DeepEX offers a variety of slope stability analysis methods that can calculate the safety factors of circular and non-circular slope surfaces. The following methods are available:
A. Simplified Bishop Method
The simplified Bishop method uses the method of slices to discretize the soil mass and determine the FS (Factor of Safety). This method satisfies vertical force equilibrium for each slice and overall moment equilibrium about the center of the circular trial surface. Since horizontal forces are not considered at each slice, the simplified Bishop method also assumes zero interslice shear forces.
In the Bishop method, only circular failure surfaces should be examined. One of the major limitations of the Bishop method is that only moment equilibrium is considered. To simplifiy the analysis and verification, support effects in the Bishop method are calculated as an additional moment resistance that is applied on the overal moment safety factor equation. The moment resistance is calculated for each support about the center of rotation. If a support is encompassed by the failure circle then this support is ignored for slope stability purposes.
B. Generalized Limit Equilibrium Method (GLE – Morgenstern-Price)
The GLE method is an extension of Spencer’s (1973) method, which has been generalized by Chugh (1986). The GLE method adopts a function to assign the interslice force angle on the right-hand side of each slice. There are several interslice force angle functions that can be adopted to emlate any slope shape.
In the General Limit Equilibrium method, the support forces are considered in the overall vertical and horizontal directions for both moment and horizontal equilibrium. Since supports are always installed first on a vertical face of the wall slice, the general equilibrium equation with the moments is expanded to include the exact point where each support force is applied. The total vertical and horizontal support force is included.
C. Spencer Method
The Spencer method is analyzed in the same manner as the GLE method within the software program. The only difference is that a single interslice angle is assumed for all the slices. In the Spencer method, the support forces are considered in the overall vertical and horizontal directions for both moment and horizontal equilibrium. The supports in Spencer method are considered exactly the same way as in GLE method.
D. Ordinary Swedish Method
We can select to apply a slope stability method in the Slope tab of DeepEX.
Figure 8.1.1: Select a slope stability analysis method
After selecting a method, we can define the method parameters by pressing the button “Options” in the Slope tab of DeepEX. In the dialog that appears we can define several parameters for all methods (preliminary slice width, minimum number of slices etc.), as well as parameters for the equations when GLE method (Morgenstern-Price) is selected.
Figure 8.1.2: Define slope stability analysis method options
We can select the options to use either circular slope surfaces or circular surfaces with active and/or passive wedges in the Slope tab of DeepEX. After this selection we have to define the position of a slope center or a rectangular of centers, as well as, define the points where the circular surface radius would possibly pass from.
Figure 8.2.1: Select to use circular slope surfaces
Using a Single Slope Center
When we wish to use a single point as a center for the slope surfaces, we have to use the tool from the Draw tools option in the Slope tab of DeepEX. Next, we have to click on the model area, close to the point we wish to add the center. By double-clicking on the center we can define the exact position.
Figure 8.2.2: Add a single slope center and edit center position
Using a Rectangle of Centers
When we wish to check several spots at once as possible slope centers, we can select from the Draw tools options in the Slope tab of DeepEX to add a rectangular of centers. By double-clicking on the rectangle, we can define the exact position and number of increments, increasing or decreasing the number of the possible centers.
Figure 8.2.3: Add and edit a rectangle of slope centers
Defining Radius Search Options
Right below the wall, we can locate a green line with points. This line represents the radius search limits and the points will be used as possible points where the slope surfaces will pass from. The software will calculate and return the most critical slope surface. By double-clicking on the green line, we can modify the slope search limits and number of increments. In addition, instead of limits, we can also define a specific slope radius.
Figure 8.2.4: Edit radius search limits
Sometimes, it is required to check the stability of a specific, non-circular slope surface. In this case, we can select the option “User specified surface” in the Slope tab of DeepEX.
Figure 8.3.1: Select to use a custom specified surface
From the Draw tools in the slope tab of DeepEX, we can select the tool to draw a user defined surface. Then we need to click on points on the model area, where we wish the slope surface to pass from. It is good to start from a point on the ground surface and then define all points from left to right. When we pass the last point, we need to press the “Enter” button from the keyboard. The custom slope surface is generated. By double-clicking on it, we can define the exact position of all points.
Figure 8.3.2: Add a user-defined slope surface
DeepEX has an option locate the most critical failure surface automatically, within the model limits. This option is available in the Slope tab of DeepEX.
Figure 8.4.1: Select to use the automatic failure surface search option
When the automatic search option is selected, two green lines appear on the left and right side of the model, representing the left and right slope search limits. We can double-click on each line and define the x-coordinates of the start and end point of each search limit.
Figure 8.4.2: Automatic slope search limits
On a sloped ground surface in DeepEX, we can select to add a single row or a group of rows of soil nails. The soil nails can be added, using the tools in the Slope tab of DeepEX. Later, we can access and define the exact position, installation angle, horizontal spacing, length and structural section of each soil nail row.
Figure 8.5.1: Add/Edit a single soil nail row
Figure 8.5.2: Add/Edit a group of soil nail rows
To run the slope stability analysis in a model, this model needs to be analyzed first. When the general analysis is performed, we can select to run additionally the slope stability analysis from the Slope tab of DeepEX.
Figure 8.6.1: Option to run slope stability analysis (model needs to be analyzed first)
After the slope stability analysis is performed, the most critical slope surface and the slope stability safety factor appear on the model area.
Figure 8.6.2: Calculated critical surface and slope stability FS
From the Results tab of DeepEX, we can select to present the results for the slices. By double-clicking on a slice, we can review the result diagram of the specific slice.
Figure 8.6.3: Slope stability results - slices
By selecting the option “Global FS Contours” in the Results tab of DeepEX, we can review in the rectangle of centers the safety factors calculated on for all possible slope centers.
Figure 8.6.4: Slope stability results – global FS contours
When soil nails are used in the model, DeepEX presents the soil nail results on the model area and in the soil nails partial dialog (when we double-click on a soil nail after the analysis is performed). On the model area, we can review the stresses along the soil nail and the soil nail reaction. In the partial dialog, we can review the soil nail results in tables.
Figure 8.6.5: Soil nail results on the model area
Figure 8.6.6: Soil nail results in tables
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