Understanding and Optimizing the Geosynthetic

Understanding and Optimizing the
Geosynthetic-Reinforced Steep Slopes
Zhenhua Huang
Assistant Professor, College of Engineering, University of North Texas, 3940 N.
Elm St. F115M, Denton, TX, 76207
Corresponding author; e-mail: zhenhua.huang@unt.edu
Qutaibah Al-Saad
Research Assistant, College of Engineering, University of North Texas, 3940 N.
Elm St. F115, Denton, TX,76207
e-mail: qutaibahalsaad@my.unt.edu
Seifollah Nasrazadani
Professor, College of Engineering, University of North Texas, 3940 N. Elm St.
F115X, Denton, TX,76207
e-mail: seifollah.nasrazadani@unt.edu
H. Felix Wu
Senior Director, Office of Research and Economic Development, University of
North Texas, 1155 Union Circle, Denton, TX, 76203
e-mail: felix.wu@unt.edu
ABSTRACT
Geosynthetic materials are broadly adopted in geotechnical, transportation, environmental, and
hydraulic engineering, such as roadway and railway stabilization and reinforcement, pavement
solutions, retaining wall stabilization and landscape, embankments stabilization and differential
settlement limitation, landfill and waste containment drainage and filtration enhancement, and
steep slope solutions. The use of geosynthetic materials may lead to significant savings in
material costs and construction time when they can be used instead of traditional materials and
construction methods. Recently, more and more government agencies and highway/bridge
engineers have found the need to get familiar with the background knowledge, design
methodologies and construction practices of the geosynthetic materials, especially the
geosynthetic reinforced steep slopes. This paper educates bridge and geotechnical engineers by
reviewing the basic concepts, histories, applications, and researches of geosynthetic materials,
demonstrating detailed case studies on the design and construction practices of geosynthetic
reinforced steep slopes, and introducing the basic failure mechanisms for the geosynthetic
reinforced steep slopes. Furthermore, this paper explores optimum design for the geosynthetic
reinforced steep slopes and recommends that the optimum design of geosynthetic reinforcement
could be easily obtained with a 10 degree backfill slope angle or a horizontal crest length larger
than or equal to half of the total slope length.
KEYWORDS: Geosynthetics, Reinforced
earth, Steep Slopes, Optimizing
INTRODUCTION
Geosynthetic materials are broadly adopted in geotechnical, transportation, environmental,
and hydraulic engineering. The use of geosynthetic materials may lead to significant savings in
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material costs and construction time. Geosynthetic reinforced steep slopes are one of the primary
applications of geosynthetic materials. The geosynthetic reinforcement provides extra tensile
resistances and enhances the slope stability. It enables slopes to be constructed higher and
steeper and to exhibit environmentally friendly vegetated and wrapped faces. Those benefits are
significant in projects involving bridges and embankments that can accommodate a slope but
probably not having adequate space for vegetation. In addition, the use of geosynthetic
reinforced slopes often constitutes the most cost effective solution in highway projects. In recent
years, more and more government agencies and highway/bridge engineers have shown their
needs to get familiar with the background knowledge, design methodologies and construction
practices of the geosynthetic reinforced steep slopes. For example, in last couple of years, the
U.S. Texas Department of Transportation (TxDOT) funded several projects to conduct synthesis
researches on how to adopt geosynthetic reinforced steep slopes for the highway construction in
Texas. The goal of this study is to explore the application of geosynthetic materials, especially
geosynthetic reinforced steep slopes, and to advance the design methodology of geosynthetic
reinforced steep slopes. In detail, this study will (1) review the basic concepts, histories,
applications, and researches of geosynthetic materials, (2) conduct detailed case studies on the
design and construction practices of geosynthetic reinforced steep slopes, (3) study the basic
failure mechanisms for the geosynthetic reinforced slopes, and (4) explore the optimum design
of geosynthetic reinforced steep slopes.
INTRODUCTION TO GEOSYNTHETICS
Geosynthetic materials, according to American Society for Testing and Materials (ASTM),
are defined as the polymeric materials used to strengthen soil, rock, earth, or other geotechnicalrelated materials. Soil has high compressive strength but almost null in tensile strength. By using
a geosynthetic material, the soil tensile strength could be improved. Those geosynthetic
materials used for reinforcing soil need to be light-weighted and flexible and possess extensively
high tensile strength. The soil structure with increased strength allows engineers to construct on
steep slopes. In addition, geosynthetic strengthened soil structures are less costly compared to
steel structures. This has made it a common global mode of construction used today.
