Understanding and Optimizing the Geosynthetic
Transcription
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: [email protected] Qutaibah Al-Saad Research Assistant, College of Engineering, University of North Texas, 3940 N. Elm St. F115, Denton, TX,76207 e-mail: [email protected] Seifollah Nasrazadani Professor, College of Engineering, University of North Texas, 3940 N. Elm St. F115X, Denton, TX,76207 e-mail: [email protected] H. Felix Wu Senior Director, Office of Research and Economic Development, University of North Texas, 1155 Union Circle, Denton, TX, 76203 e-mail: [email protected] 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 - 5793 - Vol. 19 [2014], Bund. T 5794 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 Vol. 19 [2014], Bund. T 5795 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 Vol. 19 [2014], Bund. T 5796 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 (46β48%); and the high decrease of rutting strain (16β34%) 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- Vol. 19 [2014], Bund. T 5797 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 Vol. 19 [2014], Bund. T 5798 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. Vol. 19 [2014], Bund. T 5799 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. Vol. 19 [2014], Bund. T 5800 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 manufacturerβs 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. Vol. 19 [2014], Bund. T 5801 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, π=π π=π π=1 π=1 οΏ½ ππ ππ πππΌπ = οΏ½ 1 β² ππ πππ πΌπ (π + π‘πππ·β²)(βπΏπ )(π) πΉπ βπΏπ (1) Vol. 19 [2014], Bund. T 5802 where πΉπ is the safety factor, Ξ¦β² is the angle of friction, cβ² 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. Vol. 19 [2014], Bund. T 5803 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. Vol. 19 [2014], Bund. T 5804 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 Ξ΄, the inter-wedge force inclination. The maximum value of the interwedge force, P, is found by varying ΞΈ 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 ππ΅ = (ππ΅ tanππ + ππ πΏππ )πΆππ (2) ππ and ππ are the friction angle and the cohesion for the foundation or the reinforced soil whichever is smaller. With the calculated ππ΅ , the actual factor of safety for direct sliding Fs-ds is gained by πΉπ βππ = ππ΅ ππππ πΏ (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. Vol. 19 [2014], Bund. T 5805 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. Bishopβs 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. Bishopβs 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. Vol. 19 [2014], Bund. T 5806 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 (Ξ²), 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 Ξ². 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. Vol. 19 [2014], Bund. T 5807 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 Ξ² 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 Vol. 19 [2014], Bund. T 5808 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 Vol. 19 [2014], Bund. T 5809 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 Ξ². 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 Vol. 19 [2014], Bund. T 5810 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 Ξ² 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. 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