coating each layer of reinforced soil), The
Geotextile fabric allow free drainage of water from the reinforced fill into
18
the granular layer while preventing the migration of fines into the
drainable soil inside the fabric.
7- Retained soil:
Is the fill material located between the mechanically stabilized soil mass
and the natural soil. This could be either soil excavated from the site
existing ground or imported fill. For this project, retained soil is the
existing soils on-site.
8- Topping, asphalt and barrier:
The pavement layer is placed on top the first layer with thickness equal to
30 cm.
Flexible post and beam barriers, when used, shall be placed at a minimum
distance of 1.0 m. (3.3 ft) from the wall face, driven 1.5 m (5 ft) below
grade, and spaced to miss the reinforcements where possible. If the
reinforcements cannot be missed, the wall shall be designed accounting
for the presence of an obstruction.
19
Figure 5 Section Geogrid reinforced modular block wall
20
6.3.1.2 INFORMATION DETAILS
Geometry
This submittal is prepared based on the received plans, the typical
geometry of the proposed wall is listed table below:
Table 4 Geometry design information
Geometry
stations
Height
range
(m)
Notes
from to
1 0+260 0+330 6.8 β 7.0
Single
wall with
traffic
surcharge
The proposed walls will be designed at height average equal to 7 meters,
with horizontal backfill. The facing material is to be composed of modular
blocks with inclination of 5Β° from the vertical.
Material properties
The properties of the reinforced fill, retained fill and foundation soils are
based on the geotechnical report prepared by others for this project and
available information. Detailing of the wall elements also specified in
statement method of construction above.
21
Water, boundary loads and seismicity
Water table is beyond the depth of influence. Accordingly, water will not
consider in design calculations.
Traffic load: A live traffic surcharge load of 20.0 kPa distributed was
applied to the top of the wall.
The preliminarily design incorporated seismic factor of 0.15 g.
6.3.1.3 DESIGN STANDARD AND FACTORS
The standard used for the design of this project is AASHTOO-2002/NHI-
043. This is based on allowable stress design (ASD) which is well
document and approved worldwide. The available resistances (shall
exceed the maximum calculated loads by a factor, called facto of safety
(FS). AASHTOO specified the minimum factors of safety, listed in table:
Table 5 Minimum requirement for safe design (LSD).
Item Factor of safety
(static)
Factor of safety
(seismic)
70% of static
Internal stability
pullout 1.5 1.05
Direct sliding at each
Geogrid level 1.5 1.05
Strength (Rapture) 1.5 1.05
Connection
(Geogrid-block) 1.5 1.05
External stability
Bearing capacity 2.5 1.875
Overturning e < B/6 e < B/3
Overall stability 1.5 1.125
External sliding 1.5 1.125
22
6.3.1.4 GEOSYNTHETICS REINFORCEMENT
The long term design strength (LTDS) of the flexible Geogrid is obtained
b applying a reduction factors o the material properties obtained from
standard laboratory testing.
The design factor of safety is applied to account for the uncertainty in the
determination if the material properties as well as the calculation and
mathematical modular error. The reduced strength is achieved by applying
these factors as shown in the following equation:
ππππ πππ =ππ’ππ‘
π πΉπ· Γ π πΉππ· Γ π πΉπ Γ π πΉππ Γ πΉπ
Where:
ππππ πππ = Maximum allowable design strength:.
ππ’ππ‘ = Ultimate tensile strength.
π πΉπ· = Strength Reduction factor due to creep: .
π πΉππ· =Strength Reduction factor due to installation damage.
π πΉπ = Strength Reduction factor for connection of seams .
π πΉππ = Strength Reduction factor for durability.
πΉπ
= Global factor of safety for design manufacture and extrapolation of data.
23
6.3.1.4 GEOTECHNICAL REPORT PARAMETERS
SOIL PROPERTIES:
REINFORCED SOIL PROPERTIES
Design value of internal angle of friction ππ
34.0Β°
Unit weight πΎπ 18.0 kN/mΒ³
Cohesion ππ 0.0
RETAINED SOIL PROPERTIES
Design value of internal angle of friction ππ
32.0Β°
Unit weight πΎπ 18.0 kN/mΒ³
Cohesion ππ 0.0
FOUNDATION SOIL PROPERTIES
Design value of internal angle of friction ππ
45Β°
Unit weight πΎπ
18.0 kN/mΒ³
Cohesion ππ
15.00 kPa
24
LATERAL EARTH PRESSURE COEFFICIENT:
Internal Stability
Reinforced soil earth pressure
coefficient πππ
0.283
Seismic inertia angle Ο
62.00Β°
External Stability
Retained soil earth pressure
coefficient πππ
0.307
Adhesive between Geogrid and
reinforced soil πΏ
32.00Β°
BEARING CAPACITY:
ππ 133.87
ππΎ 271.75
ππ 134.88
SEISMICITY:
Max. ground acceleration coefficients πΌΒ° 0.15 π
πΎππ πΌΒ° = 0.0 0.2771
πΎππ πΌΒ° = 0.150 0.4393
βπΎππ = πΎππ πΌΒ° = 0.150 β πΎππ πΌΒ° = 0.0 0.1622
25
Data Base for Geogrid with Block:
Ultimate strength of Geogrid= 35.0 kN/mΒ²
Cover ratio = 1.00
Table 6 Reduction Factors for reinforcement Geogrid
Reinforcement reduction factors
item Factor
Strength Reduction factor for
durability, πΉππ 1.03
Strength Reduction factor
installation damage, πΉπππ« 1.09
Strength Reduction factor creep,
πΉππ 1.60
Strength Reduction factor for
connection seams, πΉπππ 1.00
Reinforcement-Reinforced Soil Interaction Parameters:
Interaction parameter Factor
DIRECT SLIDING ANALYSIS FACTORS
Friction angle along Geogrid-soil
interface, Ο
29.0
PULLOUT COMPUTING FACTORS
26
Pullout resistance factors, F 0.9tanππ
Scale-effect correction factor, β 1.0Ω
Interaction coefficient determined
from pullout testing for a
particular reinforcement type Ci
0.9
Ξ± = 1.0 determined in laboratory specific tests performed on theΩGeogrid used.
