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PORE WATER PRESSURE.

the Groundwater Method in Project Settings determines how pore water pressure will be modeled in Slide. Six options are available:

 

Water Surfaces Ru Coefficients Water Pressure Grid (Total Head) Water Pressure Grid (Pressure Head) Water Pressure Grid (Pore Pressure) Finite Element Analysis

You may also use the B-bar method to calculate excess pore pressure due to undrained loading, by selecting the Calculate Excess Pore Pressure checkbox.

Pore Pressure Definition: Ground Water Analysis

Slide now has the capability to carry out finite element based groundwater analysis for saturated/ unsaturated, steady-state flow conditions. Slide's groundwater analysis function allows the user to easily define and analyze a groundwater problem using the same model as the slope stability problem. The boundaries of the problem only need to be defined once; definitions will then be used for both the groundwater analysis and the slope stability analysis.

Although Slide's groundwater analysis is geared towards the calculation of pore pressures for slope stability problems, it is not restricted to slope geometry configurations. The groundwater modeling and analysis capabilities in Slide can be used to analyze an arbitrary 2-D groundwater problem for saturated/unsaturated, steady-state flow conditions.

Slide's groundwater analysis component is completely self-contained and can be used entirely independently of the slope stability functionality of Slide.

Groundwater Modeling

The groundwater modeling options in Slide are all contained within the Slide model program. In order to enable groundwater modeling, it is first necessary to set the Groundwater Method in Project Settings to Finite Element Analysis. When this is done, an Analysis Mode option will be available, which allows you to select either Slope Stability analysis mode or Groundwater analysis mode. When you are in Groundwater analysis mode, the menu and toolbar will present

all of the necessary groundwater modeling options.

Groundwater Compute

In Slide, the groundwater analysis engine and the slope stability analysis engine are separate. You may perform a groundwater analysis in Slide without performing a slope stability analysis. After groundwater analysis is performed, the results (pore pressures) can be automatically utilized by Slide's slope stability analysis engine.

Groundwater Interpret

The Slope stability and groundwater interpreters are combined into one Interpreter. You can view contours of groundwater data at the same time as viewing slope stability results. This lets you spend less time creating output that is suitable for presentation in a report.

 

 

 

Pore Pressure Definition: Water Surfaces

Both phreatic and piezometric surfaces can be defined in Slide. The analysis uses these surfaces to determine the pore pressure within the soil. Every material can be assigned a water surface (same or different) for pore pressure calculation. To determine the pore pressure at a particular point, the program determines the distance to the water table or piezometric surface and uses the unit weight and Hu value to calculate the pore pressure. The Hu value is a simple reduction factor to account for seepage and can be either defined by the user or automatically calculated based on the slope of the water surface. Since there may be multiple water surfaces and any material can be given its own surface, soil units such as aquifers with different pore pressure profiles can easily be modeled.

Single water table - all soil units use this water surface for pore pressure calculation.

Same model as above but green layer is an aquifer with its own piezometric surface (surface #1) - other soil (yellow) uses the water table for pore pressures.

 

 

 

Pore Pressure Definition: RU Factors

Ru coefficients can be used to calculate pore pressure. The Ru coefficient used in Slide is the most widely used. It simply models the pore pressure as a fraction of the vertical earth pressure for each slice. Each soil can have a different Ru value.

 

 

Pore Pressure Definition: Pore Pressure Grids

Pore pressure grids are another way of including pore pressures in a Slide slope stability analysis. The pore pressures can come from field piezometer values, a flow net or a groundwater (seepage) analysis program. All you have to do is fill in a table of coordinates and values of head (total or pressure) or pore pressure.

Data entry for a grid of total head values.

If one of the three Water Pressure Grid options is selected, the user may also select the method of interpolation, which is used to obtain the water pressure at any point in the soil from the grid data. Several different interpolation methods are available.

Model showing a pore pressure grid (blue triangles) - data is from field piezometers.

Model showing a total head grid (blue triangles) - data is from a flow net.

 

Pore Pressure Definition: Interpolation Methods

If one of the three Water Pressure Grid options is selected, then the user may also select the method of interpolation, which is used to obtain the water pressure at any point in the soil from the grid data. If the strength type for a soil is Discrete Function, then interpolation is done to determine the strength of the soil at any point within the soil region. In Slide, the following methods are available: Thin Plate Spline, Chugh, Modified Chugh, Local Thin-Plate Spline, TIN triangulation, Inverse Distance, and Linear by Elevation.

Thin-Plate Spline

The Thin-Plate Spline method utilizes the concept of an infinite thin elastic plate under tension to determine a spline surface (a smooth 3-dimensional surface which fits through all of the data points). The spline surface is used to determine the sample value at any location. See Franke (1985).

Chugh's Method

This is an interpolation method based on finding the nearest water pressure grid point in each of the four quadrants with origin centered at the point where the interpolation is required (e.g. at the midpoint of the base of a slice). A plane is then fit through each combination of three quadrant grid points and an interpolation is performed for each plane. This results in four interpolations, which are then averaged to obtain the final interpolated value at the desired point. See Chugh (1981).

