Error message with **ERROR-STIFFNESS MATRIX IS NON-POSITIVE DEFINITE FOR LOAD CASE#


Troubleshooting of issues such as this can be found in the PSI manual in the Troubleshooting Common Problem section.  However, this is an example showing how to solve a common problem that SACS users usually face.  The soil plot below can be generated by using ‘Soil Plot Data’ from Utilities on SACS Executive.  The plot shows a sharp slope discontinuity of a T-Z soil curve.  This causes convergence difficulty as stated in the PSI manual.  One way to resolve this issue is to enter TABR input lines.  The users can read more information about this in the PSI manual.

The sharp slope discontinuity is located at Z axial values of 1.5cm.  So, the users should ensure that they enter Axial Deflection Values between 1.0cm and 2.0cm. An example of TABR AXIAL data is entered as shown below for both the pile tension and compression.

If the users do not know from where to start this TABR input data, they can run PSI analysis and find the TABR generated data in the output listing.  If there is no TABR data in the output listing generated, the users can use a small load case to run the PSI analysis and generate TABR in the output listing.  Then, they can use the program’s generated TABR in the output listing and enter those in the PSI input file and adjust those data accordingly.  The users should enter and try different TABR values and use the trial-and-error method until the analysis convergence is achieved.  The TABR value should be entered by a small amount so that the pile solution will be removed from the point of slope discontinuity

In addition, the user should also be aware that the number of iterations, the number of pile increments, convergence tolerance, etc are also important in achieving PSI analysis convergence depending on the PSI input data used.  These options can be changed from the PSIOPT line as shown below.

The user can also enter Axial Loads instead of Axial Deflections.  The user can run linear Basic Static analysis and get the joint reactions at the base of the structure.  Then, using the biggest reaction values the user can enter different loads intervals from big to small as shown below.

Alternatively, the problem can also be corrected by replacing the soil curves with sharp slope discontinuities with ones with a more gradual transition from one position to another.