VARIATION OF LATERAL EARTH PRESSURE COEFFICIENT
WITH DEPTH:
πΎ
πΎππππ πΏ β πΌΒ°
According to AASHTOO forπΌΒ° < 10:
πΏ = 0.0 And πΌΒ° = 0.0 is used
For all depth:
πΎ
πΎππππ 0 β 0 = 1.0
27
6.3.1.5 STABILITY ANALYSIS AND FINAL DESIGN
(A) CALCULATE THE EXTERNAL STABILITY-STATIC ANALYSIS
q = 20.0 kN/m Β²
LR Le
Soil
pre
ssu
re
Surc
harg
e p
ressure
Figure 6 Pressure due to the soil and surcharge load.
Retained soil lateral earth pressure coefficient:
Kab= tanΒ² 45 β
Οb
2
πΎππ = π‘ππΒ² 45 β32
2 = 0.307
Minimum Geogrid length:
πΏ
π» β₯ 0.7
45 +π
2
Sv
vv
P1
P2 + P3
28
πΏ
7β₯ 0.7 β πΏ = 0.7 Γ 7 = 4.9 π
Total Lateral load calculations
Geostatic earth load:
π1 =1
2Γ πΎπ Γ π»2 Γ πΎππ
π1 =1
2Γ 18 Γ 72 Γ 0.307 = 135.39
ππ
π
Live load:
π2 = ππΏ.πΏπΎππ Γ π»
π2 = 20 Γ 0.307 Γ 7 = 42.98 ππ
π
π3 = ππππ£πππππ‘ πΎππ Γ π»
π3 = 0.3 22 0.307 Γ 7 = 14.18 ππ
π
ππ = ππ‘ππ‘ππ = 135.39 + 42.98 + 14.18 = 192.55 ππ
π
ππ = 192.55ππ
π
29
(1) Check for the sliding stability
πΉππ =πΉ
ππ πΉ: πππ ππ π‘πππ πππππ
πΉ = π Γ π
π = tan πΏ
Where
πΏ : Adhesive between bottom Geogrid layer and foundation soil
πΏ = 32.0Β°
π = tan 32Β°
πΎπ = 18 ππ
π3
π = πΎπ Γ π» Γ πΏ
πΉ = 18 Γ 7 Γ 4.9 Γ tan 32Β° = 385.97 ππ
π
Factor of safety against sliding
πΉππ =πΉ
ππ=
385.79
192.55= 2.00 > 1.5
30
Check for the overturning stability
πΉπππ =ππΊ
πππ
ππΊ = π ΓπΏ
2= 617.4 Γ
4.9
2= 1512.63
ππ.π
π
πππ£ = π1 Γπ»
3+ π2 Γ
π»
2Γ π3 Γ
π»
2
πππ£ = 135.39 Γ7
3+ 42.98 Γ
7
2+ 14.18 Γ
7
2= 515.97
ππ.π
π
Factor of safety against overturning
πΉπππ =1512.63
515.97= 2.93 > 1.5
(2) Check for the bearing capacity
Check for the tension beneath the footing:
β― = ππππππ‘πππππ‘π¦ =πππ£
βπ
βπ = π + π1 Γ πΏ + π2 Γ πΏ
βπ = 617.4 + 20 Γ 4.9 + 6.6 Γ 4.9 = 747.77 ππ
π
31
β― =515.97
747.77= 0.69 π
β― <πΏ
6=
4.9
6
0.69 < 0.82
(3) Check for bearing capacity
Shallow foundation bearing capacity theory:
ππ’ππ‘ = πππ + πππ + 0.5πΎπΏππΎ
π = 0.0
ππ’ππ‘ = 45 Γ 133.87 + 0.5 Γ 4.9 Γ 23.0 Γ 271.75 = 21337.26 πππ
π΄ππ‘πππ πππππ‘π = πΏβ² = πΏ β 2 β―
πΏβ² = 4.9 β 2 Γ 0.69 = 3.52 π
π΅ππππππ ππππ π π’ππ = ππππ₯ = [ πΎπ Γ π» + ππΏ.πΏ + ππππ£ ] Γ πΏ
πΏβ²
ππππ₯ = 18 Γ 7 + 20 + 6.6 Γ 4.9
3.52 = 212.43 πππ
Factor of safety against bearing capacity failure:
32
πΉππ =21337.26
212.43= 100 β« 2.5
(B) CALCULATE THE INTERNAL STABILITY-STATIC ANALYSIS
ππ = πππ + πππ .π + πππππ£
Find the lateral earth pressure coefficient for reinforced soil:
ππ = 34Β°
πΎππ = π‘ππΒ² 45 βππ2
πΎππ = π‘ππΒ² 45 β34
2 = 0.283
ππ = πΎπ Γ π§ Γ πΎππ + ππΏ.πΏπΎππ + ππππ£πΎππ
ππ = 18 Γ π§ Γ 0.283 + 20 Γ 0.283 + 6.6 Γ 0.283
ππ = 5.094π§ + 7.5
(1) Find Geogrid vertical spacing
ππππ πππ =ππ£ππ
πΆπ
33
Where:
ππ£ = ππππ‘ππππ π ππππππ πππ‘π€πππ π‘π€π πππ¦ππ ππ πππππππ πππ‘πππππ
πΆπ = πΆππ£ππ πππ‘ππ = 1.00
Find Maximum Allowable Design Strength:
ππππ πππ =ππ’ππ‘
π πΉπ· Γ π πΉππ· Γ π πΉπ Γ π πΉππ Γ πΉπ
ππππ πππ =35
1.03 Γ 1.09 Γ 1.60 Γ 1.5 Γ 1.0= 12.99
ππ
π
Note: RFcn is equal to 1.0 because No connection seams Geogrid exist.
