# Geosynthetic Reinforced Steep Slopes: Current Technology in the United States
## Appendix B FHWA Design Guidelines with Chart Solution  
The following example provides a step by step procedure for performing a GRSS preliminary design with a chart solution in order to evaluate the feasibility of specific project parameters. **Define Slope Geometry, Loading, and Performance**  
The first step was to establish the geometric, loading, and performance requirements for the design. Factors of safety recommended by the FHWA were used for the analysis. Geometric and Load Requirements:  
Slope Height (H) = 6.1 m  
Slope Angle (\(\beta\)) = 70\({}^{\circ}\)  
Surcharge Load (q) = 12 kN/m\({}^{2}\)  
Crest Width (A) = 6.1 m  
Performance Requirements:  
Internal Stability: FS = 1.5  
External Stability: FS = 1.5  
**Define Engineering Properties of Soils**  
The parameters listed below were determined for the foundation, retained, and reinforced soils. Foundation and Retained Soils:  
Internal Friction Angle (\(\phi_{\mathrm{u}}\)\({}^{\prime}\)) = 34\({}^{\circ}\)  
Cohesion (c\({}_{\mathrm{u}}\)\({}^{\prime}\)) = 0  
Density (\(\gamma_{\mathrm{u}}\)) = 19.6 kN/m\({}^{3}\)  
Reinforced Soil:  
Internal Friction Angle (\(\phi_{\mathrm{r}}\)\({}^{\prime}\)) = 34\({}^{\circ}\)  
Cohesion (c\({}_{\mathrm{r}}\)\({}^{\prime}\)) = 0  
Density (\(\gamma_{\mathrm{r}}\)) = 19.6 kN/m\({}^{3}\)  
Depth of Water Table (d\({}_{\mathrm{w}}\)) = 5 ft  
**Determine the Geogrid Force Coefficient and Total Design Tension**  
\(\phi_{\mathrm{f}}\) = [tan\({}^{-1}\times\) (tan\(\phi_{\mathrm{r}}\)/FS)] = [tan\({}^{-1}\times\) (tan34\({}^{\circ}\)/1.5)] = 24.2\({}^{\circ}\)  
K = 0.34 as per reference 10  
\(\mathrm{T_{S-MAX}}\) = [0.5 \(\times\) K \(\times\) \(\gamma_{\mathrm{r}}\)\(\times\) (H\({}^{\prime}\))\({}^{2}\)] = [0.5 \(\times\) 0.34 \(\times\) 19.6 \(\times\) [6.1 + (12/19.6)]\({}^{2}\)] = 150.1 kN/m  
**Determine the Reinforcement Vertical Spacing and Design Tension per Reinforcement Layer**  
S\({}_{\mathrm{v}}\) = 0.4 m  
\(\mathrm{T_{MAX}}\) = [(\(\mathrm{T_{S-MAX}}\times\) S\({}_{\mathrm{v}}\))/H] \(\times\) (RF\({}_{\mathrm{ID}}\)\(\times\) RF\({}_{\mathrm{CR}}\)\(\times\) RF\({}_{\mathrm{D}}\))  
\(=\) [(150.1 \(\times\) 0.4)/6.1)] \(\times\) (1.2 \(\times\) 3.0 \(\times\) 1.25)  
\(\mathrm{=44.3\ kN/m}\)  
**Determine Length of Reinforcement**  
L/H\({}^{\prime}\) = 0.8 as per reference 10\[\mathrm{L}=(\mathrm{L}/\mathrm{H}^{\prime})\times\mathrm{H}^{\prime}=0.8\times[6.1+(12 /19.6)]=5.37\;\mathrm{m}\]  
**Jewell Method**  
The following example provides a step by step procedure for performing a GRSS preliminary design using the Jewell Method in order to evaluate the feasibility of specific project parameters. Consider a slope with the following parameters:  
\[\mathrm{H}=6.1\;\mathrm{m}\] (height) \[\mathrm{\beta}=70^{\circ}\] (slope angle) \[\mathrm{q}=10.1\;\mathrm{kN/m^{2}}\] (surcharge load) \[\mathrm{c}=0\] (soil cohesion) \[\mathrm{\phi}=32^{\circ}\] (soil internal friction angle) \[\mathrm{\gamma}=20\;\mathrm{kN/m^{3}}\] (soil unit weight) \[\mathrm{FS_{design}}=1.30\] (design factor of safety) \[\mathrm{FS_{grid}}=2.75\] (geogrid factor of safety) \[\mathrm{T_{ult}}=65.7\;\mathrm{kN/m}\] (geogrid tensile strength) \[\mathrm{H}=6.1\;\mathrm{m}\]0 (pore water pressure coefficient)  
1. Calculate the allowable tensile strength (\(\mathrm{T_{allow}}\)) and design tensile strength (P). \[\mathrm{H}=6.1\;\mathrm{m}\]1 \[\mathrm{H}=6.1\;\mathrm{m}\]2
2. Based on the pore water pressure coefficient, determine the coefficient of earth pressure (K) and the ratios of reinforcement length to embankment height (\(\mathrm{L}/\mathrm{H}\))\({}_{\mathrm{overall}}\) and (\(\mathrm{L}/\mathrm{H}\))\({}_{\mathrm{sliding}}\) using the charts in reference 10, then calculate the reinforcement length. \[\mathrm{H}=6.1\;\mathrm{m}\]3 \[\mathrm{H}=6.1\;\mathrm{m}\]4 \[\mathrm{H}=6.1\;\mathrm{m}\]5 \[\mathrm{H}=6.1\;\mathrm{m}\]6 \[\mathrm{H}=6.1\;\mathrm{m}\]7
3. Define the spacing constant (Q) for the slope in terms of the minimum spacing (v) to be used. \[\mathrm{H}=6.1\;\mathrm{m}\]8 \[\mathrm{H}=6.1\;\mathrm{m}\]9
4.