Strange PSA Amplification in FLAC Plastic Hardening vs Plaxis HS-Small in 1D Model

FLAC
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Hi all,

I’m running a 1D site response analysis consisting of 8 horizontal layers. The top 7 layers are modeled using PM4Sand and PM4Silt, and the bottom layer (Layer 8) uses the Plastic Hardening (PH) model in FLAC2D, with the small-strain stiffness feature turned on.
I recreated the same model in Plaxis 2D using HS-Small for Layer 8 and identical geometry, parameters (stiffness, OCR, φ′, etc.), and Rayleigh damping.
What I observed is that the PSA spectra at the ground surface are close between FLAC and Plaxis, which is expected.However, at the top of Layer 8, the PSA from FLAC is significantly amplified, whereas Plaxis shows the attenuation. This suggests a mismatch in how damping (especially hysteretic damping) is handled in the PH model in FLAC.

I’ve attached a figure below. The left plot compares surface spectra; the right plot shows spectra just above Layer 8. As seen, FLAC significantly amplifies the input motion at depth, unlike Plaxis.

Resim3
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I have a few questions about the issue:

  1. Has anyone experienced similar amplification in the Plastic Hardening model with small-strain stiffness activated?
  2. Could this be caused by insufficient hysteretic damping in FLAC’s PH model (even with Rayleigh damping defined)?
  3. Is there a way to tune or calibrate hysteretic behavior in the PH model to behave more like HS-Small?
    Any suggestions or experience would be greatly appreciated!
    Thanks in advance.
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Without datafile, it is insufficient for us to locate what occurred. Please sent your datafile to flac3dsupport@oneitasca.com or zcheng@oneitasca.com.

I also suggest you use a simpler model, e.g., elastic, to Zone 8 to check if it is narrow the issue to the PH-SS & HS-Small model.

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Hi Emirhan,
I suggest you first to performe a 1-zone test to compare the of PH Small strain response with respect to other hysteretic models available in FLAC, such as elastic+hysteretic damping (sig3, sig4, etc.) or UBCHyst, all with the same additional Rayleigh damping. This way you are going to be able to see if the model, and your calibration, are capable to capture the response you are looking for at least in terms of G/G0 vs gamma and damping vs gamma. Comparing in terms of system response, at least in my experience, could be misleading if you are not sure of the response of the material (or the constitutive model) itself. I hope this is helpful to you.

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I did a quick check of your data file and did not identify apparent abnormal inputs. One issue, however, is strain localization in the PM4Silt zone just above the PH-SS zones. This localization (softening) may reflect and amplify waves propagated from the base. In this opinion, the amplified result appears quite reasonable. Does the Plaxis model also predict this strain localization?

Other comments:

  1. FLAC uses a new Brick algorithm (with 12 scales), which eliminates the overshooting observed in the original Benz algorithm and provides better numerical performance for nested hysteretic loops. Does Plaxis use the same algorithm and scales, or is it still based on the older Benz approach?
  2. The PH-SS model includes sufficient intrinsic constitutive-level “hysteretic” damping, so stiffness-proportional Rayleigh damping is not implemented for this model. However, mass-proportional Rayleigh damping should still apply.
  3. Mohr-Coulomb model + hysteretic damping should be close to PH-SS model.
  4. As jmbarbagelata and I have suggested:
  • Try replacing PH with an elastic/MC model to see if the issue persists.
  • Run single-zone tests with PH-SS and HS-Small to check for consistency.
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