(2) Find Geogrid vertical spacing at depth z=7 m
ππ£ =πΆπππππ πππ
ππ
Where:
πΆπ = Cover ratio
Height of the modular block unit will be consider when computing
Geogrid vertical spacing, that minimum vertical spacing is equal to that
standard height of one modular block unit (20 cm).
34
ππ£ =1.00 Γ 12.99
5.094 Γ 7 + 7.53= 0.30 π π’π π 0.2 π π ππππππ
Spacing will consider is equal to 20 cm (equivalent to 1 Block unit height)
By try and error, check if the spacing can be opened up to 0.4 m at depth z
= 4.8 m
ππ£ =1.00 Γ 12.99
5.094 Γ 4.8 + 7.53= 0.41 π’π π 0.4 π π ππππππ
Spacing will consider is equal to 40 cm (equivalent to 2 Block unit height)
By try and error, check if the spacing can be opened up to 0.60 m at depth
z = 2.4 m
ππ£ =1.00 Γ 12.99
5.094 Γ 2.4 + 7.53= 0.66 π’π π 0.60 π π ππππππ
Spacing will consider is equal to 60 cm (equivalent to 6 Block unit height)
Find number of layer of compacted soil for each spacing:
ππ’ππππ ππ πππ¦ππ ππ£ = 0.2 =7 β 4.8
0.2= 11 πππ¦ππ
35
ππ’ππππ ππ πππ¦ππ ππ£ = 0.4 =4.8 β 2.4
0.4= 6 πππ¦ππ
ππ’ππππ ππ πππ¦ππ ππ£ = 0.6 =2.4
0.6= 4 πππ¦ππ
Now; Figure (8) show the vertical spacing between reinforcement layers.
For the embedment length:
ππ£ Γ ππ Γ πΉπππ’ππππ’π‘ = 2 Γ πΏπ Γ ππ£ Γ πΆπtanππ Γ πΆπ Γβ
πΏπ =ππ£ Γ ππ Γ πΉπππ’ππππ’π‘
2 Γ ππ£ Γ πΆπtanππ Γ πΆπ Γβ
Where:
πΉπππ’ππππ’π‘ = 1.5
πΆπ = 0.9
tanππ = tan 34Β°
β= 1.0
36
No. of layer
Modular concrete block Vertical spacing ππ£
490
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
70
0
60
40
20
Figure 7 vertical spacing for each layer
Geogrid
37
(3) Find the total length by consider the embedment length plus the non
acting rankine length
πΏπ =ππ£ 5.094π§ + 7.53 1.5
2 Γ 0.9 Γ 18π§ Γ tan 34 Γ 0.8 Γ 1.0= 7.64π§ + 11.3 ππ£
17.48π§
For the nonacting rankine length:
πΏπ = π» β π§ tan 45 βππ2
πΏπ = 7 β π§ tan 45 β34
2
πΏπ = 3.72 β 0.532π§
38
Table 7 Final total length computation
LAYER NO.
DEPTH Z (m)
SPACING πΊπ (m)
π³π (m)
π³ππππ
(m)
π³πΉ (m)
π³ππππ (m)
π³ππππ
(m)
21 0.6 0.6 0.91 1.0 3.40 4.40 5.0
20 1.2 0.6 0.59 1.0 3.08 4.08 5.0
19 1.8 0.6 0.48 1.0 2.76 3.76 5.0
18 2.4 0.6 0.42 1.0 2.44 3.44 5.0
17 2.8 0.4 0.27 1.0 2.23 3.23 5.0
16 3.2 0.4 0.26 1.0 2.02 3.02 5.0
15 3.6 0.4 0.25 1.0 1.80 2.80 5.0
14 4.0 0.4 0.24 1.0 1.59 2.59 5.0
13 4.4 0.4 0.23 1.0 1.38 2.38 5.0
12 4.8 0.4 0.23 1.0 1.17 2.17 5.0
11 5.0 0.2 0.11 1.0 1.06 2.06 5.0
10 5.2 0.2 0.11 1.0 0.95 1.95 5.0
9 5.4 0.2 0.11 1.0 0.85 1.85 5.0
8 5.6 0.2 0.11 1.0 0.74 1.74 5.0
7 5.8 0.2 0.11 1.0 0.63 1.63 5.0
6 6.0 0.2 0.11 1.0 0.52 1.52 5.0
5 6.2 0.2 0.11 1.0 0.42 1.42 5.0
4 6.4 0.2 0.11 1.0 0.32 1.32 5.0
3 6.6 0.2 0.11 1.0 0.20 1.20 5.0
2 6.8 0.2 0.11 1.0 0.10 1.10 5.0
1 7.0 0.2 0.11 1.0 0.0 1 5.0
39
π»ππ
π€π
π¦
π»πππππ
π€π
π¦
π³πππππππ
(m)
π³ππ ππππππππ
(m)
π³π πππππ
(m)
8.17 14.52 1.97 2.88 6.28
5.30 13.49 1.42 2.01 5.09
4.31 14.33 1.23 1.71 4.47
3.77 15.62 1.13 1.55 3.99
2.43 11.14 1.10 1.37 3.60
2.43 11.96 1.08 1.34 3.36
2.25 12.59 1.05 1.30 3.10
2.16 13.32 1.03 1.27 2.86
2.10 14.07 1.01 1.24 2.62
2.10 14.90 1.00 1.23 2.40
1 7.60 0.99 1.10 2.16
1 7.80 0.99 1.10 2.05
1 8.00 0.98 1.09 1.94
1 8.21 0.98 1.09 1.83
1 8.42 0.98 1.09 1.72
1 8.62 0.97 1.08 1.60
1 8.82 0.97 1.08 1.50
1 9.02 0.97 1.08 1.40
1 9.23 0.97 1.08 1.28
1 9.43 0.96 1.07 1.17
1 9.64 0.96 1.07 1.07
40
(C) CALCULATE THE INTERNAL STABILITY-DYNAMIC
ANALYSIS
Seismic loads produce an inertial force PI (see figure) acting horizontally,
in addition to the existing static forces.
