Homework - Infinite Slope Analysis
The proposed site for an offshore structure is located in a region of gradually varying bottom slope off the California coast. Due to the seismicity of this region the owner has asked for your preliminary evaluation of the stability of the slope during an earthquake.
The significant water depth contours (in fathoms) are shown on the plan view of the site in the following map:
Previous exploration in the vicinity of the site indicates that the soil profile is relatively uniform over a large area, and for this and economic reasons only one soil boring was taken for the current investigation. The location of this boring (Boring A) is shown in the map above and the boring log details are as follows:
The shear strength values shown on the boring log were measured in unconsolidated undrained triaxial compression tests.
Recall that for a submerged slope under undrained conditions the infinite slope factor of safety can be found using the following equation:
\(FS = \dfrac{c}{\gamma'z} \dfrac{2}{sin(2\beta)}\)
where:
\(c\) = undrained cohesion of the soil
\(\gamma'\) = effective unit weight of the soil
\(z\) = depth of the slope
\(\beta\) = angle of the slope with the horizontal
The unit weight of the soil can be calculated from the specific gravity of the soil and the moisture content of the soil as follows:
\(\gamma_{sat} = \left(\dfrac{1+w}{1+w G_s}\right)G_s\gamma_{w}\)
where:
\(G_s\) = specific gravity of the soil
\(w\) = moisture content of the soil
\(\gamma_{w}\) = unit weight of water
The effective unit weight of the soil can then be calculated as:
\(\gamma' = \gamma_{sat} - \gamma_w\)
As a first approximation for the stability during an earthquake compute the static factor of safety of the slope using an infinite slope analysis and a cross-section along the line A-A'. For many clay slopes a factor of safety of 2.0 or greater with respect to static stability is adequate to ensure that stability will be maintained during an earthquake. Using the data above, calculate the factor of safety of the slope.
Excel starter file: infslope.xlsx
TIPS:
1) Note the slope details at the bottom of the sheet. Use the cells in part one to estimate the average slope angle of the middle steeper section.
2) Use the table in part 2 to calculate the FS at each depth. Be sure to use the correct FS equation.
3) At each depth, use the undrained strength at that depth, but the average unit wt above that depth.
Submission
Submit the completed Excel file to Learning Suite.
Grading Rubric
Total: 30 points
| Criteria | Points |
|---|---|
| Average slope angle calculation | 5 |
| Unit weight calculations at each depth | 5 |
| Effective unit weight calculations | 5 |
| Factor of safety calculations at each depth | 10 |
| Identification of critical depth and FS | 3 |
| Documentation and work shown clearly | 2 |