The use of geosynthetic materials could be traced back to the Pyramids of Egypt and the
Ziggurat at Aqar Quf Temple of Mesopotamia (Iraq) five thousand years ago. These structures
used strengthened soil that was mixed with natural fibers, fabrics or vegetation.
The earliest user of geosynthetics was Karl Terzaghi. Terzaghi and Lacroix (1964) used
filter fabrics (today, geotextiles) as flexible forms to help make closure between steel sheet
piling and rock abutments at the Mission Dam (now Terzaghi Dam) in British Columbia,
Canada. In this same project, pond liners (today, geo-membranes) were used to keep an
upstream clay seepage-control liner from desiccating.
Since their introduction in the 1960s, geosynthetics have been proven to be versatile and
cost-effective ground modification materials. The advent of the first conference on geosynthetics
was in 1977 in Paris. Koerner and Welsh (1980) published the first book on geosynthetics. The
International Geosynthetics Society was founded in 1983, and a number of journals, magazines,
and newsletters specializing in geosynthetics started in the 1980s.
The usage of geosynthetic materials has been increased significantly in geotechnical and
environmental engineering for the last 10 years. Geosynthetic products have helped designers
and contractors to solve several types of engineering problems where the use of conventional
construction materials would be restricted or considerably more expensive. Geosynthetic
manufacturers have consistently been involved in pushing the frontiers of the technology. There
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are more than 40 manufacturers of geosynthetic materials that provide products for the North
American marketplace. More than half of the manufacturers are located in the southeastern U.S.
The whole geosynthetic industry provides more than 12,000 jobs in the U.S. in manufacturing,
fabrication, distribution, and installation of geosynthetic materials.
There are a significant number of geosynthetic types and geosynthetic applications in
geotechnical and environmental engineering. Commonly used geosynthetic materials for soil
reinforcement include geotextiles (particularly woven geotextiles), geogrids, and geocells
(Bathurst 2007). Geotextiles (Figure 1 Left) are continuous sheets of woven, nonwoven, knitted,
or stitch-bonded fibers or yarns. The sheets are flexible and permeable and generally have the
appearance of a fabric. Geogrids (Figure 1 Middle), have a uniformly distributed array of
apertures between their longitudinal and transverse elements. These apertures allow direct
contact between soil particles on either side of the sheet. Geocells (Figure 1 Right) are relatively
thick, three-dimensional networks constructed from strips of polymeric sheet. The strips are
joined together to form interconnected cells that are filled with soil and sometimes concrete. In
some cases, 0.5 m to 1 m wide strips of polyolefin geogrids have been linked together with
vertical polymeric rods to form deep geocells layers called geomattresses.
Geotextiles
Geogrids
Geocells
Figure 1: Geosynthetics commonly used for soil reinforcement (Left to right:
Earthaidusa 2014, Reimers Kaufman 2014, Bolu 2014)
Geosynthetic materials are broadly adopted in geotechnical, transportation, environmental
and hydraulic engineering, such as roadway and railway stabilization and reinforcement,
pavement solutions, retaining wall stabilization and landscape, embankments stabilization and
differential settlement limitation, landfill and waste containment drainage and filtration
enhancement, and steep slope solutions.
Applications of geosynthetics in roadway and railway stabilization and reinforcement
include road base course reinforcement, road sub grade stabilization, and railway soft
foundations embankment stabilization and reinforcement. Figure 2 illustrates application cases
of using geogrids: case (a) - widening the railway embankment in Ontario, Canada (Tencate
2014) and case (b) providing support to the highway by the California Department of
Transportation (Maccaferri-USA 2014). For case (a), in order to construct the new reinforced fill
slope and obtain the necessary geogrids reinforcement embedment lengths, it was necessary to
excavate into the existing embankment slope, which was subsequently nailed to provide
temporary stability. The reinforced fill slope was then toed into the excavated, nailed
embankment slope with the primary geogrids product. Zheng et al. (2009) proved that
geosynthetic material can be very useful and cost effective for treating expansive soil cut slopes,
as well as for reinforcing embankments built with expansive soil, based on their testing on the
NanYou highway in China. Indraratna et al. (2010) found that geocomposite can effectively
reduce vertical and lateral strains of the ballast with obvious implications for improved railway
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track stability and reduced maintenance costs. Indraratna et al. (2011) further evaluated the
effectiveness of using geocomposite in railway stabilization and reinforcement through field
measurements and finite element analyses. The first fully instrumented, comprehensive field
railways trials were conducted in Australia, and it was very encouraging to see the field
observations matching the numerical predictions. Caverson and Lowry (2011) presented a
successful case study using a retaining wall that combined a steel fascia with geosynthetic
reinforcement to widen the rail embankments of Lakeshore West Line in Mississauga, Canada.
