From cc1e3ee916fecb362f37a5f08214a52e62a0d09b Mon Sep 17 00:00:00 2001 From: Javad Esmaeelpour Date: Thu, 25 Jun 2026 21:11:40 -0400 Subject: [PATCH 1/2] Replace CreepMaterial documentation with CreepShrinkageACI209 --- .../user/manual/material/uniaxialMaterial.rst | 2 +- .../material/uniaxialMaterials/Creep.rst | 41 --------- .../CreepShrinkageACI209.rst | 90 +++++++++++++++++++ 3 files changed, 91 insertions(+), 42 deletions(-) delete mode 100644 source/user/manual/material/uniaxialMaterials/Creep.rst create mode 100644 source/user/manual/material/uniaxialMaterials/CreepShrinkageACI209.rst diff --git a/source/user/manual/material/uniaxialMaterial.rst b/source/user/manual/material/uniaxialMaterial.rst index 98ec7f83..e7097787 100644 --- a/source/user/manual/material/uniaxialMaterial.rst +++ b/source/user/manual/material/uniaxialMaterial.rst @@ -47,7 +47,7 @@ The following subsections contain information about **$matType** uniaxialMaterials/Concrete04 uniaxialMaterials/ASDConcrete1D uniaxialMaterials/GMG_CyclicReinforcedConcrete - uniaxialMaterials/Creep + uniaxialMaterials/CreepShrinkageACI209 .. uniaxialMaterials/Concrete06 .. uniaxialMaterials/Concrete07 diff --git a/source/user/manual/material/uniaxialMaterials/Creep.rst b/source/user/manual/material/uniaxialMaterials/Creep.rst deleted file mode 100644 index ed4f9c5f..00000000 --- a/source/user/manual/material/uniaxialMaterials/Creep.rst +++ /dev/null @@ -1,41 +0,0 @@ -.. _Creep : - -Creep Material -- Wrapper Creep Material -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -This command is used to construct a uniaxial time-dependent material object that wraps around a given base material to simulate both creep and shrinkage under sustained loads. The creep and shrinkage are modeled following the guidelines of ACI 209R-92. - -.. function:: uniaxialMaterial Creep $matTag $baseMaterial $tD $epsshu $psish $Tcr $phiu $psicr1 $psicr2 $tcast - -.. csv-table:: - :header: "Argument", "Type", "Description" - :widths: 6, 4, 40 - - "``$matTag``", integer, "Integer tag identifying material." - "``$baseMaterial``", integer, "Integer tag identifying base material." - "``$tD``", float, "Analysis time at initiation of drying (in days)." - "``$epsshu``", float, "Ultimate shrinkage strain denoted as :math:`(ϵ_{sh})_u` in Eq. 2-7 of ACI 209R-92." - "``$psish``", float, "Fitting parameter of the shrinkage time evolution function denoted as :math:`f` in Eq. 2-7 of ACI 209R-92." - "``$Tcr``", float, "Creep model age (in days) used for the calculation of ``$phiu``." - "``$phiu``", float, "Ultimate creep coefficient defined as the ratio of creep strain to initial strain, denoted as :math:`ν_u` in Eq. 2-6 of ACI 209R-92." - "``$psicr1``", float, "Fitting parameter of the creep time evolution function denoted as :math:`ψ` in Eq. 2-6 of ACI 209R-92." - "``$psicr2``", float, "Fitting parameter of the creep time evolution function denoted as :math:`d` in Eq. 2-6 of ACI 209R-92." - "``$tcast``", float, "Analysis time corresponding to concrete casting (in days)." - - -.. note:: - 1. Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). - - -**References** - -This wrapper creep material was adapted from the TDConcrete material by Michael Scott. The TDConcrete material was developed by A. M. Knaack and Y. C. Kurama. A manual describing the use of the TDConcrete concrete model can be found at: `https://data.mendeley.com/datasets/z4gxnhchky/5 `_ - -Detailed descriptions of the model and its implementation can be found in the following: - -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. - diff --git a/source/user/manual/material/uniaxialMaterials/CreepShrinkageACI209.rst b/source/user/manual/material/uniaxialMaterials/CreepShrinkageACI209.rst new file mode 100644 index 00000000..b5ae31a7 --- /dev/null +++ b/source/user/manual/material/uniaxialMaterials/CreepShrinkageACI209.rst @@ -0,0 +1,90 @@ +.. _CreepShrinkageACI209 : + +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. + +.. function:: uniaxialMaterial CreepShrinkageACI209 $matTag $baseMaterial $tD $epsshu $psish $Tcr $phiu $psicr1 $psicr2 $tcast + +.. csv-table:: + :header: "Argument", "Type", "Description" + :widths: 6, 4, 40 + + "``$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)." + "``$epsshu``", float, "Ultimate shrinkage strain :math:`(\varepsilon_{sh})_u` in ACI 209R-92 Eq. 2-7 (input as negative)." + "``$psish``", float, "Shrinkage time-evolution parameter :math:`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." + "``$phiu``", float, "Ultimate creep coefficient :math:`\phi_u` in ACI 209R-92 Eq. 2-6. Standard ACI 209 value is 2.35." + "``$psicr1``", float, "Creep time-evolution parameter :math:`\psi` in ACI 209R-92 Eq. 2-6." + "``$psicr2``", float, "Creep time-evolution parameter :math:`d` in ACI 209R-92 Eq. 2-6." + "``$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): + +.. math:: + + \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): + +.. math:: + + \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 :math:`t_i` is the time of each previous