This force will lead to incremental dynamic increases in the maximum
tensile forces in the reinforcements. It is assumed that the location and
slope of the maximum tensile force line does not change during seismic
loading.
FHWA-NHI-00-043 document recommends that the horizontal seismic
load acceleration coefficient at the center of the wall mass is taken by:
ππ = πΌΒ° 1.45 β πΌΒ°
Where:
ππ : Horizontal seismic load acceleration coefficient.
πΌΒ°: Maximum ground acceleration coefficients
ππ = 0.15 1.45 β 0.15 = 0.195
Find force PI per unit width acting above the base
ππΌ = ππ Γ ππ΄
41
Where:
ππΌ : Inertial force due to Seismic load.
ππ΄ : The weight of the active zone (shaded area on figure).
For Ο = 62.0Β°:
ππ΄ = π΄πππ Γ πΎπ
ππΌ = 0.195 Γ1
2Γ 7 Γ 7 Γ tan 28Β° Γ 18 = 45.72
ππ
π
62Β°
372,2
70
0
Figure 8 Weight of the active zone
Compute the Dynamic Tensile Strength:
πππ = ππΌπΏππ
β πΏππππ=1
See table (7) for πππ calculations for each layer
42
The maximum tensile force:
ππ‘ππ‘ππ = ππππ₯ + πππ
ππ‘ππ‘ππ = ππ£ππ + ππΌπΏππ
β πΏππππ=1
At depth = 7 m
ππ‘ππ‘ππ = ππ£ 5.094π§ + 7.53 + ππΌ0.11
5.09
ππ‘ππ‘ππ = 0.2 5.094 Γ 7 + 7.53 + 1 = 9.64 ππ
π
See table (7) for ππ‘ππ‘ππ calculations for each layer.
For Geosynthetics reinforcement rupture, the reinforcement must be
designed to resist the static and dynamic component of the load as
follows:
For the static component:
ππππ₯ = ππ£ππ
ππππ₯ =πππ Γ πΆπ
0.7 Γ π πΉ Γ πΉπ
Where:
43
πππ : Reinforcement strength per unit width needed to resist the static
component of load.
π πΉ: Reduction factors.
For the dynamic component, where the load is applied for a short time,
creep reduction is not required and therefore:
πππ =πππ‘ Γ πΆπ
0.7 Γ π πΉ Γ πΉπ
Where:
πππ‘ : Reinforcement strength needed to resist the dynamic or transient
component of load.
For the total pullout under seismic loading, for all reinforcements, the
friction coefficient F* should be reduced to 100 % percent of the static
value, leading to
ππππ =πππ + πππ‘
π πΉ
ππ‘ππ‘ππ =ππππΓπΆπ
0.7 Γ πΉπππ’ππππ’π‘
ππ‘ππ‘ππ =2 Γ 1.0 Γ πΉβ Γ ππ£ππ Γ πΏππππ£ππππππ Γ πΆπ
0.7 Γ πΉπππ’ππππ’π‘
πΉπππ’ππππ’π‘ = 1.5
44
πΏπππ₯π‘πππ =0.7 Γ 1.5 Γ ππ‘ππ‘ππ
2 Γ 1.0 Γ 0.9 tan 34 Γ ππ£ 5.094π§ + 7.53 Γ 1.0
At depth = 7 m
πΏπππ₯π‘πππ =0.7 Γ 1.5 Γ 9.64
2 Γ 1.0 Γ 0.9 tan 34 Γ 0.2 5.094 Γ 7 + 7.53 Γ 1= 0.695 π
See table (7) forπΏππππ£ππππππ for each layer.
6.3.1.6 CONNECTION STRENGTH BETWEEN
GEOSYNTHETICS REINFORCEMENT AND MODULAR BLOCK
UNIT
For the connection strength theoretically the tensile stress at the
connection of the reinforcements to the modular block units is must to
checked this is indeed the case of unit block, reinforcement , and soil
backfill stay in horizontal alignment in the same manner as this
constructed.
Settlement of the backfill and perhaps of the foundation soil usually
occurs, thereby deforming the reinforcement and imposing stresses which
effect interaction between the internal face of the block units and
reinforcement .the amount of this stresses is depend on the backfill soil
type, density, moisture content, compactive effort and foundation
condition.
Determining Connection strength between Geosynthetics reinforcement
and modular block unit:
45
MSE walls constructed with MBW units are connected either by a
structural connection subject to verification under AASHTO Article 8.31
or by friction between the units and the reinforcement, including the
friction developed from the aggregate contained within the core of the
units or by a combination of friction and shear from connection devices.
This strength will vary with each unit depending on its geometry, unit
batter, normal pressure and depth of unit. The connection strength is
therefore specific to each unit/reinforcement combination and must be
developed uniquely by test for each combination.
ASTM provides a method to indicate the connection strength between
Geosynthetics reinforcement and modular block unit.
ASTM D 6638-06 is a recommended test use to indicate the ultimate
strength provides by unit block weights to prevent the failure occurs due
to pullout force induced and probability breaking failure of the
reinforcement material is some cases.
ASTM D 6638-06 STANDARD PARAMETER AND RESULTS:
Test parameter
Test direction MD (machine direction)
Tensile strength 35.0
Dimension of single(L X W X H) 30 x 40 x20 cm
Weight of single 38.9 kg
Strands per meter 44.2
Specimen width (strands) 43
Connectors Friction
Pullout speed 40 mm/min
Granular fill Crushed gravel 8/16
Temperature 21Β° C
46
Humidity 50 %
Displacement measuring device Rope displacement gauge
RESULTS:
Load Stages
Normal Load kN/m
Equivalent Wall
height m
Peak connection capacity ππππππππ‘πππ
kN/m
1st
Test 2nd
Test 3rd
Test
1 3.5 0.6 8.7 - -
2 10.5 1.8 15.9 - -
3 17.5 3.0 15.8 16.2 17.8
4 24.5 4.2 18.0 - -
5 33.8 5.8 18.1 - -
A relatively conservative approach is to use the design strength of the
reinforcement material as the required connection strength. For our
project:
ππππππππ‘πππ β₯ 1.0ππππ πππ
47
7 CONVENTIONAL CANTILEVER CONCRETE RETAINING
WALL DEIGNS APPROACH
The other solution for the instability soil is the reinforced concrete
retaining wall which is the commonly method and widely used in
geotechnical field. The next design approach will describe the Design
details of the imposed cantilever retaining wall.