(a)
(b)
Figure 2: Geosynthetics applications to railway stabilization and roadway
reinforcement (Tencate 2014, Maccaferri-USA 2014)
Pavement solutions represent some special geosynthetic materials that offer robust
mechanical properties coupled with high water flow capabilities that extend pavement life by
retarding reflective cracking, waterproofing, and reinforcing asphalt pavements. For example,
woven geotextiles had been used to improve the subgrade at the intersection of Highway 59 and
Highway 169 in Garnett, Kansas (Tencate 2014). The geotextiles not only provided a much
higher tensile strength at low strains, but also provided the separation needed for the high water
table, which could cause failure of the pavement (Leshchnisky et al 1995). Saad et al. (2006)
found that placing the geosynthetic reinforcement at the asphalt concrete interface led to a high
reduction of the fatigue strain (46–48%); and the high decrease of rutting strain (16–34%)
occurred when the geosynthetic reinforcement was placed at a height of 1/3 of the base thickness
from the concrete. Han et al. (2011) demonstrated that the novel polymeric alloy geocells
reinforcement can improve the performance of unpaved recycled asphalt pavement sections by
widening the stress distribution angle and reducing the rut depth if the base courses were equally
compacted in unreinforced and reinforced sections.
The application of geosynthetic materials on temporary and permanent retaining walls can
help the stability of the retaining walls economically, efficiently, and aesthetically. The
geosynthetic material has been increasingly employed for these critical applications. Figure 3
illustrates application cases of using geogrids to strengthen the retaining wall of the Randolph
College Athletic Field, Lynchburg, Virginia (Tencate 2014). Simac and Elton (2010) described
the engineering analysis, design procedures, and some of the installation details utilized for
geosynthetic-reinforced retaining walls for the traditional retaining wall loadings, plus the
additional procedures to account for the pile induced lateral loads. A review of the performance
of geosynthetic walls based on deformed shape measurement of the wall facing after ten years of
service was also presented to assess their performance. Liu (2011) studied geosyntheticreinforced soil retaining walls at a height of 9 m with different tiered configurations. It was
found that the seismic performance of multi-tiered walls was better than that of single-
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tiered walls, and that the improvement increased with a decrease in reinforcement
spacing.
Figure 3: Geosynthetics application to retaining walls (Tencate 2014)
Another application of geosynthetic materials is to provide stability and limit differential
settlement for embankments. Figure 4 shows an application of geosynthetic material to protect
the river bank in Santa Fe, New Mexico (Maccaferri-USA 2014). Geogrids were used to
reinforce the reinstated embankment and to facilitate the reuse of on-site material. Geotextiles
were installed on the back of the gabion facing units to prevent the structural backfill migrating
into the voids within the gabion, particularly during high water flow conditions in the river.
Figure 4: Geosynthetics in embankments application (Maccaferri-USA 2014)
Geosynthetic materials could also be applied to enhance drainage and filtration in landfill
and waste containment. An example application is the Shanghai Laogang Municipal Solid Waste
Landfill located at Laogang town, 60 km from the Shanghai city center in China (Tencate 2014).
