User reduction curves with PIMY & PDMY

[ChrisS]

Following the discussion in the previous post:
http://opensees.berkeley.edu/community/ ... =2&t=63386.

I have not fully comprehended the procedures used in the source code but I believe I have found some more errors:
Assuming that the $r values, used with PIMY & PDMY materials, refer to engineering strains (for eg. to use the EPRI reduction curves, the strain values are used unmodified) then the formulas used in note 3 of the documentation of the PIMY material should be corrected to:
--------------------------------------------------------------------------------
c = sigma_m
sin(phi) = (3*(2*sigma_m - 2*c)/p'_r ) / (6+(2*sigma_m - 2*c)/p'_r)

The following lines should be used in the source code (PressureIndependMultiYield.cpp):
--------------------------------------------------------------------------------
line 1102: Mnys = -(2. * tmax - 2. * cohesion) / refPressure;
line 1104: cohesion = tmax;
line 1122: cohesion = tmax;
line 1142: size = 2. * stress1 * coneHeight);
line 1161: size = 2. * stress2 * coneHeight);

Also the PDMY material documentation should be corrected to:
--------------------------------------------------------------------------------
sin(phi) = (3*(2*sigma_m)/p'_r ) / (6+(2*sigma_m)/p'_r)

The following lines should be used in the source code (PressureDependMultiYield.cpp):
--------------------------------------------------------------------------------
line 1513: double Mnys = -(2. * tmax - 2. * cohesion) / refPressure;
line 1541: ratio1 = 2. * stress1 * coneHeight;
line 1542: ratio2 = 2. * stress2 * coneHeight;

PDMY2 should be checked too.

The errors appear because the input stresses ($r * $G0 * $Gs) are used in the p-q plane after being multiplied by sqrt(3.) instead of 2.0 .

If the $r values were to be treated as octahedral trains then input stresses should be multiplied by a factor of sqrt(8) /3. to be used in p-q plane and more lines of source code should be changed.

Looking forward to your comments.

Chris Sioulis
sioulischris@teemail.gr