# Geosynthetic Reinforced Steep Slopes: Current Technology in the United States
## 4 Design Methods  
The majority of survey respondents recommended the use of the FHWA guidelines for the design of reinforced slopes as per Figure 3. The technique has been adopted by many transportation agencies in the United States and South America [33]. Less advocated approaches included Eurocode and other design methods, such as EBGEO (Empfehlungen fur den Entwurf und die Berechnung von Erdkorpern mit Bewehrungen aus Geokunststoffen) and British Standard 8006. Additionally, 88 percent recommended the use of geogrid or a combination of geogrid and geotextile for slope reinforcement, while others recommended independent use of geotextile. Some prefer high strength geotextiles over geogrids, as they provide a separation function and can be more cost effective in certain cases. See Appendix A for the case studies.  
The internal stability of a soil slope can be determined by four basic factors, including the slope angle in degrees (\(\beta\)), soil weight in N (\(W\)), cohesion in N/m\({}^{2}\) (\(c\)), and internal friction angle in phi (\(\phi\)) as per Figure 4. The cohesion is a measure of the forces that cement particles of soil, and the internal friction angle is a measure of the shear strength of soils due to friction. The force causing failure, the resisting strength, and the factor of safety are also dependent upon the length of the plane of weakness in m (\(L\)) as follows [34]:  
\[\text{Force Causing Failure}=(W\times sin\beta) \tag{5}\]  
\[\text{Resisting Strength}=(c\times L)+(W\times cos\beta\times tan\phi) \tag{6}\]  
\[\text{Factor of Safety}=(\text{Resisting Strength/Force Causing Failure}) \tag{7}\]  
The factor of safety is the ratio of the resisting strength to the force causing failure, which is indicative of the stability of a slope. The forces are in equilibrium when the factor of safety is equal to 1.0. If the forces causing failure are greater than the resisting strength, then the factor of safety is less than 1.0 and the slope will fail. However, a higher factor of safety designates a greater resistance to collapse.  
Figure 4: Internal Stability of a Soil Slope.  
Figure 3: Recommended Design Methods.  
Granular soils (sand and gravel) do not display cohesive behavior under unconfined conditions. A small amount of apparent cohesion may exist due to negative pore water pressure within unsaturated soil particles, although it should not be relied upon for the design of slopes. Additionally, the high permeability of granular soils effectively prevents excess pore water pressure. Conversely, considerable cohesive strength is found in fine grained soils (clay and silt) due to inherent negative pore water pressure that leads to increased effective stress. Since pore water pressure increases in a soil mass with low permeability, the analysis for fine grained soils may be performed using an undrained Mohr-Coulomb failure envelope with an internal friction angle equal to zero [34].  
According to the Mohr-Coulomb failure criteria theory, a material fails because of a combination of normal stress and shear stress. The combination of stresses creates a more critical limiting state than would exist if the principal stresses were acting individually. This concept is illustrated by the Mohr-Coulomb failure envelope in Figure 5[34]. Circle A is indicative of a safe stress state since it is plotted below the failure line. Conversely, a critical stress combination is evident for Circle B, which is tangential to the failure envelope.  
The shear strength in N/m\({}^{2}\) (\(\tau\)) of an undrained saturated soil is controlled by the material properties and effective stress conditions [35]:  
\[\tau=c^{\prime}+[(\alpha_{n}-\mu_{w})\times tan\phi^{\prime}] \tag{8}\]  
where:  
\(c^{\prime}=\) effective cohesion of the soil, N/m\({}^{2}\).  
\(\sigma_{n}=\) normal stress, N/m\({}^{2}\).  
\(\mu_{w}=\) pore water pressure, N/m\({}^{2}\).  
\(\phi^{\prime}=\) effective internal friction angle of the soil, degrees.