Introduction
Pile Structure Interaction (PSI) is a program which models and analyzes the non-linear behavior of the soil for a pile supported structure. Gap is a program which models non-linear one way elements in the structure. Occasionally, analyses require the modeling of both non-linear pile soil interaction and non-linear one way elements. Due to the non-linear nature of the individual programs SACS must iterate over the solution to achieve convergence.
In some situations, it is acceptable to linearize the piles using the pile superelement feature in PSI and then running the Gap analysis with the pile superelement. However, this method assumes that there isn't much interaction between the non-linear elements (i.e. the non-linear gap elements do not significantly affect the pilehead stiffness). In cases where there is significant interaction the non-linear analyses must be combined into one non-linear analysis where both solutions converge for each load step.
The combination of Gap and PSI analyses can be achieved using Collapse. However there are a few modifications that must be made to the model in order to accurately model the Gap elements.
Collapse Input
Collapse Options
Member material non-linearity may be turned off with the All Members/Plates Elastic option on the CLPOPT line. Large deformations, non-linear springs and non-linear soil behavior will still be considered with this option.
Gap Element Modeling
In order to model the Gap elements in Collapse, the Gap elements must be replaced with non-linear joint-to-joint springs (NLSPJJ).
A Gap element is simply an axial non-linear joint-to-joint spring where one portion of the stiffness curve has a slope of zero and the other portion of the stiffness curve is the axial stiffness expressed as:
where
is the cross-sectional area
is the modulus of elasticity
and is the length of the element
Below is an example of a non-linear joint-to-joint spring for a tension element:
Non-Linear Joint-to-Joint Spring
Note that the slope of the force deflection curve is zero when the deflection is below zero. The deflection is calculated as the difference between the initial joint distance for the element and the joint distance for the element after the displacements have been determined, so a negative deflection would represent compression.
Output Options
A common solution file may be generated by Collapse which contains the solution of the final load step for each load sequence in the analysis. This common solution file can then be used for code checking. This option may be turned on using the Create Collapse Common Solution file in the Non-Linear / Plastic Analysis Options in the Collapse run file.
SACS Example 1
In this example, a Gap analysis will be converted into a Collapse analysis and the results are compared.
Consider a tower structure supported laterally by four wire cables as shown below. The wire cables, group 'CBL', are modeled using tension only Gap elements with shear capacity releases at joint 2.
SACS GAP model
Two basic load conditions are specified; load case WGT structure self-weight and load case LAT a lateral load in the positive global X direction applied at joints 2 and 3.
No Gap input file was required for the Gap analysis. All required Gap analysis data information was specified in the model file that follows:
OPTIONS EN SDUC 1 1 DDC C PT PTPT PTPT
PCODE DNVC201 1.15020.600
SECT
SECT CABLE TUB3.750 0.100 0.100 0.100 0.010 0.001
GRUP
GRUP CBL CABLE 13.0011.6036.00 9 1.001.00 0.500N490.00
GRUP FLG 24.000 0.625 29.0011.6036.00 1 1.001.00 0.500N490.00
MEMBER
MEMBER 10012 CBL T 011
MEMBER 10022 CBL T 011
MEMBER 10032 CBL T 011
MEMBER 10042 CBL T 011
MEMBER 1 2 FLG
MEMBER 2 3 FLG
JOINT
JOINT 1 0. 0. 0. 111111
JOINT 2 0. 0. 30.
JOINT 3 0. 0. 50.
JOINT 1001 -15. -15. 0. 111000
JOINT 1002 15. -15. 0. 111000
JOINT 1003 -15. 15. 0. 111000
JOINT 1004 15. 15. 0. 111000
LOAD
LOADCN LAT
LOAD 3 25.0000 GLOB JOIN LATERAL
LOAD 2 25.0000 GLOB JOIN LATERAL
LOADCN WGT
LOAD Z 1 2 -0.0330 -0.0330 GLOB UNIF DEADWT
LOAD Z 2 3 -0.0330 -0.0330 GLOB UNIF DEADWT
LCOMB
LCOMB CMB1 WGT 1.0000LAT 1.0000
LCOMB CMB2 WGT 1.0000LAT -1.000
END
**JNCV** 0 0 0 0 0 0 1
END Note: This is a slightly modified model from Sample 1 in the Gap manual.
