3.1.5.18. CreepShrinkageACI209 – Wrapper Creep Material

This command is used to construct a uniaxial time-dependent material object that wraps around an existing base material to simulate creep and shrinkage under sustained loads. The creep and shrinkage evolution equations follow ACI 209R-92. The wrapper subtracts the computed creep and shrinkage strains from the total applied strain before passing the resulting mechanical strain to the base material, so any uniaxialMaterial can be made time-dependent with this wrapper.

uniaxialMaterial CreepShrinkageACI209 $matTag $baseMaterial $tD $epsshu $psish $Tcr $phiu $psicr1 $psicr2 $tcast

Argument	Type	Description
$matTag	integer	Unique integer tag for this material.
$baseMaterial	integer	Tag of an existing uniaxialMaterial to wrap.
$tD	float	Analysis time at initiation of drying (days).
$epsshu	float	Ultimate shrinkage strain \((\varepsilon_{sh})_u\) in ACI 209R-92 Eq. 2-7 (input as negative).
$psish	float	Shrinkage time-evolution parameter \(f\) in ACI 209R-92 Eq. 2-7. Typical values: 35 (moist-cured 7 days), 55 (steam-cured).
$Tcr	float	Reference concrete age at loading (days) for which $phiu is defined.
$phiu	float	Ultimate creep coefficient \(\phi_u\) in ACI 209R-92 Eq. 2-6. Standard ACI 209 value is 2.35.
$psicr1	float	Creep time-evolution parameter \(\psi\) in ACI 209R-92 Eq. 2-6.
$psicr2	float	Creep time-evolution parameter \(d\) in ACI 209R-92 Eq. 2-6.
$tcast	float	Analysis time at concrete casting (days).

The material implements the following ACI 209R-92 equations.

Shrinkage strain (ACI 209R-92 Eq. 2-7):

\[\varepsilon_{sh}(t) = \frac{t - t_D}{f + (t - t_D)} \cdot (\varepsilon_{sh})_u\]

Creep coefficient (ACI 209R-92 Eq. 2-6, summed over all past stress increments):

\[\phi(t,\, t_i) = \frac{(t - t_i)^{\psi}}{d + (t - t_i)^{\psi}} \cdot \phi_u \cdot \left(\frac{t_{cr}}{t_i - t_{cast}}\right)^{0.118}\]

where \(t_i\) is the time of each previous stress increment and the factor \((t_{cr}/(t_i - t_{cast}))^{0.118}\) is the ACI 209 age-at-loading correction.

Note

1. Shrinkage parameters should be input as negative values; if given positive they are converted to negative internally.

2. Time values ($tD, $Tcr, $tcast) must be in the same time units used in the analysis (days are assumed).

3. Creep is only active when the OpenSees ops_Creep flag is set to 1.

Example

The following example constructs a Concrete02IS base material (tag 1) and wraps it with CreepShrinkageACI209 (tag 2) using standard ACI 209R-92 parameters for 7-day moist-cured concrete loaded at 28 days.

1. Tcl Code

# Base concrete material (Concrete02IS, tag 1)
# E0  fpc    epsc0   fpcu   epscu
uniaxialMaterial Concrete02IS 1 4000.0 -4.0 -0.002 -0.8 -0.01

# Wrap with ACI 209 creep/shrinkage (tag 2)
# matTag baseMat tD   epsshu    psish  Tcr   phiu  psicr1 psicr2 tcast
uniaxialMaterial CreepShrinkageACI209 2 1 7.0 -780e-6 35.0 28.0 2.35 0.6 10.0 0.0

2. Python Code

import openseespy.opensees as ops

# Base concrete material (Concrete02IS, tag 1)
ops.uniaxialMaterial('Concrete02IS', 1, 4000.0, -4.0, -0.002, -0.8, -0.01)

# Wrap with ACI 209 creep/shrinkage (tag 2)
ops.uniaxialMaterial('CreepShrinkageACI209', 2, 1, 7.0, -780e-6, 35.0, 28.0, 2.35, 0.6, 10.0, 0.0)

References

This wrapper creep material was adapted from the TDConcrete material. A manual describing TDConcrete can be found at: https://data.mendeley.com/datasets/z4gxnhchky/5

1. American Concrete Institute (ACI). (2002). ACI PRC-209-92: Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures (Reapproved 2008). ACI Committee 209. ISBN: 9780870311222.

2. Knaack, A. M., & Kurama, Y. C. (2018). Modeling Time-Dependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural Journal, 115(1).

3. Knaack, A. (2013). Sustainable concrete structures using recycled concrete aggregate: Short-term and long-term behavior considering material variability (Doctoral dissertation, University of Notre Dame), 680 pp.

Code developed by: Javad Esmaeelpour, Mark D. Denavit, and Michael H. Scott. Based on TDConcrete by Adam M. Knaack and Yahya C. Kurama.