Multi-Plane Analysis (MPA™) in SVSLOPE®
Slope stability analysis is often targeted at topographically complex sites whose features vary greatly in three dimensions, or seemingly simple surface topology with strong and weak internal layers that vary across the site. For these types of sites, it can be difficult to determine where the location of the failure is most likely to be. Typically, an engineer would be required to perform tedious and time-consuming analysis at multiple different locations in sequence in order to find the location of the failure. SVSLOPE® now supports a new feature called Multi-Plane Analysis that enables rapid, thorough, and simple to perform analysis of a 3D site at many different locations simultaneously.
Multi-Plane Analysis requires a 3D model of the site, which may be created through SVDESIGNER™ or SVSLOPE®3D. When executing the solver, each location and direction (i.e., plane) undergoes full limit equilibrium analysis through SVSLOPE®, with a choice of either 2D or 3D analysis being available. This approach allows users to quickly and easily create many different 2D slices or rotated 3D models of the site in an automated manner, while still using the same underlying analysis method that they are familiar and comfortable with. Once the location of the failure surface is located through Multi-Plane Analysis, standard search methods can be performed as follow-up to refine the solution, if desired.
In order to demonstrate the feature, we will briefly look at the process of analyzing a tailings dam site with curved banks on both sides of the crest, and varying underground material layers. There is a weak layer that varies in thickness and depth across both banks.
Multi-Plane Analysis is defined by creating a number of planes across the model. Each plane defines a 2D slice of the model and contains configuration parameters such as the slope limits and slip surface search methods. The entire plane configuration process is designed such that it is quick to perform on one or many planes at once. For example, the slope limits may be defined for all planes at once by simply drawing a polygon that encloses the area of interest on the 3D model. The slip surface search method is automated, with some options available to the user.
Figure 1 shows the example model with a series of planes already defined. The planes are represented by the light gray lines projected on top of the model. There are multiple ways to create planes. The most common one, and the one used in this case, is to simply select a point on each of the two banks. Planes are then created along the slope automatically, at configurable distance intervals. The direction for each plane is set automatically based on the surface geometry. Each plane can be set to use multiple similar directions so that the critical direction is more likely to be found.
The Multi-Plane Analysis solver makes full use of all CPU power available on the system, which allows for rapid iteration. The solver collects the results of each individual analysis and aggregates them into the original 3D model for visualization.
Figure 2 shows the results of 2D analysis projected onto the 3D model. The factor of safety for each plane is shown and contoured, which gives an overview of slope stability results throughout the model. Each line represents the extents of the 2D critical slip surface transformed onto the coordinates of the 3D model. In this example, the top left area of the model has the lowest factor of safety due to the weak layer being dominant in that region. As well, for similar reasons, the right bank has some areas with a lower factor of safety than their surroundings.
The shape and size of each slip surface can also be visualized for one or more planes at once.
Figure 3 shows the shape of the 6 slip surfaces with the lowest factor of safety at each location. The slip surfaces were raised by the user above the model for visualization purposes, since the lines would normally be below the ground surface.
Analysis of each model may be performed in 3D simply by setting the Multi-Plane Analysis mode to 3D and uses the same model setup procedure. Switching from a 2D MPA analysis to 3D, or vice versa, takes seconds.
Figure 4 shows the results of the same tailings dam model after being analyzed in 3D. Critical slip surfaces are now shown on the model as outlines indicating their extents on the top surface. Each trial can also be selected with its full 3D ellipsoid visualized. In addition, a Factor of Safety Map is draped onto the top surface. The color at each location on this map indicates the lowest factor of safety of any trial surface that has passed through that location.
The Multi-Plane Analysis feature is an additional feature that works by allowing the user to specify and analyze many sections of a 3D model at once. Additional help about the specifics of this implementation is available in the User Manual.
Hazardous processes such as landslides occurring in hilly regions around the world have increased in frequency in recent years due to climate change and the expansion of settled areas. Computing the landslide risk over large regions is becoming more commonly required. The risk also impacts the effort to build or maintain larger geotechnical structures such as earth dams.
Other risks include riverbank stability or the stability of roads or railways through the mountain.The expansion of cities around the world often requires the building of structures on hillslopes or mountainsides where the landslide risk is higher. Engineers are requiring tools of increased accuracy for stability calculations.
Traditional tools based on closed-form solutions are often too simplistic to capture the physical mechanics of slope failure. Geotechnical engineers have long relied on 2D limit equilibrium and finite element numerical methods to assess slope stability. Such methods have traditionally been limited in their ability to assess stability in a 3D regional world.