The following is a portion of the output listing file created by the Gap program module:
SACS-IV SYSTEM JOINT DEFLECTIONS AND ROTATIONS
******************* INCHES ****************** ****************** RADIANS ******************
JOINT LOAD DEFL(X) DEFL(Y) DEFL(Z) ROT(X) ROT(Y) ROT(Z)
NUMBER CASE
1 CMB1 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
CMB2 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 CMB1 1.8141258 0.0000000 -0.0350815 0.0000000 0.0135753 0.0000000
CMB2 -1.8141258 0.0000000 -0.0350815 0.0000000 -0.0135753 0.0000000
3 CMB1 6.3610625 0.0000000 -0.0351410 0.0000000 0.0214899 0.0000000
CMB2 -6.3610625 0.0000000 -0.0351410 0.0000000 -0.0214899 0.0000000
1001 CMB1 0.0000000 0.0000000 0.0000000 0.0000000 0.0135753 0.0000000
CMB2 0.0000000 0.0000000 0.0000000 0.0000000 -0.0135753 0.0000000
1002 CMB1 0.0000000 0.0000000 0.0000000 0.0000000 0.0135753 0.0000000
CMB2 0.0000000 0.0000000 0.0000000 0.0000000 -0.0135753 0.0000000
1003 CMB1 0.0000000 0.0000000 0.0000000 0.0000000 0.0135753 0.0000000
CMB2 0.0000000 0.0000000 0.0000000 0.0000000 -0.0135753 0.0000000
1004 CMB1 0.0000000 0.0000000 0.0000000 0.0000000 0.0135753 0.0000000
CMB2 0.0000000 0.0000000 0.0000000 0.0000000 -0.0135753 0.0000000 SACS-IV SYSTEM FIXED JOINTS REACTION FORCES AND MOMENTS
******************** KIPS ******************* ****************** FT-KIPS ******************
JOINT LOAD FORCE(X) FORCE(Y) FORCE(Z) MOMENT(X) MOMENT(Y) MOMENT(Z)
NUMBER CASE
1 CMB1 14.275 0.000 130.199 0.000 -71.738 0.000
CMB2 -14.275 0.000 130.199 0.000 71.738 0.000
1001 CMB1 -32.138 -32.138 -64.275 0.000 0.000 0.000
CMB2 0.000 0.000 0.000 0.000 0.000 0.000
1002 CMB1 0.000 0.000 0.000 0.000 0.000 0.000
CMB2 32.138 -32.138 -64.275 0.000 0.000 0.000
1003 CMB1 -32.138 32.138 -64.275 0.000 0.000 0.000
CMB2 0.000 0.000 0.000 0.000 0.000 0.000
1004 CMB1 0.000 0.000 0.000 0.000 0.000 0.000
CMB2 32.138 32.138 -64.275 0.000 0.000 0.000 SACS-IV SYSTEM MEMBER INTERNAL LOADS SUMMARY REPORT
MAX. CRIT LOAD DIST * * * * * * * * * * I N T E R N A L L O A D S * * * * * * * * * NEXT TWO HIGHEST CASES
MEMBER GRP UNITY COND COND FROM AXIAL SHEAR SHEAR TORSION BENDING BENDING UNITY LD UNITY LD
CHECK NO. END Y Z Y-Y Z-Z CHECK CN CHECK CN
FT KIPS KIPS KIPS IN-KIP IN-KIP IN-KIP
1- 2 FLG 1.00 C<.15 CMB1 30.0 -129.21 14.275 0.0000 -0.33690E-18-0.30943E-12 6000.0 1.0 CMB2 0.0
2- 3 FLG 0.85 C<.15 CMB1 0.0 -0.66000 -25.000 0.0000 -0.24571E-34 0.0000 6000.0 0.9 CMB2 0.0 Now the analysis be converted into an equivalent Collapse analysis. First, the SACS model file is modified by deleting the Gap elements.