7.1 STABILITY ANALYSIS AND DESIGN DETAILS OF 7 m
HEIGHT CANTILEVER RETAINING WALL SYSTEM.
GENERAL CONSIDRATIONS
1
2
Note: All geometery shown in Figure A
hight wall average (H) = 7.0 m
Assume D = 1.5 m > 0.6 m
H' = H + D = 7.0 + 1.5 = 8.5 m
D - 0.1 8.5 = 1.5 - 0.85 = 0.65 m
H = 7 + 0.65 = 7.65 m
H = 0.1 8.5 = 0.85 m
48
RANKINE ACTIVE FORCE PER UNIT LENGTH
total soil L.L pav
soil
r
1
1
a a + a + a
a 1 a
a
Ο = 34.0Β°
kNΞ³ = 18.0
mΒ²Ξ± = 0.0
P = P P P
1P = Ξ³ H'Β²K
2
ΟK = tanΒ² 45 -
2
a34Β°
K = tanΒ² 45 - = 0.2832
49
510
765
85
50
30
100
8585 340
140
150
1 4
3
2
Figure 9 Geometries information of retaining wall.
20.0 kPa
Pavement
layer
layer layer
50
Force due to the soil:
a1 kN
P = 18 8.5 Β² 0.283 = 184 2 m
Live load calculations:
L.L L.L
L.L
pav pav
pav asphalt pav
pav
total h
soil pav L.L
a a
a
a a
a
a
v a
v
P = q K H'
kNP = 20 0.283 8.5 = 48.11
m
P = q K H'
kNq = Ξ³ H = (22)(0.3) = 6.6
mΒ²kN
P = 6.6 0.283 8.5 = 15.9 m
kNP = P = 184 + 48.11 + 15.9 = 248
mP = P sin + P + P
P = 0 + 20 3. kN
4 22 0.3 3.4 90.44 m
51
Factor of safety against overturning
βMR
Moment kN.m
Moment arm from
point C m
Weight/unit length kN/m
Area mΒ²
Section No.
130.78 1.45 90.194 (0.5)(7.65) = 3.825 1
34.20 1.08 31.57 (0.5)(0.35)(7.65)=
1.34 2
260.66 2.55 102.22 (0.85)(5.1) = 4.34 3
1591.81 3.4 468.18 (3.4)(7.65) = 26.01 4
231 3.4 (20)(3.4)=68 - 5
76.30 3.4 (22)(0.3)(3.4)=22.44 - 6
βMR = 2324.75
βV = 782.6
Ξ³ Concrete = 23.58 kNlmΒ³
52
soil L.L pavo a a a
Roverturning
o
H' H'H'M = P + P + P3 2 2
8.5 8.5 8.5 kN.m= 184 + 48.11 + 15.9 = 793.38
3 2 2 m
M 2324.75FS = = = 2.93 < 1.5
M 793.38
BCheck for e <
6
net R o
net
( minimum requirment for LSD )
kN.mM = M - M = 2324.75 - 793.38 = 1531.4
mM 1531.4
X = = = 1.957 mV 782.6
B 5.1e = - X = - 1.957 = 0.593
2 2B
e < = 0.856
53
Factor of safety against sliding
1 1
1
1
2p
p
p p 2 2 p
p
2 2 psliding
a
2
sliding
Ξ΄ = 0.95Ο
Ξ΄ = 0.95 34Β° = 32Β°
D = 1.5 m
ΟK = tanΒ² 45 +
2
45K = tanΒ² 45 + = 5.828
2
1P = K Ξ³ DΒ² + 2c K D
21
P = 5.828 23 1.5 Β² + 2 15 5.828 1.52
kN = 259.44
m
V tanΞ΄ + Bk c + PFS =
Pk = 0.95
782.6 tan32Β° + 5.1FS =
0.95 15 + 259.44= 3.3 > 1.5
248
54
Factor of safety against bearing capacity
max toe
heel min
2
2
2
cd
V 6e 782.6 6 x0.593q = q = 1 Β± = 1 + = 260.5
B B 5.1 5.1
782.6 6x0.593 q = q = 1 - = 46.4
5.1 5.1
Ο = 45.0Β°
Ξ³ = 23.0
q = Ξ³ D = 23.0 1.5 = 34.5
B' = B - 2e = 5.1 - 2 0.593 = 3.914
D 1.5F = 1 + 0.4 = 1 + 0.4 = 1.
