Water and pore pressure

Pore pressure enters the factor of safety through the effective normal stress on the base of each slice, so the water conditions of the model affect the result directly. OGR Slip2D obtains pore pressures from water surfaces drawn on the model, from a pore-pressure ratio, from a constant, from a grid of measured or computed values, or from a finite-element seepage analysis. Which of these a given material uses depends on the groundwater method of the project and on its own water parameters.

2.4.1Choosing the groundwater method#

Two choices work together. The project's Method, on the Groundwater page of Analysis → Project Settings… (Section 2.1.4), says whether pore pressures come from a grid or from a finite-element analysis. Each material's Water Parameters, in Properties → Define Materials… (Water parameters), say where that material takes its pore pressure from. A new material is dry until its water parameters point at something.

2.4.2How a material takes its pore pressure#

The Type in a material's Water Parameters decides the pore pressure $u$ at every point of the material, and so at the base of every slice in it. The theory behind each one is in Section 3.6.

With a grid method the grid overrides these types, except constant and ru, for every material whose Use the water pressure grid box is ticked (Section 2.4.5).

Water surfaces and Hu#

Below a water table or a piezometric line, the pore pressure is hydrostatic, scaled by the coefficient $H_u$:

where

$\gamma_w$

unit weight of the pore fluid, Pore Fluid Unit Weight in Project Settings (9.81 kN/m³)

$h$

vertical distance from the point up to the water surface (m); $u = 0$ where the point is above it

$H_u$

the material's Hu coefficient when ticked, otherwise the project's Default Hu (1.0); with Auto Hu ticked in the material or in the project, $H_u = \cos^2\alpha$, with $\alpha$ the inclination of the water surface above the point

$H_u = 1$ is the hydrostatic pressure under a horizontal water surface. $H_u = \cos^2\alpha$ assumes that the equipotential through the point is straight, which is exact only for an infinite slope with seepage parallel to its surface. The pore pressure is zero at any abscissa outside the horizontal extent of the water surface, so draw water surfaces across the whole width of the materials they serve.

The pore-pressure ratio ru#

With the type ru, the pore pressure is a fixed fraction of the vertical stress at the point:

where

$r_u$

the material's Ru coefficient, 0 to 1

$\gamma, z$

unit weight of the material that contains the point (its saturated unit weight when it uses one), applied over the whole depth, and depth $z$ of the point below the ground surface

$d_w$

depth of any ponded water above the ground at that abscissa

External loads (distributed, line and seismic) are not part of $\sigma_v$.

2.4.3Water tables and piezometric lines#

A water table is the phreatic surface; a piezometric line records a pressure head measured or estimated somewhere in the ground. Both give pore pressure by Eq. (2.4.1), but they are not interchangeable:

• a model has one water table at most, and any number of piezometric lines, numbered 1, 2, … in the order they are drawn;
• only the water table forms ponded water where it rises above the ground (Section 2.4.4);
• only the water table allows a separate saturated unit weight below it (General);
• only the water table limits a water pressure grid: with both, $u = 0$ above the water table.

To add one:

1. Choose Boundaries → Add Water Table (Ctrl+3) or Boundaries → Add Piezometric Line (Ctrl+5).
2. Click its vertices from left to right, covering the whole width of the materials it serves, and finish with Enter.
3. If the project has materials, the Assign Water Surface dialog opens on the line just drawn: tick the materials that take their pore pressure from it and press OK.

Assign Water Surface#

The dialog also opens from Properties → Assign Water Surface…, and assigns one water surface to several materials at once. Choose the surface in Water Surface; the table lists every material with a check box, ticked for those already assigned to it, and the Current Water Surface of each. Select All and Clear All tick or untick the whole list.

• Ticking a material assigns the surface to it and sets its type to water_table or piezometric to match.
• Unticking a material that was assigned to this surface removes the assignment and makes it dry again.
• Materials assigned to a different surface are never changed by unticking.

