Unsaturated Behaviors

The unsaturated behavior of soil can be defined in the Unsaturated Zone Calculations section. It locates under the Strength tab in the Define Material Properties dialog. Note that:

• This option can only be enabled if the Groundwater Method = Finite Element Analysis in Project Settings.

In unsaturated soils, matric suction (negative pore pressure) influences soil behaviors, impacting both its strength and permeability. Negative pore pressures can result from:

• Finite element groundwater analysis (either steady-state or transient)
• Water pressure grid interpolation
• Water tables or piezo lines (negative pore pressures are automatically computed above the water surface)

For any of the above groundwater methods:

• If negative pore pressures are calculated AND

• You define unsaturated shear strength parameters,

then materials in the unsaturated zone above the water table will exhibit additional shear strength due to matric suction.

NOTE: by convention, the term matric suction implies the POSITIVE, or absolute value of the negative pore pressures calculated in the unsaturated zone.

Approaches

The unsaturated soil mechanics can be predicted in various ways. The single effective stress or shear strength in the unsaturated zone can be calculated.

The following options are provided to interpret unsaturated behavior:

• None – unsaturated behavior will not be included, only saturated behaviors of soil are considered.
• Unsaturated Shear Strength
• Single Effective Stress

To be mentioned, if Failure Criterion = Barcelona Basic is selected, the unsaturated behavior will be accounted for automatically using the total stress within the constitutive model. See the Constitutive Models section below for details.

Each approach is explained below. For more information, see the “Soil Behaviors in Unsaturated Zones” theory manual.

Single Effective Stress

The Single Effective Stress calculation approach is available for all failure criteria models except for the Barcelona model. To enable the approach, the Use effective stress analysis option must be selected under the Stress Analysis page in Project Settings dialog.

According to Bishop (1959), the single effective stress for unsaturated soils is written as:

Where is the effective stress, is the total stress, is a coefficient, is the pore-air pressure, and is the pore water pressure. In practice, is omitted from the equation, thus the effective stress will be calculated as:

or it can be written as:

where is the suction, and is the unit matrix.

In RS2, the value ofcan be determined by nine different methods. Note that=1 for saturated soils when the Unsaturated Zone Calculations is off. For more information, see the “Soil Behaviors in Unsaturated Zones” theory manual.

1. Bishop (1959)
2. Tabular Values – with respect to suction
   • Users define a table ofvs. matric suction values.
3. Tabular Values – with respect to degree of saturation
   • Users define a table ofvs. degree of saturation ( ) values.
4. Tabular Values – with respect to effective degree of saturation
   • Users define a table of vs. effective degree of saturation () values.
5. Gudehus (1995)
6. Khalili (2004)
7. Bolzon (1996)
8. Aitchison (1961)
9. Kohgo (1993)

Use Cutoff

The Use Cutoff option is subjected to the Single Effective Stress approach only, intended for limiting the suction (). In the calculation based on the equation above, an upper limit cutoff value can be set for the term. The default input is -100 kPa.

Unsaturated Shear Strength

The Unsaturated Shear Strength calculation option is only available for the Mohr Coulomb criterion. Two methods are provided: Fredlund and Vanapalli.

Fredlund (1978)

Suggested by Fredlund et al (1978), the unsaturated shear strength is calculated as:

Where is the effective saturated cohesion, is the total stress, is the net normal stress on the plane of failure at failure, is the matric suction, is the pore-air pressure, is the pore water pressure, is the effective saturated angle of friction, and is the angle of friction accounting for matric suction contribution to shear strength. Users need to input the unsaturated shear strength angle () and an air entry value. See the Air Entry Value section below for details about air entry value with Fredlund (1978). Note that:

1. In order to account for the approach correctly, the option of Maximum negative PWP on the Groundwater page of the Project Settings dialog needs to be ON with an input value of 0 to avoid double counting of suction effects.
2. The Unsaturated Shear Strength Angle is usually not a well-known quantity. To obtain an appreciation of its importance, a parametric study can be carried out, in which the Unsaturated Shear Strength Angle is varied between 0 and the Friction Angle of the material.

Vanapalli (1996)

Proposed by Vanapalli et al (1996), the unsaturated shear strength can be represented using either the degree of saturation or the water content.

With degree of saturation,

where is the residual degree of saturation and is degree of saturation.

With water content,

where is the water content, is the residual water content, and is the saturated water content. The water content or degree of saturation values are to be inputted on the Hydraulic tab of the Define Material Properties dialog.

Constitutive models that account for unsaturated behaviors

For the Failure Criterion = Barcelona Basic under the Strength tab in the Define Material Properties dialog, alternative to single effective stress, the effect of suction on mechanical behaviors can be interpreted using constitutive models that account for the matric suction and/or degree of saturation.

In such cases, the effective stress for fully saturated zone will be calculated as usual, however, in the unsaturated zone, the total stress will be employed () and the unsaturated behavior will be considered in the constitutive model.

Negative Pore Pressure Cutoff

You can set a cutoff value as the specified limit for pore water pressure (static method) or suction (steady and transient analysis). This option is available in the Groundwater page under the Project Settings dialog from the Analysis menu.

In steady and transient groundwater analysis, the suction used in calculation of effective stress will be limited at the Maximum Negative PWP value; the suction used to account for the unsaturated strength will be limited at the Maximum Negative PWP for Unsaturated Strength value. See the Groundwater Method topic for more information.

Depending on the selected unsaturated behavior model, instructions pertained to the two options are stated below.

Unsaturated Behavior = Unsaturated Shear Strength (Fredlund)

• The Maximum Negative PWP option has to be selected and the value set to 0.

• The Maximum Negative PWP for Unsaturated Strength option is available for this model.

Unsaturated Behavior = Unsaturated Shear Strength (Vanapalli)

• The Maximum Negative PWP option has to be selected and the value set to 0.
• The Maximum Negative PWP for Unsaturated Strength option has no effect on this model.

Unsaturated Behavior = Single Effective Stress

• The Maximum Negative PWP option has no effect on this model.
• The Maximum Negative PWP for Unsaturated Strength option has no effect on this model.

Failure Criterion = Barcelona Basic

• The Maximum Negative PWP option has to be selected and the value set to 0.
• The Maximum Negative PWP for Unsaturated Strength option has no effect on this model.

Air Entry Value

Air Entry Value is defined in Fredlund and Rahardjo (1993) as the matric suction value that must be exceeded before air recedes into the soil pores. The Air Entry Value is also referred to as the "displacement pressure" in petroleum engineering or the "bubbling pressure" in ceramics engineering.

Air Entry Value for Fredlund (1978)

In RS2, the air entry value calculation depends on the method. When Fredlund (1978) method is used for unsaturated shear strength calculations in a Mohr-Coulomb model, the unsaturated soil strength deviates by the air entry value.

If matric suction exceeds the air entry value, the strength is assumed to follow a linear envelope with Phi_b as the friction angle. Thus RS2 uses a bilinear strength envelope where:

• c' and phi' are used with positive pore pressures, and with negative pore pressures (matric suction) up to the air entry value
• Phi_b is used when negative pore pressure exceeds the air entry value.

The following figure (after Fredlund (2000) ) illustrates the effect of the air entry value. For matric suction less than the air entry value, the saturated effective stress friction angle is used. For matric suction greater than the air entry value, the unsaturated shear strength angle, Phi_b is used.

Effect of air entry value (aev) on unsaturated shear strength envelopes.