The landfill is located adjacent to the coast and occupies 360 hectares with an anticipated total
capacity of more than 34 million tons of waste over a 20-year concession contract. To ensure
quick and controlled consolidation of the soft clay foundation, a drainage layer in conjunction
with Prefabricated Vertical Drains (PVDs) was installed across the base of the landfill. The
drainage layer consisted of a woven monofilament geotextile filter placed directly on the soft
clay foundation prior to placement of the granular drainage layer. The geotextile filter combines
the properties of good tensile strength and efficient filtering capability. Glendinning et al. (2010)
investigated the potential for using electro-kinetic geosynthetics (EKGs) to dewater slurry waste
from a tunneling operation. The results demonstrated that the EKG was reproducible for
different slurries and that the process can significantly dewater tunneling slurry wastes. The
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potential of three different forms of EKG to treat tunneling slurry was discussed and a
conceptual scheme for an EKG enhanced belt press was proposed.
Coastal regions and waterways are characterized by uneven land contours, changing
subgrades, continuous scour and many other harsh conditions. These characteristics make
construction along these areas unfavorable. Advanced geogrids and geotextile materials
integrated with available fill and/or vegetation could be used for construction and protection in
coastal regions and waterways to control erosion and scour, form foundations or cores for
breakwaters, groins, underwater utility/pipeline installations, build high-strength fills in
submerged conditions or with weak fill materials, protect channel linings and bridge scour,
protect causeways, levees, dikes and bridge approach, provide under-layers for riprap in
submerged and soft soils, in situ capping of contaminated sediments, and protect shore and
dewater sediment. In addition, the geogrids are capable of resisting natural occurrences caused
by chemicals, biological or environmental degradation coming from industrial runoffs and salty
ocean water (Starrett 2009). One example of this application is the construction of the seawall
for the Brisbane Port expansion in Australia. The geotextile reinforcement was used for the basal
reinforcement and beneath the rock armor to prevent corrosion.
GEOSYNTHETICS FOR STEEP SLOPES
Geosynthetic materials can also deliver solutions that increase the construction of steep
slopes by enhancing stability and providing tensile resistance and superior reinforcement.
Reinforced steep slopes are mainly compacted fill embankments made up of geosynthetic tensile
reinforcements in horizontal layers. This tensile reinforcement assists in holding the soil mass
together across any possible failure place to promote slope stability. These products enable
slopes to be constructed to any height at any slope angle and to exhibit environmentally friendly
vegetated and wrapped faces. The following geosynthetic application examples are documented
by the research team based on raw materials provided by a major U.S. geosynthetic material
manufacturer (Tencate 2014).
Case 1: Yeager Airport Runway Extension in West
Virginia
Yeager Airport in Charleston, West Virginia, was constructed in the 1940s atop a
mountainous terrain. Due to the mountainous conditions, the ground surface around the airport
slopes down steeply over 300 feet to the surrounding Elk and Kanawha Rivers, roadways,
churches, houses and other structures. In order to meet recent Federal Aviation Administration
(FAA) safety standards, updates to the airport runways had to be performed. These
improvements included extending Runway 5 approximately 500 feet to create an emergency
stopping apron for airplanes. The challenge for designers was how to extend the runway 500 feet
outward on the side of a mountain.
Soil conditions: The on-site geomorphology consisted of weathered sandstone underlain by
sandstone and some shale. Testing of the weathered sandstone soil showed a maximum dry
density of 20 kN/m3 and a peak friction angle of 39°. This made it ideal for the reinforced fill in
the reinforced steep slope. The compressive strength of the rock foundation varied from 30 MPa
to 95 MPa. The high bearing capacity of the underlying sandstone foundation and the high
friction angle of the onsite weathered sandstone soil meant that the extent of the reinforced slope
could be kept to a minimum, and maximum use could be made of the onsite soil.
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Slope geometry and design criteria: Construction options for extending the runway past the
existing hillside included bridge structures, retaining walls, and reinforced steep slopes.
Engineering evaluation indicated the reinforced steep slope provided the most cost effective and
easiest constructed option of the structures considered. In addition, the vegetated facing of the
completed steep slope would provide a structure that will blend into the surrounding green hills
of Charleston. The final design was a 1H:1V (H: horizontal; V: vertical) reinforced steep slope
(RSS), 242 feet high, making it the tallest reinforced 1H:1V slope in North America. The design
utilized geogrids as the primary geosynthetic reinforcement with geomesh for erosion control at
the slope face. The design also incorporated drainage composite behind the reinforced mass.
