Clarification on CDP Calibration and Peak Stress in FLAC3D Uniaxial Compression Tests

Dear Zhao Cheng,
Based on the CDP concrete model, the stress obtained in a uniaxial compression test should be scaled by the factor (1−D), where D is the damage variable. Consequently, the nominal (real) stress cannot reach the maximum compressive strength fc_m​; instead, the peak stress should be approximately (1−D) fc_m​.

However, in the FLAC3D uniaxial compression examples, the reported stress (not the effective stress) reaches fc_m​. This raises a fundamental question regarding the calibration strategy used. If damage initiates at fc_0​, then reaching fc_m​ with the nominal stress should not be possible—only the effective stress would reach this value.

Could you clarify how the calibration was performed? Specifically:

  • Did you assume a constant beta parameter, or did you use an evolving beta controlling the expansion or contraction of the yield surface based on the ratio of the current compressive and tensile strengths?

  • If the latter approach was used, how did you address the numerical difficulties that arise when the tensile strength ft​ becomes very small, causing beta to increase sharply and often leading to convergence issues or failure of the Newton–Raphson solver?

  • Alternatively, did you adopt an internal calibration strategy, such as using an increased fc_m​ in the effective stress formulation and accounting for damage at peak compression (e.g., Dc,peak)?

I would appreciate clarification on which approach was used and how these issues were handled.

Many thanks,
Mojtaba