SVSLOPE®/MPA™ represents a combination of the classic geotechnical analysis of slope stability by the limit equilibrium method while allowing application over large regions. The analysis can be performed using 2D slices or full 3D. The analysis can consider the effect of pore-water pressure and climate. These factors allow analysis of landslide risk with increased rigor. Regions up to 10km x 10km can be reasonably set up and analyzed in the software with an easy-to-use graphical user interface (GUI).
Regional geometry can be built from LiDAR, survey data or files imported from GIS systems or Google Earth. Likewise, boreholes can be imported and geostrata built. Many different soil strength models can be selected and pore-water pressures can be represented from piezometers or imported from regional groundwater software models. Climatic calculation of actual evaporation (AE) based on weather station data can be incorporated into the model as well, in order to model seasonal precipitation effects or climate change effects.
A semi-automated graphical method of searching for potential slides allows the user to intuitively guide the searching procedure.
Hundreds, thousands ormillions of analyses can be set up and managed on massively parallel systems and the software can provide quick solutions through a managed parallel solver controller module. The results are assembled and plotted visually in a 3D graphical environment. Aerial photos can be overlaid on the results to locate zones of high risk in their relation to nearby structures, buildings, or residential areas.
SVSLOPE®/MPA™ allows municipal planners, geotechnical, and geological engineers access to an analysis tool of increased rigor for more accurate calculations of regional landslide risk.
1. MUNICIPAL DESIGN
The rapid growth of cities around the world has resulted in the expansion into hilly or mountainous areas of higher landslide risk. Such risk requires city planning engineers to estimate the potential stability of large areas subject to municipal development.
SVSLOPE®/MPA™ allows analysis of such large areas based on topography, borehole, and piezometric water table data. LiDAR can be utilized to build detailed maps of topology for integration into the numerical model. The model can also be calibrated to existing known slope failures. The resulting output of the 2D or 3D analysis allows the risk zones to be identified. Aerial photos can be overlaid on the high quality 3D results for increased interpretations.
2. ROADS AND RAILWAYS
Engineered roads or railways may often be required through hilly or mountainous zones. The risk of landslides must be mitigated in order to ensure the passage remains safe and useable. The SVSLOPE®/MPA™ software allows stability analysis along long continuous passages of roads or railways through the input of surface topology from LiDAR, GIS, or Google maps data. SVDESIGNER also implements multiple methods of representing complex geostrata as input to SVSLOPE®. An example of analysis of a road through mountains may be seen above.
3. RIVERBANK, LAKES AND RESERVOIR STABILITY
Riverbanks and lakefronts are particularly problematic due to changing water levels which can create rapid drawdown slope stability risks. Changes in climate can also re-activate known landslide zones which may be difficult for residential or commercial structures nearby. SVSLOPE®/MPA™ allows the creation of long riverbanks or the geo-strata surrounding lakes or reservoirs for a more complete picture. The entire site can then be analyzed in 2D or 3D and the factor of safety plotted in 2D plan view or in full 3D view with beautifully detailed graphics as shown below.
4. DAMS AND LEVEES
Analysis of large and long geotechnical structures is often problematic. Difficulties have been experienced particularly in larger tailings dams at 3D intersections. Often the engineer can control the engineered structure but the foundation may be subject to varying geo-strata which can affect the stability in a 3D manner. Use of the SVSLOPE®/MPA™ methodology can provide the engineer with a more comprehensive picture of stability of the structure by performing many stability analyses based on the entire representation of the 3D site.
Simply stated...Slope stability analysis is often targeted at topologically complex sites whose features vary greatly in three dimensions, or seemingly simple surface topology with strong and weak internal layers that vary across the site. For these types of sites, it can be difficult to determine where the location of the failure is most likely to be. Typically, an engineer would be required to perform tedious and time-consuming analysis at multiple different locations in sequence in order to find the location of the failure. SVSLOPE®/MPA™ enables rapid, thorough, and simple to perform analysis of a 3D site at many different locations simultaneously.
Computing the landslide risk over large-scale regions is becoming a more common requirement.
The risk also impacts the effort to build or maintain larger geotechnical structures such as earth dams. Other related risks include riverbank stability, natural slopes, or the stability of roads and railways through the mountains. The expansion of cities around the world often requires the building of structures on hillslopes or mountainsides where the landslide risk is higher.
Engineers are requiring tools of increased accuracy for stability calculations. Traditional tools based on closed form solutions are often too simplistic to capture the physical mechanics of slope failure. SVSLOPE®/MPA™ represents a combination of the classic geotechnical analysis of slope stability by the limit equilibrium method while allowing application over large 3D regions. The analysis can consider the effect of pore-water pressure and climate and allows analysis of landslide risk with increased rigor.
We are actively seeking research partnerships to explore this analysis area in more detail. If you would like to collaborate on research please or you would like more information on this feature, feel free to contact us directly.