B' 3.914
qd 2 2
a
ci qi
d
154
DF = 1 + 2 tan Ο 1 - sin Ο Β²
B'1.5
= 1 + 2 tan 45Β° 1 - sin 45Β° Β² = 1.0663.914
P cos Ξ± 248.0Ο = tan -ΒΉ = tan -ΒΉ = 17.58Β°
Γ₯V 782.6
ΟΒ° 17.58Β°F = F = 1 - = 1 - Β² = 0.647
90Β° 90Β°
FΞ³ = 1
55
Ξ³i
2
u
ubearing capacity
toe
ΟΒ° 17.58Β°F = 1 - Β² = 1 - Β² = 0.371
Ο Β° 45.0Β°
q = 15 133.88 1.154 0.647 + 34.5 134.88 1.066 0.647
1+ 23 3.914 271.76 1 0.371 = 9246.97
2
q 9246.97FS = = = 35.5 >> 3
q 260.5
bearing capacity
FS > 2.5 ( minimum requirment for LSD )
STEM DESIGN
ππ = πΎ1π§ + ππππ£ + ππΏ.πΏ πΎπ
ππππ π’ππ‘πππ‘ = 1
2πΎ1π§
2 + ππππ£ π§ + ππππ£ π§ πΎπ
π = π Γ πππ = π§
3
1
2πΎ1π§
2 + π§
2 ππππ£ π§ +
π§
2 ππΏ .πΏπ§ πΎπ
π = 1
6πΎ1π§
3 +1
2ππππ£ π§
2 +1
2ππΏ.πΏπ§
2 πΎπ
Find Mu (Ultimate design moment):
ACI Code Appendix C9.2.3 defined required factored load for structures
resist due to pressure o soil should be not less:
56
ππ’ = 1.7π
ππ’ = 1.7 1
6πΎ1π§
3 +1
2ππππ£ π§
2 +1
2ππΏ.πΏπ§
2 πΎπ equ. A
π΄π =0.85πβ²πππ
ππ¦=
0.85 Γ 27.58 Γ π Γ 1
413.7= 0.0567π equ. B
ππ’ = β π΄π ππ¦ π βπ
2
π = 0.9
ππ’ = 0.9 Γ 0.0567π Γ 413.7 Γ 103ππ
π2 Γ π βπ
2
ππ’ = 21111.11ππ β 10555.56π2 equ. C
z (m)
Thickness of stem
(m)
d (m)
π΄π (kN.m/m)
a (m)
π¨π (cmΒ²)
0 0.5 0.42 0 0 0
1.53 0.57 0.49 20.15 0.0019 1.08
3.06 0.64 0.56 101.27 0.0086 4.88
4.56 0.71 0.63 269.90 0.0206 11.68
6.12 0.78 0.7 570.49 0.0397 22.51
7.65 0.85 0.77 1020.63 0.0656 37.19
57
d=thickness of stem β 0.08 m
π΄π from equation (A)
a from equation(C)
π¨π from equation(B)
Note: for π¨π < π¨π πππ use π¨π πππ = ππ.ππ cmΒ²
π΄π πππ ACCORDING ACI CODE SEC. 14.3.2:
π΄π πππ = 0.0015 Γ ππππ π π€πππ ππππ
π΄π πππ = 0.0015 Γ 1.0 Γ 0.85 = 12.75 ππ2
Reinforcement of Stem:
Try bars of 25-mm diameter and 8 bars:
π΄π = 8 Γ π Γ 25
2
2
Γ 10β2 = 39.25 ππ2 = 0.003925 πΒ²
π ππππππ =1000 Γ
π4
Γ 252 Γ 10β6
0.003925= 125.1 ππ
Use spacing of 120 cm c/c
58
π =π΄π
0.0561=
39.25 Γ 10β4 π
0.0567= 0.0692 π
ππ’ = 21111.11 Γ 0.0692π β 10555.56 Γ 0.06922
ππ’ = 1460.88π β 50.55
For π΄π πππ :
Try bars of 20-mm diameter and 4 bars:
π΄π = 4 Γ π Γ 20
2
2
Γ 10β2 = 15.70 ππ2
π ππππππ =1000 Γ
π4
Γ 202 Γ 10β6
0.00157= 200.10 ππ
Use spacing of 200 mm c/c
π =π΄π
0.0567=
15.70 Γ 10β4 π
0.0567= 0.0280 π
ππ’ = 21111.11 Γ 0.0280π β 10555.56 Γ 0.02802
ππ’ = 591.11π β 8.28 equ. D
59
For lapping of 20-mm diameter bars to the 25-mm diameter bars refer to
ACI Code Section 12.15 and because 100% of the bars are to lapped, the
lap splice class is B:
βπ = ππ¦ΓπΉπΓπΉπ‘
1.7π π β² π ππ
βπ =413.7 Γ 1 Γ 1
1.7 Γ 1 Γ 27.58= 1185.5 ππ
βπ = 1185.5 ππ β 1.186 π
πππ πππ π‘ππππ = 1.3 Γ 1.186 = 1.542 π
Cutoff point indicated by combining equations (equ.A) and (equ.D):
1.7 1
6πΎ1π§
3 +1
2ππππ£ π§
2 +1
2ππΏ.πΏπ§
2 πΎπ = 591.11π β 8.28
Where π = 0.046π§ + 0.42
60
1.7 1
6(18)π§3 +
1
2 6.6 π§2 +
1
2(20)π§2 0.283 = 591.11 0.046π§ + 0.42 β 8.28
π§ = 5.23 π
The extend of 25-mm diameter bars above the base of the stem is equal
to:
7.65 β 5.23 + 1.542 = 3.96 π
d at z= (3.69 m)
π = 0.046 Γ 3.69 + 0.42 = 0.590
0.17π π β² πππ = 0.17 0.75 27.58 0.590 = 0.3951 ππ
= 395.1 ππ
395.1 Γ 23 = 263.4 ππ
ππ’ = 1.7 Γ 1
2Γ 18 Γ 3.692 + 20 Γ 2.04 + 6.6 Γ 2.04 Γ 0.283 = 106.18 ππ
ππ’ = 106.18 ππ < 270.11 ππ
61
Determining the development length of the main reinforcement bars into
the foundation:
According to ACI Code sec. 12.2.2:
ππ = 1186 ππ
But ππ > 0.85 π, so:
Obtain the development length in tension using standard hooks:
Tensile stress of a standard development hook:
ππ = π₯ π β² π
X for 25 mm equal 30
ππ = 30 27.58 = 157.55 πππ
The remaining stress to be developed is:
ππ¦ β 157.55 = 413.7 β 157.55 = 256.15 πππ
62
The extra embedment length required to develop the stress of 256.15 is:
256.15
ππ¦Γ ππ =
256.15
413.7Γ 1186 = 734.3 ππ β 0.73 π
For cover 75 mm:
The minimum thickness of the base slab to the bottom of the hook:
0.73 + 3 Γ 0.025 + 0.075 = 0.88 π
Where (3 x 0.025) is the radius of standard hook.