Construction procedures: Geogrids were selected as the primary reinforcement for the
project and were installed in conjunction with the backfill material. The geogrids were installed
as horizontal reinforcing elements into the slope. Embedment lengths of the geogrids were on
the order of 195 feet in length. The drainage composite was installed along the back of the
excavation to intercept and drain seepage water from the existing mountain side away from the
reinforced mass. Geomesh was installed on the face of the slope at 2-foot vertical intervals, with
3-foot embedded into the slope face and 2.5 feet down the face for facial stability and erosion
protection. Geomesh is an open mesh biaxial geosynthetic material specifically designed as a
face wrap material for RSS applications.
Performance: The extension of Runway 5 at Yeager Airport in Charleston, West Virginia,
would have been extremely costly without a geosynthetic reinforcement solution. The RSS
allowed for an economical solution and less complicated construction than the other, traditional
methods that were considered. The reinforced steep slope was successfully completed and is
performing as expected. The geogrids provided the high strength required for the structure of
this size and the geomesh allowed for facing stability and quick germination of surficial
vegetation for improved stability. The structure allowed the airport to meet recent FAA safety
standards while creating an engineered structure that blends into the scenic green hills of
Charleston (Figure 5).
Figure 5: Yeager airport runway extensions (Tencate 2014)
Case 2: Highway I-695 at Highway I-83S in Maryland
In widening Highway I-695 at Highway I-83S, the Maryland State Highway Administration
(MDSHA) required the slope adjacent to an off ramp to be steeper that 2H:1V due to the
delineated environmental impact at the toe of the slope. The required slope face angle meant that
geosynthetic reinforcement was needed to build the structure and the face needed to be protected
against erosion both short term, prior to vegetation, and long term.
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Design: The initial design called for the slope to be reinforced with uniaxial geogrids and
the face of the slope to be reinforced with biaxial geogrids-erosion control blanket combination.
Finally, a design of geogrids for the slope reinforcement and geomesh to replace the
combination of secondary reinforcement and erosion control blanket was selected, since
geomesh provides both the biaxial strength and erosion control needed for the project.
Construction: The manufacturer’s representative was at the project during startup and
guided the contractor during the initial installation procedure. This allowed the contractor to
complete the job without subsequent construction issues. Geosynthetic products were installed
during a rainy period, and a geomesh product retained enough soil at the slope face, making the
soil loss negligible.
Performance: Thanks to geosynthetic materials, the slope took on an immediate natural look
with its green color. After just one growing season, the slope has a high concentration of
vegetative growth. Figure 6 illustrates three phases during the slope construction.
Figure 6: Construction of Steep Slope at I-695 @ I-83S in Maryland (Tencate 2014)
Case 3: Stabilized Slope on Highway I-495 in Lawrence,
Massachusetts
Part of a Massachusetts Highway Department contract required the relocation of the existing
highway I-495 northbound ramp at Marston Street in Lawrence, Massachusetts. The existing
2H:1V slope was steepened to 1H:1V, keeping the toe of the slope at approximately the same
location and replicating a small existing wetland area that was within the slope profile.
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Design and Construction: Construction of the slope began in April 2002 and was completed
in several stages because of adjacent construction of bridge abutments at each end of the slope.
The lower portion of the slope contained 6 layers of dense geogrids as the primary reinforcement
spaced 0.6 m (1.96 ft) vertically with a 0.9 m (3.0 ft) embedment length, and the upper portion
of the slope used dense geogrids spaced 1.0 m (3.3 ft) vertically and an 8.0 m (26.2 ft)
embedment length. Sparse geogrids was used as intermediate geogrids spaced 0.5 m (1.6 ft)
vertically with an embedment length of 2.0 m (6.6 ft) and placed in the upper portion of the
slope in between the layers of dense geogrids. The drainage composite was installed at the back
of the slope against the native soil and up 1/3 of the slope in height. The slope face was loamed,
seeded and covered with a synthetic permanent erosion control mat.
Performance: Highway I-495 steep slope and relocated northbound ramp has been in use for
approximately one year, and the 1:1 slope is fully vegetated and performing as expected (Figure
7).
Figure 7: Stabilized Slope in I-495 in Lawrence, MA (Tencate 2014)
FAILURE MECHANISMS FOR GEOSYNTHETICREINFORCED STEEP SLOPES
To determine the stability or to design a steep slope, civil engineers have used limit
equilibrium (LE) for decades, which is also known as the critical equation. LE was usually used
to check the safety of natural slopes, slopes of excavations and other field such as embankments.
