Application | PLAXIS 2D PLAXIS 3D |

Version | PLAXIS 2D 2023.1 PLAXIS 3D 2023.1 |

Date created | 8 May 2023 |

Date modified | 8 May 2023 |

Original author | Faseel Khan - Bentley Technical Support Group |

PLAXIS 2D and PLAXIS 3D offer a wide range of tools to model saturated and unsaturated soil behavior. Unsaturated soils, if included in the geotechnical design, can significantly impact the construction cost. This article describes how PLAXIS can be used to include unsaturated soil behavior in your geotechnical designs to better assist with defining construction costs.

In PLAXIS, suction represents a positive value of the difference between pore air and water pressures: (p_{a} - p_{water}). In PLAXIS, the air pressure is taken zero as a reference value. Therefore, suction is the tension component in p_{water}.

For fully saturated soil the 'active pore pressure' is equal to the 'pore water pressure', so S_{eff} = 1.

PLAXIS uses the term 'active pore pressures' to denote the contribution of the pore stresses in the total stresses:

where: S_{eff} is the effective degree of saturation, S is the degree of saturation, S_{res} is the residual degree of saturation, S_{sat} is the saturated degree of saturation, usually equal to 1.0.

For unsaturated soils, S_{eff} , determines the proportion of the suction included in the active pore stresses. This depends on the soil-water retention curve (SWCC) as defined in the material data set of the soil layer because there is a relationship between degree of saturation and suction. This relationship, S(Ψ), is one of the inputs for unsaturated material properties. PLAXIS provides hydraulic models for inputting such relationships in the form of SWCC, such as a popular model, the van Genuchten model.

The effect of suction on hydraulic conductivity is captured by specifying appropriate relationships, k(Ψ), in form of a SWCC. For a detailed description of specifying the SWCC in terms of degree of saturation and hydraulic conductivity, refer to Chapter 19 of the PLAXIS 2D/3D 2023.01 Material Models manual.

It is often required to convert measured data concerning the degree of saturation (S) to volumetric water content (θ) and for that you can refer to the following article for converting the functional forms θ(Ψ) and k(Ψ) to the functional form S(Ψ) and k(Ψ) or vice versa: Hydraulic conductivity input in PLAXIS using van Genuchten functional forms in a groundwater flow analysis

PLAXIS allows the input of unsaturated unit weight, which is considered for the material above the phreatic level.

Bishop’s effective stress (Bishop & Blight, 1963) is used in PLAXIS to handle unsaturated soil conditions. The following figure (Fig. 1) shows the different components of the effective stress equation:

Fig. 1 Different components of the Bishop’s effective stress equation

Shear strength, as per the Mohr-Coulomb failure criterion is defined as:

When suction is not ignored, the mechanical effects of suction are introduced via the definition of effective stress:

Note that S_{eff} , as described above, includes the relationship between S and suction through the SWCC. In PLAXIS suction pore water pressures are positive with respect to the atmospheric pressure. Below the phreatic level, the pore water pressures are considered negative in PLAXIS, and the soil is saturated.

The effect of increasing soil suction on shear strength can be shown by first creating a constant stress state in a soil, then increasing the suction in subsequent phases till the sample reaches its shear strength capacity. The results in the figure (Fig. 2) below show this effect such that the load-carrying capacity of the soil increases with an increase in suction. It is also noted that the load carrying capacity will decrease with a reduction in soil suction. So, care must be taken in specifying the appropriate SWCC for the soil as an overestimation of shear strength may lead to an unsafe design.

Fig. 2 Effect of suction on shear strength

This increase in shear strength can readily be visualized in slope stability analysis. If a large part of the slip surface passes through an unsaturated zone and if the design allows to take unsaturated soil properties into consideration then the profound effect of suction can be taken into consideration for an economic design of a slope.

In Fig. 3, we can see that an increase or decrease in soil suction has a considerable effect on increasing or decreasing the factor of safety, allowing for a steeper or flatter slope depending on the ambient weather conditions. This will, in turn, affect the construction cost of the project as a steeper slope will require lesser excavation or in other words, an unsaturated slope with high suction in the unsaturated zone will require less slope stabilizing measures compared to a slope which has low suction stresses in the unsaturated zone.

Fig. 3 Effect of suction on factor of safety

The effect of soil suction on compressibility is such that after the air-entry value the soil becomes stiffer, and a larger amount of soil suction is needed to reduce the same amount of void ratio compared to when soil deforms in a saturated state.

This is illustrated in the Fig. 4 (Fredlund and Rahardjo, 1993). Initially, when the soil is saturated, effective stress and soil suction have the same effect in reducing the void ratio. In other words, they have the same effect in increasing the deformations. Past the air-entry value, for the same increment in effective stress or soil suction, the effective stress increases the deformation by a greater amount compared to the deformations caused by an increase in soil suction.

Fig. 4 Effect of net normal stress and suction on void ratio

Fig. 5 was developed by first creating a suction state in the soil and then applying a constant load. In subsequent phases, suction was increased, whereas the load value was kept constant.

The results also show that if the effective stresses are reduced by reducing the soil suction, the deformations will increase. This is typically the case in a rainfall or water runoff event. Therefore, for short-term designs, if proper precautions are taken into consideration regarding any rainfall/runoff event, the increased stiffness of the soil can help reduce construction costs. This reduction in cost can come from an increased bearing capacity of soil which will require a smaller foundation or a slope can be cut at a steeper angle to reduce excavation costs and so on.

Fig.5 Effect of suction on soil compressibility

In a time-dependent analysis, the rate of decrease or increase of shear strength or deformations or factor of safety with respect to an increase or decrease in soil suction is dependent on whether we are starting from a saturated state and going towards a drier state or starting from a drier state and moving towards a saturated state. This is because the saturated hydraulic conductivity is many orders of magnitude larger than the unsaturated hydraulic conductivity at a drier state. If the soil desaturates from a saturated state, the initial saturated hydraulic conductivity is high (compared to the drier state) and so we will see a faster increase in shear strength, a decrease in deformations and an increase in factors of safety. If, on the other hand, we start from an initially dry state, the initial unsaturated hydraulic conductivity is many orders of magnitude lower than the saturated hydraulic conductivity and so we will see a much slower reduction in shear strength, increase in deformations and reduction in factor of safety.