PROBLEM:

Most slopes are typically analyzed within the context of a circular slip surface. However, there is no guarantee that in actuality the slip surface will be perfectly circular. The critical issue for many slope stability analyses is what is the shape of the slip surface and what searching algorithm are we too used to find it. Algorithms which searched for noncircular failure surfaces are very limited. There is also the question of “Will any given slip surface follow a weak layer?”. Answering this type of question is impossible with a circular slip surface.

SOLUTION:

Dynamic programming (also called the SAFE method) provides a method of searching through a stress field for the most likely failure surface. The searching method is less restrained than most other searching methods and therefore there is a higher probability that the method will find a more optimal critical slip surface. In a thesis published by Ha Pham the re-analysis of a number of classic slope stability benchmarks resulted in a more optimal slip surface being found most of the time when compared to grid and radius search techniques. It is worthy of note that dynamic programming is a searching method only. The equations used to calculate the factor of safety are the same as used in limit equilibrium methods.

This example is used to verify the SVSLOPE-SAFE is a simple homogenous slope at 2:1 with a groundwater table passing through the toe of the slope. The soil is assumed to behave as a linear elastic material.

Model filename: Slopes_SAFE > Pham_Ch4_Figure4_1.svm

Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_10.svm

SAFE: Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_10_SAFE.svm

Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_11.svm

SAFE: Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_11_SAFE.svm

Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_12.svm

SAFE: Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_12_SAFE.svm

Figure 5_28 to 5_33 show locations of the critical slip surfaces obtained both by Pham (2002) as well as by other methods of slice, such as the M-P method, the Bishop's Simplified method and the Enhanced (Stress-Based) method. The Poisson's ratio value used in Figure 5_28 to 5_30 was 0.33, and Figure 5_31 to 5_33 was 0.48.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_29.svm

SAFE: Figure 5_28 to 5_33 show locations of the critical slip surfaces obtained both by Pham (2002) as well as by other methods of slice, such as the M-P method, the Bishop's Simplified method and the Enhanced (Stress-Based) method. The Poisson's ratio value used in Figure 5_28 to 5_30 was 0.33, and Figure 5_31 to 5_33 was 0.48.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_29_SAFE.svm

Figure 5_28 to 5_33 show locations of the critical slip surfaces obtained both by Pham (2002) as well as by other methods of slice, such as the M-P method, the Bishop's Simplified method and the Enhanced (Stress-Based) method. The Poisson's ratio value used in Figure 5_28 to 5_30 was 0.33, and Figure 5_31 to 5_33 was 0.48.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_33.svm

SAFE: Figure 5_28 to 5_33 show locations of the critical slip surfaces obtained both by Pham (2002) as well as by other methods of slice, such as the M-P method, the Bishop's Simplified method and the Enhanced (Stress-Based) method. The Poisson's ratio value used in Figure 5_28 to 5_30 was 0.33, and Figure 5_31 to 5_33 was 0.48.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_33_SAFE.svm

This example problem contains two soil layers with shear strength parameters.

Model filename: Slopes_SAFE > Pham_ch5_Figure5_44.svm

The slope stability studies by Pham (2002) contain three layers of soil with the base layers considerable harder than the above layers. The soil is described using a linear elastic.

Model filename: Slopes_SAFE > Pham_ch5_Figure5_48.svm

The bedrock layer was modeled as a relatively hard soil layer with high shear strength parameters. The slope is partly submerged with water.This example is typical of the case the anticipated block movement is the most likely mode of failure.

Model filename: Slopes_SAFE > Pham_ch5_Figure5_52.svm

SAFE: The bedrock layer was modeled as a relatively hard soil layer with high shear strength parameters. The slope is partly submerged with water.This example is typical of the case the anticipated block movement is the most likely mode of failure.

Model filename: Slopes_SAFE > Pham_ch5_Figure5_52_SAFE.svm

This example is considered as a homogenous slope with shear strength parameters equal to the average published values.

Model filename: Slopes_SAFE > Pham_ch5_Figure5_56.svm

Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_8.svm

SAFE: Figure5_7 to 5_12 show the locations of the critical slip surfaces obtain by various methods. The results from the SVSLOPE-SAFE software as well as the M-P method, the Bishop's Simplified method, and the Enhanced (i.e: Stress-Based) method. Various conditions were analyzed with different soil properties used in each use. The symbol S34-1030 means that the case has a submerged slope. Poisson's ratio is 0.48 and the soil cohension and the angle of the internal friction are 10 kPa and 30°, respectively.

Model filename: Slopes_SAFE > Pham_Ch5_Figure5_8_SAFE.svm