LE could be adopted for the design of geosynthetic reinforced steep slopes.
A typical method to illustrate LE is the ordinary method of slices. In this method the soil
above the trial failure surface is divided into vertical slices as shown in Figure 8. The slice
length along the horizontal direction is represented as bn; Wn is the weight of the soil slice. In
order to get equilibrium, the follow equation can be drawn,
𝑛=𝑝
𝑛=𝑝
𝑛=1
𝑛=1
� 𝑊𝑛 𝑟𝑠𝑖𝑛𝛼𝑛 = �
1 ′ 𝑊𝑛 𝑐𝑜𝑠𝛼𝑛
(𝑐 +
𝑡𝑎𝑛𝛷′)(∆𝐿𝑛 )(𝑟)
𝐹𝑠
∆𝐿𝑛
(1)
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5802
where 𝐹𝑆 is the safety factor, Φ′ is the angle of friction, c′ is cohesion, and r is the radius of the
failure surface (Das 2010).
Figure 8: Ordinary method of slices
When using LE to design the geosynthetic reinforcement, the tieback analysis is introduced
to estimate the required reinforcement tensile resistance of each layer. Consequently, the
designer can verify whether an individual layer is overstressed or understressed, regardless of
the overall stability of the slope. Once the problem of 'local stability' is resolved, overall stability
of the slope is assessed through rotational (compound failure) and translational (direct sliding)
mechanisms. Finally, deep-seated analysis using Bishop Method checks the bearing capacity of
the foundation soil. The following section briefly describes those analyses. More detailed
information can be found in Leshchinsky (1997) and Leshchinsky et al. (1995).
Tieback Analysis
Tieback analysis, also known as internal stability analysis, is a way to determine the required
tensile resistance of each reinforcement layer (geosynthetics) to make sure the reinforced soil is
safe against internal collapse due to its own weight and loading from surrounding charges. This
analysis identifies the tensile force needed to resist the active lateral earth pressure at the face of
the steep slope. Figure 9 shows the notation and convention for the tieback analysis. Surcharge
loadings, Q1, Q2, and Q3, are applied along the top of the slope. The force in each reinforcement
layer is activated by an unstable soil mass. By applying LE for each soil layer (soil mass
between two consecutive reinforcement layers), the reactive force in each reinforcement layer (t1
to tn in Figure 9) and the critical shear surface could be determined. The log spiral failure
surfaces are assumed in the analysis.
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Figure 9: Notation for tie back analysis
Compound Stability Assessment
The tieback analysis results in the minimum required allowable strength of reinforcement at
each layer. In reality, the allowable strength of most reinforcement layers will exceed the
minimum required value. Consequently, if viewed from global stability, only m layers (m<n) of
reinforcement are needed; i.e., reinforcement selected based on tieback analysis may produce
more reinforcement than needed for global stability. These bottom m layers may contribute their
full allowable strength in the compound analysis, which deals only the aspect of global stability.
The upper layers (m+1) through n may contribute only to their calculated tieback values.
Therefore, the geosynthetic reinforcement for the upper layers could be truncated at some points
such as A, B, and C as shown in Figure 10. And the lower layers (1 through m) could also be
truncated at some points such as D, E, F, and G in Figure 10 to satisfy a predefined design safety
factor Fs. Leshchinsky (1997) presented the procedure of truncation.
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Figure 10: Compound stability analyses
Direct Sliding Analysis
The reinforcement layout satisfying the requirement against rotational failures (through
compound analysis) does not assure sufficient resistance against direct sliding of the reinforced
soil mass along its interface with the foundation soil or along any reinforcement layer. The
length required to make sure a stable mass against direct sliding, Lds, is determined from the
two-part wedge method which is a LE analysis that satisfies force equilibrium. Figure 11 shows
the free body diagram for the two-part wedge method. The method first assumes an initial value
of Lds and a value for δ, the inter-wedge force inclination. The maximum value of the interwedge force, P, is found by varying θ while solving the two force equilibrium equations for the
active Wedge A. Based on the vertical force equilibrium equation for Wedge B, bearing force
NB is solved. The sliding resisting force, TB, along the base Lds is calculated by
𝑇𝐵 = (𝑁𝐵 tan𝜙𝑑 + 𝑐𝑑 𝐿𝑑𝑠 )𝐶𝑑𝑠
(2)
𝜙𝑑 and 𝑐𝑑 are the friction angle and the cohesion for the foundation or the reinforced soil
whichever is smaller. With the calculated 𝑇𝐵 , the actual factor of safety for direct sliding Fs-ds is
gained by
𝐹𝑠−𝑑𝑠 =
𝑇𝐵
𝑃𝑐𝑜𝑠𝛿
(3)
By changing Lds and repeating the process for Wedge A and Wedge B, the iteration
procedure stopped until the computed factor of safety against direct sliding equals to a
predefined value.