 

Modified Chugh

This is based on the Chugh method, with the additional requirement that the interpolation point must be WITHIN the triangle formed by any combination of three quadrant points. If the interpolation point is NOT within a triangle, then this combination of quadrant points is NOT used. This check insures that EXTRAPOLATED values are not included in the average interpolated value. This avoids numerical inaccuracies which sometimes occur with the Chugh method, due to excessively large extrapolated values.

Local Thin-Plate Spline

The Local Thin-Plate Spline method is an extension of the Thin-Plate Spline interpolation technique for use with a large number of data points (>200). The only difference between the methods is that instead of using all the data points for the interpolation, the Local version takes a maximum of 10 closest points to the sample point and fits a spline surface through them. If there are less than 10 data points, then this method defaults to the non-local version. The local spline surface is then used to determine the sample value.

TIN Triangulation

TIN (Triangulated Irregular Network) triangulation takes the data points and triangulates them using the Delaunay triangulation method. To calculate the value at a sample point, the program first determines which triangle the point lies within. If the point lies outside the convex hull of the data, then the secondary interpolation method is used. The convex hull is a convex polygon with data points for vertices that wrap around the perimeter of the data points. Once the triangle that contains the sample point is found, the interpolated value is calculated using linear interpolation. This is done by calculating the plane equation that fits through the 3 data points at the triangle vertices, then solving for the value using the coordinates of the sample point and the plane equation.

Inverse Distance

The Inverse Distance Interpolation method weights every data point according to its distance to the sample point. This scheme is also known as the Shepard method (Shepard, 1968) and can be written in the form:

where P is the location of the point to be interpolated, F(P) is the interpolated value, Pi the location of the scattered data, Fi are the scattered data values, and ||P-Pi||2 represents the distance from P to Pi. The main deficiencies of this method are, 1) the local extrema are typically located at the data points and this results in poor shape properties, and 2) undue influence of points which are far away. See Shepard (1968).

Linear by Elevation

The Linear by Elevation method only utilizes the elevation (y-coordinate) of each data point. The method simply determines the closest data point (elevation) above the sample point and the closest data point (elevation) below the sample point, and linearly interpolates the sample value based on these two data points. Interpolation is done in the vertical direction only. This method is meant for horizontally bedded soils where data varies by depth only. It is extremely useful for cases where a complicated strength or pore pressure profile exists in only the vertical direction. The x-coordinate of the data points is not used in the interpolation process. However, it is used to display the data on your model.

Secondary Interpolation Method

In methods such as the TIN Triangulation and the Chugh method, cases exist where interpolation of a sample point can not be performed. In the case of TIN triangulation, an interpolation value can not be calculated if the sample point lies outside the convex hull of the user-defined data

points. In the Chugh method, if a data point does not exist in all four quadrants surrounding the sample point, then an interpolated value can not be calculated. In both these cases, a secondary interpolation method is used. By default in Slide, the Local Thin-Plate Spline method is used as the secondary interpolation method. This insures that an interpolated value is always calculated at a sample point.

Display of Interpolation Contours

The Slide Interpeter allows you to view contours of the approximate results of the interpolation process, directly on the model. The interpolation results should always be looked at to ensure that the interpolation correctly simulates your field data. If it does not, then use more data points or a different interpolation technique. Since no interpolation method is guaranteed to work for all datasets, different methods should be tried in order to determine the best method for your data.

Contours of Discrete Strength function interpolation. The strength was interpolated using 13000 data points generated from a finite-element model. Notice the complex distribution of strength.

 

References

Franke, Richard. (1985), Thin plate splines with tension, Computer Aided Geometric Design 2 87 - 95, North-Holland. Chugh, A.K. (1981), Pore Water Pressure in Natural Slope, InternationalJournal for Numerical and Analytical Methods in Geomechanics, Vol. 5, 449 - 454, John Wiley & Sons Ltd. Shepard, D. (1968), A two dimensional interpolation function for irregularly spaced data, Proc. 23rd Nat. Conf. ACM, 517?524.

 

 

Pore Pressure Definition: Excess Pore Pressure

In Slide, you can model the effect of excess pore pressure resulting from undrained loading by selecting the "Calculate Excess Pore Pressure (B-bar method)" checkbox. The B-bar method allows you to account for short term (transient) changes in pore pressure due to rapidly applied loading conditions. These loading conditions may include:

Added Material Weight Vertical Seismic Loading Vertical External Loading

 Select checkbox to enable Excess Pore Pressure modeling.

When you select this option, you will be able to:

Define B-bar coefficients for materials in the Define Material Properties dialog. Define which materials or loads cause the excess pore pressure.

    Excess pore pressure is equal to the B-bar coefficient multiplied by the change in vertical stress. The change in vertical stress can be due to any of the above loading conditions. The final pore pressure which is used in the stability analysis, is equal to the Initial Pore Pressure + Excess Pore Pressure.

Rapid Drawdown Analysis

If you select the "Rapid Drawdown Analysis" checkbox in Project Settings, this allows you to simulate the rapid drawdown of ponded water (e.g. earth dams), using the B-bar method. The weight of existing ponded water is used to determine the (negative) change in pore pressure for materials with a B-bar coefficient. The ponded water is then automatically removed from the model when the stability calculations are carried out.

Define B-bar coefficient in Material Properties dialog.