How does Plaxis deal with water pressures during dynamic calculations?

In relation to water pressures in a dynamic calculation we can distinguish between:

•  pseudo static approach
•  full dynamic (time-history) calculation

Pseudo static approach

A pseudo static approach is a strongly simplified approach of an earthquake situation. In this approach, we apply a constant and uniform acceleration to all the mass in the model. This approach is similar to the way gravity is introduced in the model but we can specify the magnitude and also the direction (i.e. a_x and/or a_y). Also, see the link below for further information on this approach.

Now with regard to water loads/pressures during a pseudo static calculation: realise that water loads coming from “free” or “open” water are transformed to surface loads acting perpendicular to (active) model boundaries. During a pseudo static approach we increase these surface loads with the ratio of the size of the initial gravity load vector and the resulting size of the gravity+acceleration load vector (while the load direction stays perpendicular to the model boundary). So, in the following example:

• gravity: g =  9.81 m/s²
• specified acceleration: a_x = 2.5 m/s²
• scale factor = sqrt ((g² + a_x²) / g²) = sqrt ((9.81² + 2.5²) / 9.81²) = 1.03

Note that as a result of the above method we can model to some extent the hydrodynamic overpressure in a pseudo static analysis, however, we do not take into account real effects of free or open water, such as:

• fluctuations in water level due to sloshing;
• hydrodynamic under/over pressures due to mass effects

Note: “normal” point loads and surface loads are not influenced by these additional accelerations.

Similarly, the unit weight of water used to compute the pore water pressures is scaled up by an identical factor. 

Full dynamic (time-history) analysis

As mentioned above realise that water loads coming from “free” or “open” water are transformed to surface loads acting on (active) model boundaries. As such they are simply static loads during a full dynamic (time-history) analysis. No dynamic water effects are considered.

For some situations, a trick may be to model the free or open water using a cluster with material properties assigned to it. This way, to some extend, the hydrodynamic effects may be captured on a structure. Possible settings for such a cluster may be:

• Mohr-Coulomb model
• Normal water weight
• Drainage type: Undrained C
• Strength parameters: phi = 0 and very small s_u
• Stiffness parameters: v_u=0.495 (default setting for Undrained C) and E should be selected such that the resulting K_w (bulk modulus of water) is the desired value

Note that with the above trick:

• still effects of real dynamic water behaviour are missed, such as fluctuations in water level due to sloshing;
• calculation times may increase due to the large amount of plasticity introduced in the model.