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Figure 11: Two wedges method
Deep-seated Analysis Using Bishop Method
In 1955, Bishop proposed a solution to the ordinary method of slices which works well for
the deep-seated analysis of steep slopes (Das 2010). In this method, circular slip surfaces are
examined, and the one rendering the lowest safety factor is selected. The circles examined are
restricted to those passing away from the bottom of the reinforced soil zone. The stabilizing
effects of intersecting reinforcement layers above the bottom layer with the critical circle are
ignored. Bishop’s formulation is modified to include pseudo-static forces to self-weight and
surcharge loads. By using force equilibrium equation for normal and shear forces on each layer,
the safety factor is calculated. A trial-and-error procedure is adopted to make sure the factor is
acceptable. Bishop’s method is widely used in deep-seated analysis. It yields good results in
most cases while the ordinary method of slices is too conservative.
OPTIMUM DESIGN OF GEOSYNTHETIC
REINFORCEMENT FOR STEEP SLOPES
This research conducted two case studies to explore the optimum design of geosynthetic
reinforced steep slopes. The two cases were selected based on two different site locations (one in
Europe and one in U.S.) and the design parameters availability. The design parameters for the
optimization study were provided by a U.S. geosynthetic material manufacturer. The horizontal
crest length and the backfill slope angle were defined as the control variables to conduct the
iteration analysis and obtain the optimum design.
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Case 1: Reinforced steep slope design for a building area
in Matera, Italy
Case 1 involves a construction project of a residential area on a hill in Matera, Italy. The
project designer planned constructing reinforced steep slope embankments with height variance
from 3m to 70m. The geological and morphological situation and the building construction over
the embankment required several technical solutions to reduce the settlements and the front
deformation of the steep slopes. Particularly, because of a superficial clay layer with poor
mechanical properties, the embankments were built on reinforced concrete basement founded on
piles. In addition, a soil with good mechanical properties and reinforcement with a high modulus
were chosen to reduce the embankment movements. The field-measured low deformations had
confirmed the validity of the design and construction procedures.
For this optimization case study, the available design parameters of the project include:
slope height = 30 meters; slope angle = 60°; unit weight of soil = 20 kN/m3; cohesion of soil = 0
kPa; internal angle of friction = 34° for the reinforced soil, backfill soil and foundation soil;
surcharge load over the horizontal crest length = 10 kPa; surcharge load away from backslope
length = 10 kPa; factor of safety = 1.3 for shear strength, geosynthetic strength, and geosynthetic
pullout, direct sliding; factor of safety = 1.1 for deep-seated failure (Bishop stability); ultimate
strength for geosynthetic materials = 20 kPa; maximum allowable geosynthetic spacing = 0.6 m;
and minimum allowable geosynthetic spacing = 0.3 m.
To identify the optimum design, the horizontal crest length (A) and the backfill slope angle
(β), as shown in Figure 12, were used as control variables. A set of 36 trial designs were
performed, which includes combinations of six different horizontal crest lengths and six
different backfill slope angles. Table 1 and Figure 13 demonstrate the required geosynthetic
reinforcement (in m2/m) in regards to A and β. The calculations were based upon the four failure
mechanisms, tieback stability, compound stability, direct sliding, and deep-seated failure,
discussed in the previous section. Analysis of Variance (ANOVA) had been performed to
validate the correlation between the required geosynthetic reinforcement and horizontal crest
length and the backfill slope angle. The following observation could be drawn from the study:
(1) the required amount of geosynthetic reinforcement increases along with the backfill slope
angle increases. The larger the angle is, the more geosynthetic material is needed; (2) when the
backfill slope angle is smaller than or equal to 10 degrees, the required geosynthetic
reinforcement reaches a stable value, which is close to the optimum (minimum) design value;
and (3) the required geosynthetic reinforcement reaches the optimum value when A is larger or
equal to L/2. L is the total length of the slope, which represents the horizontal distance from the
slope toe to the end of back fill.