Use base of thickness = 0.9 m
Shear strength at the base of the wall:
ππ’ = 1.7 Γ 1
2Γ 18 Γ 7.652 + 20 Γ 7.65 + 6.6 Γ 7.65 Γ 0.283 = 351.29
ππ.π
π
Shear key of 50 mm x 100 mm is used at the base of stem:
ππ’π΄πππ¦
< 0.2ππ β² π
Where 0.2ππ β²πis the nominal stress.
63
351.29
0.1 Γ 1< 0.2 Γ 0.75 Γ 27.58
3512.9 ππ π2 < 4.137 πππ = 4137 ππ π2
Temperature and Shrinkage Steel:
According ACI Code sec. 14.3.3(horizontal temperature and Shrinkage
Steel):
π΄π = 0.0025 Γ 1 Γ 0.85 = 2.125 Γ 10β3 π2
π= 21.25
ππ2
π
Where 1 Γ 0.85 is the gross wall area.
π ππππππ =1000 Γ
π4
Γ 182 Γ 10β6
2.125 Γ 10β3 = 119.689 ππ
Use 18-mm diameter bars with spacing of 120 mm c/c
64
HEEL DESIGN
Thickness of slab= 0.9 m
π = πΎπ»1 + πΎπ 0.9 β πππππ + ππ₯
π =ππ‘ππ β πππππ
π΅=
260.5 β 46.4
5.1= 42
Critical section for toe and heel
m = 421
q1
q2
q3
Pv
ππππ₯ x' x ππππ
Figure 10 Design of heel and toe of retaining wall
65
π = 18 Γ 7.65 + 23.58 Γ 0.9 β 46.4 β 42π₯ = 112.5 β 42π₯
π = πππ₯ = 112.5π₯ β42π₯2
2+ πΆ
At x = 0, V = πΆ = ππ£ =90.44 ππ
π
π = 112.5π₯ β42π₯2
2+ 90.44
π = π ππ₯ =112.5π₯2
2β
42π₯3
6+ 90.44π₯
V ultimate at x = 3.4 m (critical section):
π = 230.18 ππ
π
ππ’ = 1.7 Γ 447.24 = 391.31 ππ
π
M ultimate at x = 3.4 m:
π = 682.62 ππ.π
π
66
ππ’ = 1.7 Γ 682.62 = 1160.45 ππ.π
π
Check for shear:
b = 1, d = 0.9 β 0.075 β 0.025/2 = 0.813 m
ππ = 0.17 Γ 27.58 Γ 0.813 = 0.725 ππ
π
πππ = 0.75 Γ 0.725 = 0.5438 ππ
π= 543.8
ππ
π
πππ > ππ’ = 391.31 ππ
π
Flexural reinforcement:
ππ’ = β π΄π ππ¦ π βπ
2 = 1160.45
ππ.π
π
π΄π = 0.0567π
1160.45 = 0.9 Γ 0.0567π Γ 413.7 Γ 103 Γ 0.813 βπ
2
π = 0.0707
67
π΄π = 0.0567 Γ 0.0707 = 0.00401 π2 = 40.1 ππ2
π =π΄π ππ
=0.00401
1 Γ 0.813= 0.00493
π ππππππ =1000 Γ π Γ 12.52 Γ 10β6
0.00401= 122.41 ππ
Use spacing of 120 mm c/c
This will provide:
π΄π =1000
120Γ
π
4 2.5 2 = 40.88 ππ2
TOE DESIGN
π = βπΎπ 0.9 + ππ‘ππ βππ₯β²
π = β23.58 Γ 0.9 + 260.5 β 42π₯β² = 239.28 β 42π₯β²
π = π ππ₯β² = 239.28π₯β² β42π₯β²2
2
68
π = π ππ₯β² =239.28π₯β²2
2β
42π₯β²3
6
For the critical section (xβ = 0.85 m):
π = 188.22
ππ’ = 1.7 Γ 188.22 = 319.97
π = 82.14
ππ’ = 139.64
Check for shear:
Because the ultimate shear at the critical section of the toe is less than
ultimate shear of the critical section of the heel the section is adequate for
shear.
Flexural reinforcement:
ππ’ = β π΄π ππ¦ π βπ
2 = 1160.45
ππ.π
π
π΄π = 0.0567π
139.64 = 0.9 Γ 0.0567π Γ 413.7 Γ 103 Γ 0.813 βπ
2
69
π = 0.00818
π΄π = 0.0567π = 0.0567 Γ 0.00818 = 0.000464 π2
π =π΄π ππ
=0.000464
1 Γ 0.813= 0.000571 < ππππ
π΄π πππ = ππππ ππ‘ = 0.0018 Γ 1 Γ 0.9 = 0.00162 π2 = 16.2 ππ2
Hence provide 25-mm diameter bars at 300 mm center to center whish
give:
π΄π =1000
300Γ
π
4 2.5 2 = 16.35 ππ2
Shrinkage and Temperature Reinforcement for Heel and Toe:
For Shrinkage at and temperature reinforcement minimum steel shall be
used:
π΄π πππ = ππππ ππ‘ = 0.0018 Γ 1 Γ 0.9 = 0.00162 π2 = 16.2 ππ2
Provide 18-mm diameter bars at 150 mm center to center:
70
π΄π =1000
150Γ
π
4 1.8 2 = 16.96 ππ2
Final design sketch of the retaining wall is shown in figure (12)
Top of the base slab ππ = 25 mm
30
R7,5
73
Standard hook
12 ππ = 300 mm Rad = 3 Γ ππ = 750 ππ
Figure 11 standard hook details
71
18 mm bars at 120 c/c 20 mm bars at 200 c/c
14 mm bars at 250 c/c 25 mm bars at 120 c/c
765
90
34085 85
396
8
50 x 100 m 18 mm bars at 150 c/c Shear key 25 mm bars at 120
c/c
Standard hook 25 mm bars at 300 c/c
150 mm hook
Note:
All geometries shown are in cm.
