# Geosynthetic Reinforced Steep Slopes: Current Technology in the United States
## 3 Foundation & Backfill Materials
### Weak Foundation Soil  
Horizontal earth pressures tend to laterally spread embankments constructed on weak foundation soils. Weakened areas may be caused by sink holes, thawing ice, old stream beds, or layers of soft silt, clay, or peat. Failure will result if the foundation soil does not have adequate shear resistance to the stresses. Therefore, the design guidelines for reinforced embankments on weak soils should also consider bearing failure, rotational failure, and lateral spreading as per Figure 2[29].  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Sieve Size** & **Percent Passing (\%)** \\ \cline{2-3}
**Gradation** & 4 in. & 100 \\ \cline{2-3}
**(AASHTO T-27)** & \#4 & 100–20 \\ \cline{2-3}  & \#40 & 60–0 \\ \cline{2-3}  & \#200 & 50–0 \\ \hline
**Plasticity Index** & & PI (Plastic Index) \(\leq\) 20 \\
**(AASHTO T-90)** & & \\ \hline
**Soundness** & Magnesium sulfate soundness loss less than 30\% after 4 cycles, based on AASHTO T-104 or equivalent sodium sulfate soundness of less that 15\% after 5 cycles. \\ \hline \hline \end{tabular}
\end{table}
Table 3: Granular Reinforced Fill Recommendations [10; 24; 25; 26].  
Classical bearing capacity theory should be used when the thickness of the weak soil is much greater than the width of the embankment [30]:  
\[q_{ult}=(\gamma\times H)=(c_{u}\times N_{c}) \tag{1}\]  
where:  
\(q_{ult}=\) ultimate bearing pressure, N/m\({}^{2}\).  
\(\gamma=\) unit weight of the soil, N/m\({}^{3}\).  
\(H=\) height of the slope, m.  
\(c_{u}=\) undrained cohesion of the soil, N/m\({}^{2}\).  
\(N_{c}=\) bearing capacity factor.  
If the factor of safety for bearing capacity is insufficient, the following project parameters should be considered: increasing the embankment width, flattening the slopes, adding toe berms, or improving the foundation soils. A rotational slip surface analysis can also be used to determine the critical failure surface and the factor of safety against shear instability [1]:  
\[T=[(FS\times M_{D})-M_{\rm R}]/[R\times cos(\theta-\beta)] \tag{2}\]  
where:  
\(T=\) tensile strength of reinforcement, N/m.  
\(FS=\) factor of safety, N/m\({}^{3}\)/N/m\({}^{3}\).  
\(M_{D}=\) driving moment, N\(\cdot\)m.  
\(M_{R}=\) resisting moment, N\(\cdot\)m.  
\(R=\) radius, m.  
\(\theta=\) angle from horizontal to tangent line, degrees.  
Figure 2: Embankment Failure Modes on Weak Foundation Soils [29].  
\(\beta=0\) for brittle strain-sensitive foundation soils.  
\(=\theta/2\) for depth/width ratio \(<0.4\) and moderately compressible soils.  
\(=\theta\) for depth/width ratio \(\geq 0.4\) and highly compressible soils.  
Finally, a lateral spreading or sliding wedge stability analysis should be performed. Cohesion is assumed to equal zero for extremely soft soils and low embankments. The factor of safety is calculated as follows [31]:  
\[FS=(b\times tan\phi^{\prime})(K\times H) \tag{3}\]  
where:  
\(b=\) width of the wedge, m.  
\(\phi^{\prime}=\) effective internal friction angle of the soil, degrees.  
\(K=\) earth pressure coefficient.  
\(H=\) height of the slope, m.  
The elastic modulus of geosynthetic reinforcement is relied upon to control lateral spreading over weak foundation soils. By limiting the deformation behavior of the reinforcement, excessive deformation of the embankment can be mitigated. The distribution of lateral pressure and strain is assumed to vary linearly, increasing from zero at the toe to a maximum value beneath the crest of the embankment. The maximum strain in the reinforcement should be equal to twice the average strain in the embankment. Tolerable deformation requirement (\(J\)) is calculated as follows:  
\[J=T/\varepsilon \tag{4}\]  
where:  
\(T=\) tensile strength of reinforcement, N/m.  
\(\varepsilon=\) strain limit based on type of fill soil materials (m/m).