Boundary condition at base of a finite element/difference model can significantly affect outputs of a seismic analysis. The key to find out what base boundary condition suits our numerical model is to find out whether the earthquake motion to be applied at the base of our model is “outcrop motion” or “within motion”. Outcrop motions are recorded on top of a rock layer, while within motions are either recorded at a specific depth from soil surface or computed by performing a site response analysis. The former is rare because it is not easy to maintain an accelerogram below ground surface.

In summary you must use:

• Rigid base if input earthquake is a within motion.
• Compliant base if input earthquake is an outcrop motion.

Let me explain this a bit more. The intention of using base boundary condition is to simulate wave downward and upward propagation when earthquake motion hits the base of the model. Propagation of upward and downward waves is simulated already in computation of a within motion. The within motion is actually the upward wave which propagates towards the ground surface. Therefore, there is no need for compliant base. On the other hand, outcrop motion consists of both upward and downward propagating waves. Compliant base boundary condition is required to absorb the downward wave which would result in propagation of just the upward component of the outcrop motion.

Two crucial things to consider when compliant base is used:

• Compliant base uses the viscous dashpot scheme developed by Lysmer and Kuhlmeyer (1969). Because half of the stresses is absorbed by the viscous dashpots, you need to add a factor of two to the dashpot coefficient. Softwares like PLAXIS already includes the factor of two in the compliant base formulation, while softwares like FLAC and OpenSees do NOT.  You need to include it manually by multiplying the input motion by a factor of 2.0. So check the formulation of compliant base before applying it in your numerical model.
• Remember that outcrop motion is recorded at rock surface so based on fundamentals of wave propagation, the motion is the summation of upward and downward propagating waves. At rock surface upward motion is equal to downward motion so half of the outcrop motion must be applied to the base of your numerical model.

Considering the above two items, 2 \times 1/2 = 1.0 times the outcrop motion is ultimately applied to the numerical model. So if factor of 2.0 is NOT included in the compliant base formulation (like in OpenSees and FLAC), there is no need to multiply outcrop motion by any factor. Otherwise (like in PLAXIS), a factor of 1/2 has to be multiplied by the outcrop motion.