The concrete cover thickness is:
75 mm for flexure.
80 mm for tension (stem reinforcement)
Figure 12 Final design sketch of the retaining wall
72
Appendix A
Testing standards for Geogrid and Geocomposites Geosynthetics by ASTM and
GRI:
Terminology
D4439-00 Standard Terminology for Geosynthetics
Mechanical Properties
D4354-99 Standard Practice for Sampling of Geosynthetics for Testing
D4595-86(1994) Standard Test Method for Tensile Properties of
Geotextiles by the Wide-Width Strip Method
D4759-88(1996) Standard Practice for Determining the Specification
Conformance of Geosynthetics
D5261-92(1996) Standard Test Method for Measuring Mass per Unit Area
of Geotextiles
D5321-92(1997) Standard Test Method for Determining the Coefficient of
Soil and Geosynthetic or Geosynthetic and Geosynthetic Friction by the Direct
Shear Method
D6364-99 Standard Test Method for Determining the Short-Term
Compression Behavior of Geosynthetics
D6637-01 Standard Test Method for Determining Tensile Properties of
Geogrids by the Single or Multi-Rib Tensile Method
Endurance Properties
D1987-95 Standard Test Method for Biological Clogging of Geotextile or
Soil/Geotextile Filters
73
D4594-96 Standard Test Method for Effects of Temperature on Stability of
Geotextiles
D5262-97 Standard Test Method for Evaluating the Unconfined Tension
Creep Behavior of Geosynthetics
D5322-98 Standard Practice for Immersion Procedures for Evaluating the
Chemical Resistance of Geosynthetics to Liquids
14 Ling
D5496-98 Standard Practice for In-Field Immersion Testing of
Geosynthetics
D5596-94 Standard Test Method for Microscopic Evaluation of the
Dispersion of Carbon Black in Polyolefin Geosynthetics
D5819-99 Standard Guide for Selecting Test Methods for Experimental
Evaluation of Geosynthetic Durability
D5885-97 Standard Test Method for Oxidative Induction Time
of Polyolefin Geosynthetics by High-Pressure Differential Scanning
Calorimetry
D5970-96 Standard Practice for Deterioration of Geotextiles from Outdoor
Exposure
D6213-97 Standard Practice for Tests to Evaluate the Chemical Resistance
of Geogrids to Liquids
D6388-99 Standard Practice for Tests to Evaluate the Chemical Resistance
of Geonets to Liquids
D6389-99 Standard Practice for Tests to Evaluate the Chemical Resistance
of Geotextiles to Liquids
Permeability and Filtration
D4491-99a Standard Test Methods for Water Permeability of Geotextiles by
Permittivity
D4716-00 Standard Test Method for Determining the (In-Plane) Flow Rate
per Unit Width and Hydraulic Transmissivity of a Geosynthetic Using a Constant
Head
D4751-99a Standard Test Method for Determining Apparent Opening Size
of a Geotextile
D5141-96(1999) Standard Test Method for Determining Filtering
Efficiency and Flow Rate of a Geotextile for Silt Fence Application Using
Site-Specific Soil Civil Applications of Geosynthetics 15
D5199-01 Standard Test Method for Measuring the Nominal Thickness of
Geosynthetics
D5493-93 (1998) Standard Test Method for Permittivity of Geotextiles
74
Under Load
D5567-94(1999) Standard Test method for Hydraulic Conductivity Ratio
(HCR) Testing of Soil/Geotextile Systems
D6088-97 Standard Practice for Installation of Geocomposite Pavement
Drains
D6140-00 Standard Test Method to Determine Asphalt Retention of Paving
Fabrics Used in Asphalt Paving for Full-Width Applications
D6523-00 Standard Guide for Evaluation and Selection of Alternative
Daily Covers (ADCs) for Sanitary Landfills
D6574-00 Test Method for Determining the (In-Plane) Hydraulic Transmissivity of a Geosynthetic
75
Appendix B
References
ASTM, standard on Geosynthetics, 5th ed. Philadelphia, PA: ASTM,
2000. JP Giroud. Geosynthetics Bibliolography. Vols.1 & 2. St. Paul.
MN: international fabric Assoc. international, 1993.
Hoe 1. Ling Dov leshchinsky, Fumio Tatsuoka. Reinforced soil
engineering. Edition 1, editor, Michael D. Meyer, Library of congress.
David I. Cook. GEOSYNTHETICS, Editor, Dr. Sally Humphreys. P-32,
2003.
R.D. Holtz, Ph.D., P.E., Barry R. Christopher, Ph.D., Ryan r .berg, P.E.
Geosynthetics design and construction guidelines. Edition 1, 1998.
G Venkattapa reo, G V suryanarayana Raju. Engineering with
GEOSYNTHETICS. First reprint. Tata McGraw-hill. 1996.
GEOSYNTHETICS FOR SOIL REINFORCEMENT, 2001. P.D. Holtz,
Ph.D.R.(Report)
Dr. A. K. Haghi. Experimental analysis of Geotextile and geofibers
composites. Bub: WSEAS Press.
Robert M. Cornoer.Designing with Geosynthetics, Bub. Prentice Hall; 5
edition (April 24, 2005)
Mechanically Stabilized Earth Walls (MSE) and Reinforced Soil Slopes
(RSS), Design and Construction Guidelines Manual, by FHWA SA-96-
071, NHI β National Highway Institute.
TBU (Institut fΓΌr textile Bau- und Umwelttechnik GmbH), results ASTM
D 6638-06 test report provider.
Hueshker Synthetics GmbH (engineering with Geosynthetics),
geotechnical report parameters, material reinforcement and modular block
information details and properties provider.
76
Design and Construction Monitoring of Mechanically Stabilized Earth
Structures, by J.A. DiMaggio, FHWA, March 1994.