The same assignment can be made one material at a time with the Water Surface list of Define Materials. A material of type water_table or piezometric left at (first of this type) reads the first surface of that type in drawing order, which is the same thing when there is only one; with several piezometric lines, assign each material explicitly.

2.4.4Ponded water#

Where the water table is drawn above the ground surface (a reservoir against an embankment, or a flooded toe), the space between the two is standing water. OGR Slip2D applies it as a load that needs no assignment to the materials: a hydrostatic pressure normal to the ground surface, on the slices beneath it.

• Piezometric lines never create ponded water, and neither does the drawdown line on its own.
• With a finite-element method the standing water comes from the boundary conditions of the seepage analysis: wherever the prescribed total head is above the boundary.
• Ponded water carries no seismic force (Section 2.5.4).
• It can be shown filled or hatched on the canvas with View → Display Options…, tab Water, Ponded water.

2.4.5Water pressure grid#

A grid gives the pore pressure by interpolation from scattered data points, such as piezometer readings or the output of a seepage analysis made elsewhere.

1. In Project Settings → Groundwater choose grid_total_head, grid_pressure_head or grid_pore_pressure. The method says what the values of the grid are: total head $H$ (then $u = \gamma_w (H - y)$), pressure head $h_p$ ($u = \gamma_w h_p$) or pore pressure $u$ directly.
2. Open Groundwater → Water Pressure Grid…, which is greyed out with any other method, and enter the points: type them in the table (Add row, Delete selected, Clear) or read them with Import CSV….
3. Press OK. The status bar gives the number of points; an empty table removes the grid.

A CSV file holds three numbers per line ($x$, $y$ and the value) separated by commas, semicolons, tabs or spaces, with a point as the decimal separator; header lines, blank lines and lines starting with # are skipped. With more than 300 points, or when the spline system is ill-conditioned, the thin plate spline gives way to the inverse-distance interpolation.

The grid governs every material whose Use the water pressure grid box is ticked in Define Materials (the default), except materials of type constant or ru, which keep their own value. Untick the box to let a material take its pore pressure from its own water parameters instead. A water table in the same model sets $u = 0$ above itself. View → Display Options…, tab Water, shows the grid values on the canvas.

2.4.6Excess pore pressure (B-bar)#

A soil of low permeability loaded faster than it can drain responds with a rise in pore pressure, which Skempton (1954) writes as proportional to the change in vertical stress:

The pore pressure used in the analysis is the one the material gets from its water parameters plus this excess. To use it:

1. In Project Settings → Groundwater → Advanced choose Calculate Excess Pore Pressure (B-bar method). It cannot be combined with a rapid drawdown or a transient analysis.
2. In Define Materials, the Excess Pore Pressure group appears. Give a B-bar greater than 0 to every material that develops excess pore pressure; a material with B-bar 0 is free-draining and develops none.
3. Say what loads them. A material with Material weight creates excess pore pressure ticked loads the materials beneath it with its own weight. A distributed or line load with Load creates excess pore pressure (B-bar method) ticked loads the materials beneath it with the vertical component of its force (Section 2.5.6).

The added vertical stress is the stress applied directly above the point, transmitted straight down without spreading, as the method assumes. A line load is a concentrated force, so the stress it adds depends on the width of the slice it falls on, and its excess pore pressure grows as the slices get narrower; model a surcharge whose excess pore pressure matters as a distributed load.

2.4.7Rapid drawdown and finite elements#

Two more ways of obtaining pore pressures have pages of their own:

For a rapid drawdown, choose Rapid Drawdown analysis and a procedure on the Groundwater page of Project Settings, draw the final level with Boundaries → Add Drawdown Line (Ctrl+4), and tick Undrained Behaviour on the materials of low permeability, with a B-bar or an undrained envelope depending on the procedure (Rapid drawdown and excess pore pressure). Groundwater → Drawdown Level Sweep… repeats the analysis at a range of reservoir levels (11 by default, 2 to 101), with or without the total drawdown, and reports the critical level, because the total drawdown is not always the critical one.