SACS Collapse Model
The gap elements must then be modeled as non-linear joint-to-springs. Since Gap elements are only effective axially, Only the axial stiffness must be defined. The equivalent stiffness is calculated as:
The collapse input file is shown below:
CLPOPT ME 0.010.001 0.011000.
LDSEQ GP1 WGT 1 1.0 LAT 5 1.0
LDSEQ GP2 WGT 1 1.0 LAT 5 -1.0
NLSPJJ 1001 2 DX -100. 110.574 1.
NLSPJJ 1002 2 DX -100. 110.574 1.
NLSPJJ 1003 2 DX -100. 110.574 1.
NLSPJJ 1004 2 DX -100. 110.574 1.
END The ME option on the CLPOPT line is invoked to treat all members as elastic and non-linear joint-to-joint springs have been created for each cable element. Load sequences GP1 and GP2 are equivalent to CMB1 and CMB2 from the Gap analysis.
The following is a portion of the output listing file created by the Collapse program module:
**** FINAL DEFLECTIONS AND ROTATIONS FOR LOAD SEQUENCE GP1 ****
LOAD CASE LAT
LOAD FACTOR 1.000
****** DEFLECTIONS ****** ******* ROTATIONS *******
JOINT X Y Z X Y Z
IN IN IN RAD RAD RAD
1 0.000 0.000 0.000 0.00000 0.00000 0.00000
2 1.846 0.000 -0.045 0.00000 0.01371 0.00000
3 6.423 0.000 -0.132 0.00000 0.02162 0.00000
1001 0.000 0.000 0.000 0.00000 0.00000 0.00000
1002 0.000 0.000 0.000 0.00000 0.00000 0.00000
1003 0.000 0.000 0.000 0.00000 0.00000 0.00000
1004 0.000 0.000 0.000 0.00000 0.00000 0.00000 ** SACS COLLAPSE REACTION FORCES AND MOMENTS **
*** FINAL ***
JOINT FORCE(X) FORCE(Y) FORCE(Z) MOMENT(X) MOMENT(Y) MOMENT(Z)
NO. KIPS KIPS KIPS IN-KIP IN-KIP IN-KIP
1 14.757 0.000 131.128 0.000 -928.603 0.000
1001 -32.370 -32.370 -64.739 0.000 0.000 0.000
1002 0.000 0.000 0.000 0.000 0.000 0.000
1003 -32.370 32.370 -64.739 0.000 0.000 0.000
1004 0.000 0.000 0.000 0.000 0.000 0.000After running the Collapse analysis a code check was performed on the common solution file. The following output was generated:
SACS-IV SYSTEM MEMBER INTERNAL LOADS SUMMARY REPORT
MAX. CRIT LOAD DIST * * * * * * * * * * I N T E R N A L L O A D S * * * * * * * * * NEXT TWO HIGHEST CASES
MEMBER GRP UNITY COND COND FROM AXIAL SHEAR SHEAR TORSION BENDING BENDING UNITY LD UNITY LD
CHECK NO. END Y Z Y-Y Z-Z CHECK CN CHECK CN
FT KIPS KIPS KIPS IN-KIP IN-KIP IN-KIP
1- 2 FLG 1.00 C<.15 GP1 30.0 -130.09 14.085 0.0000 0.0000 0.0000 5998.9 1.0 GP2 0.0
2- 3 FLG 0.85 TN+BN GP1 0.0 0.48084 -24.995 0.0000 0.0000 0.0000 5998.9 0.9 GP2 0.0 In general, there is good agreement between the Gap and Collapse analysis. There are slight differences between deflections, reactions, etc. This is mainly due to the difference between the solution methods and should not significantly impact the results.