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Figure 12: Optimization analysis control variables
Table 1: Case 1 Design Results (Geosynthetic material needed in m2)
Horizontal
Crest
Length A
3L/4
2L/3
L/2
L/3
L/4
0
Std. Dev.
Backfill Slope Angle β
34°
1808
1846
1946
4211
3502
2470
1004
25°
1781
1804
1863
3119
2565
2157
534
20°
1769
1785
1827
2591
2127
2026
314
10°
1749
1754
1770
1790
1803
1830
31
5°
1739
1743
1748
1754
1760
1760
9
0
1731
1730
1726
1723
1721
1700
12
Std.
Dev.
29
43
83
998
693
291
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Figure 13: Required geosynthetic materials in regards to back slope angle (left) and
horizontal crest length (right) for case 1
Case 2 Reinforced steep slope design for Mississippi
River, Otsego, Minnesota
Case 2 is a re-construction project of a slope extending up from the normal river level of the
Mississippi River at a 1H: 1V slope angle. The project location is close to the Otsego town of
Minnesota. The available design parameters for this case study include: slope height = 15
meters; slope angle = 45°; unit weight of soil = 14.3 kN/m3; cohesion of soil = 0 kPa; internal
angle of friction = 23° for the reinforced soil, backfill soil and foundation soil; surcharge load
over the horizontal crest length = 10 kPa; surcharge load away from backslope length = 15 kPa;
factor of safety = 1.3 for shear strength and geosynthetic strength; factor of safety = 1.5 for
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geosynthetic pullout; factor of safety = 1.1 for direct sliding and deep-seated failure (Bishop
stability); ultimate strength for geosynthetic materials = 20 kPa.
Similar to case 1, Table 2 and Figure 14 are used to demonstrate the analysis results, the
required geosynthetic reinforcement (in m2/m) in regards to A and β. The following observation
could be drawn through case study 2: (1) same as case 1, the required amount of geosynthetic
reinforcement increases along with the backfill slope angle increases. The larger the angle, the
more geosynthetic reinforcement needed; (2) when the backfill slope angle is smaller than or
equal to 10 degrees, the required geosynthetic reinforcement reaches a relatively stable value,
which is close to the optimum design value; and (3) the required geosynthetic reinforcement
with respect to horizontal crest length A is a set of decreasing curves, the required geosynthetic
material get close to the optimum design values when A is larger or equal to L/2.
Figure 14: Required geosynthetic materials in regards to back slope angle (left) and
horizontal crest length (right) for case 2
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Table 2: Case 2 Design Results (Geosynthetic material needed in m2)
Horizontal
Crest
Length A
3L/4
2L/3
L/2
L/3
L/4
0
Std. Dev.
Backfill Slope Angle β
23°
969
960
1050
1165
1192
1395
165
20°
945
931
1013
1127
1151
1339
154
10°
890
910
951
986
1002
1070
66
5°
869
878
897
914
923
944
28
0
894
894
894
894
894
894
0
Std.
Dev.
42
32
69
123
134
228
Combined the observations from both case studies, the research team recommend that a 10
degree backfill slope angle or a horizontal crest length larger than or equal to half of the slope
length will result in a design close to optimum amount of geosynthetic reinforcement.
CONCLUSION
The usage of geosynthetic materials has been increased significantly in geotechnical and
environmental engineering for the last decade. More and more government agencies and
highway/bridge engineers have found it necessary to get familiar with the background
knowledge, design methodologies and construction practices of the geosynthetic materials,
especially in steep slope applications. This paper reviewed the basic concepts, histories,
applications, and research of geosynthetic materials, demonstrated detailed case studies on the
design and construction practices of geosynthetic reinforced steep slopes, introduced the basic
failure mechanisms for the geosynthetic reinforced steep slopes, and explored the optimum
design of geosynthetic reinforcement for steep slopes. The research team recommended that an
optimum design of geosynthetic reinforcement can be obtained with a 10 degree backfill slope
angle or a horizontal crest length larger than or equal to half of the total slope length.
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