Homework - Bishop's Simplified Procedure
For this assignment, you will use the Bishop's Simplified Procedure to analyze the stability of a slope using Excel. You will be solving the same slope we analyzed as a class exercise using the Ordinary Method of Slices (OMS). The slope is partially saturated with a piezometric line.
The slice details are as follows:
The factor of safety for the Bishop's Simplified Procedure is calculated as follows:
\(F = \dfrac{\sum {\left[\dfrac{c'\Delta l + \left(W cos\alpha - u \Delta l cos^2\alpha\right)\tan\phi'}{cos\alpha + \left(sin\alpha\tan\phi'\right)/F}\right]}}{\sum {W\sin\alpha}}\)
Where:
\(c'\) = the effective cohesion at the base of the slice
\(\phi'\) = the friction angle at the base of the slice
\(\Delta l\) = the length of the base of the slice
\(W\) = the weight of the slice
\(\alpha\) = the angle of the slope at the base of the slice
\(u\) = the pore water pressure at the base of the slice = \(\gamma_w \cdot h_w\)
\(\gamma_w\) = the unit weight of water
\(h_w\) = the height of the water above the base of the slice
Note that the factor of safety (F) is a function of the unknown factor of safety (F) itself. Therefore, the calculation must be done iteratively. You can start with an initial guess for F and then update it until the difference between the calculated F and the assumed F is less than a specified tolerance (e.g., 0.0001).
Download the Excel file below and use it to calculate the factor of safety for the slope.
Excel starter file: bsp.xlsx
Submission
Upload the completed Excel file to Learning Suite.
Grading Rubric
Total: 30 points
| Criteria | Points |
|---|---|
| Proper setup of iterative solution | 6 |
| Correct calculation of slice base lengths | 4 |
| Correct calculation of slice weights | 4 |
| Correct calculation of pore water pressures | 4 |
| Numerator term calculations | 5 |
| Denominator term calculations | 3 |
| Iterative solution converges to correct FS | 2 |
| Documentation and work shown clearly | 2 |