SACS Example 2
In this example, a PSI input file is added to the analysis and the results are compared with the previous example. The only modification to the SACS model file is that the tower joint is converted to a pile head joint; the collapse model file is identical. A PSI model was created using a 60 ft pile connected to the tower and API soil curves.
SACS Collapse + PSI Model
The PSI input file is shown below:
PSIOPT +ZENG Y EX0.002540 0.0001 20PTPTPTPTPT S3 100 490.0
PLTRQ SD DL RL ML LS UC
PLGRUP
PLGRUP PL1 24. 0.62529000.11600. 36.00 60. 1.0
PILE
PILE 1 2 PL1 SOL1 SOL1
SOIL
SOIL TZAPI HEAD 2 SOL1 ICP
SOIL API AXL SLOC 50. SAND 1.0 125.
SOIL API AXL SLOC 50.0 100. ROCK 100. 100.
SOIL TORSION HEAD 1000.SOL1 N
SOIL LATERAL HEAD 1 24. 1.0SOL1 Y
SOIL API LAT SLOC SANDSA 100. 2.0 125. 1.0
END The following is a portion of the output listing file created by the Collapse program module:
**** FINAL DEFLECTIONS AND ROTATIONS FOR LOAD SEQUENCE GP1 ****
LOAD CASE LAT
LOAD FACTOR 1.000
****** DEFLECTIONS ****** ******* ROTATIONS *******
JOINT X Y Z X Y Z
IN IN IN RAD RAD RAD
1 -0.001 0.000 -0.002 0.00000 0.00000 0.00000
2 1.850 0.000 -0.047 0.00000 0.01372 0.00000
3 6.431 0.000 -0.134 0.00000 0.02164 0.00000
1001 0.000 0.000 0.000 0.00000 0.00000 0.00000
1002 0.000 0.000 0.000 0.00000 0.00000 0.00000
1003 0.000 0.000 0.000 0.00000 0.00000 0.00000
1004 0.000 0.000 0.000 0.00000 0.00000 0.00000 ** SACS COLLAPSE REACTION FORCES AND MOMENTS **
*** FINAL ***
JOINT FORCE(X) FORCE(Y) FORCE(Z) MOMENT(X) MOMENT(Y) MOMENT(Z)
NO. KIPS KIPS KIPS IN-KIP IN-KIP IN-KIP
1001 -32.357 -32.357 -64.713 0.000 0.000 0.000
1002 0.000 0.000 0.000 0.000 0.000 0.000
1003 -32.357 32.357 -64.713 0.000 0.000 0.000
1004 0.000 0.000 0.000 0.000 0.000 0.000And the following is a portion of the output listing file created by the Post program module:
SACS-IV SYSTEM MEMBER INTERNAL LOADS SUMMARY REPORT
MAX. CRIT LOAD DIST * * * * * * * * * * I N T E R N A L L O A D S * * * * * * * * * NEXT TWO HIGHEST CASES
MEMBER GRP UNITY COND COND FROM AXIAL SHEAR SHEAR TORSION BENDING BENDING UNITY LD UNITY LD
CHECK NO. END Y Z Y-Y Z-Z CHECK CN CHECK CN
FT KIPS KIPS KIPS IN-KIP IN-KIP IN-KIP
1- 2 FLG 1.00 C<.15 GP1 30.0 -130.03 14.057 -0.10846E-16-0.39081E-15-0.83437E-17 5998.9 1.0 GP2 0.0
2- 3 FLG 0.85 TN+BN GP1 0.0 0.48472 -24.995 -0.12063E-18-0.18705E-15 0.10132E-16 5998.9 0.9 GP2 0.0 The deflection at joint 1 represents the flexibility of the pile head while the cable support reactions still indicate that the gap elements are behaving properly.
Conclusion
The non-linear joint-to-joint spring in Collapse can serve as an acceptable replacement for Gap elements.