stress increment and the factor :math:`(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. + + +.. admonition:: 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** + + .. code-block:: tcl + + # 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** + + .. code-block:: python + + 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 `_. From f38b3e68a95b98aa1ecf30751a41c196c78cb837 Mon Sep 17 00:00:00 2001 From: Javad Esmaeelpour Date: Fri, 26 Jun 2026 00:00:06 -0400 Subject: [PATCH 2/2] Update TDConcrete family documentation - Add $ prefix to argument names in parameter tables - Restore function signature style to match rest of documentation --- .../user/manual/material/uniaxialMaterial.rst | 4 ++ .../material/uniaxialMaterials/TDConcrete.rst | 39 ++++++++++++++++ .../uniaxialMaterials/TDConcreteEXP.rst | 40 +++++++++++++++++ .../uniaxialMaterials/TDConcreteMC10.rst | 43 ++++++++++++++++++ .../uniaxialMaterials/TDConcreteMC10NL.rst | 45 +++++++++++++++++++ 5 files changed, 171 insertions(+) create mode 100644 source/user/manual/material/uniaxialMaterials/TDConcrete.rst create mode 100644 source/user/manual/material/uniaxialMaterials/TDConcreteEXP.rst create mode 100644 source/user/manual/material/uniaxialMaterials/TDConcreteMC10.rst create mode 100644 source/user/manual/material/uniaxialMaterials/TDConcreteMC10NL.rst diff --git a/source/user/manual/material/uniaxialMaterial.rst b/source/user/manual/material/uniaxialMaterial.rst index e7097787..6e3e8645 100644 --- a/source/user/manual/material/uniaxialMaterial.rst +++ b/source/user/manual/material/uniaxialMaterial.rst @@ -48,6 +48,10 @@ The following subsections contain information about **$matType** uniaxialMaterials/ASDConcrete1D uniaxialMaterials/GMG_CyclicReinforcedConcrete uniaxialMaterials/CreepShrinkageACI209 + uniaxialMaterials/TDConcrete + uniaxialMaterials/TDConcreteEXP + uniaxialMaterials/TDConcreteMC10 + uniaxialMaterials/TDConcreteMC10NL .. uniaxialMaterials/Concrete06 .. uniaxialMaterials/Concrete07 diff --git a/source/user/manual/material/uniaxialMaterials/TDConcrete.rst b/source/user/manual/material/uniaxialMaterials/TDConcrete.rst new file mode 100644 index 00000000..b24d50af --- /dev/null +++ b/source/user/manual/material/uniaxialMaterials/TDConcrete.rst @@ -0,0 +1,39 @@ +TDConcrete +^^^^^^^^^^ + +This command is used to construct a uniaxial time-dependent concrete material object with linear behavior in compression, nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to ACI 209R-92. + +.. function:: uniaxialMaterial TDConcrete $matTag $fc $fct $Ec $beta $tD $epsshu $psish $Tcr $phiu $psicr1 $psicr2 $tcast + +.. csv-table:: + :header: "Argument", "Type", "Description" + :widths: 6, 4, 40 + + "``$matTag``", integer, "integer tag identifying material" + "``$fc``", float, "concrete compressive strength (compression is negative)" + "``$fct``", float, "concrete tensile strength (tension is positive)" + "``$Ec``", float, "concrete modulus of elasticity" + "``$beta``", float, "tension softening parameter (tension softening exponent)" + "``$tD``", float, "analysis time at initiation of drying (in days)" + "``$epsshu``", float, "ultimate shrinkage strain as per ACI 209R-92 (shrinkage is negative)" + "``$psish``", float, "fitting parameter of the shrinkage time evolution function as per ACI 209R-92" + "``$Tcr``", float, "creep model age (in days)" + "``$phiu``", float, "ultimate creep coefficient as per ACI 209R-92" + "``$psicr1``", float, "fitting parameter of the creep time evolution function as per ACI 209R-92" + "``$psicr2``", float, "fitting parameter of the creep time evolution function as per ACI 209R-92" + "``$tcast``", float, "analysis time corresponding to concrete casting (in days; minimum value 2.0)" + +.. note:: + + #. Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + #. Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + + +.. seealso:: + + + `Detailed descriptions of the model and its implementation can be found in the following:` + `(1) Knaack, A.M., Kurama, Y.C. 2018. Modeling Time-Dependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175-190. doi:10.14359/51701153` + `(2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: short-term and long-term behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp` + `A manual describing the use of the model and sample files can be found at:` + ``_ diff --git a/source/user/manual/material/uniaxialMaterials/TDConcreteEXP.rst b/source/user/manual/material/uniaxialMaterials/TDConcreteEXP.rst new file mode 100644 index 00000000..7885b0a6 --- /dev/null +++ b/source/user/manual/material/uniaxialMaterials/TDConcreteEXP.rst @@ -0,0 +1,40 @@ +TDConcreteEXP +^^^^^^^^^^^^^ + +This command is used to construct a uniaxial time-dependent concrete material object with linear behavior in compression, nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to ACI 209R-92. + +.. function:: uniaxialMaterial TDConcreteEXP $matTag $fc $fct $Ec $beta $tD $epsshu $psish $Tcr $epscru $sigCr $psicr1 $psicr2 $tcast + +.. csv-table:: + :header: "Argument", "Type", "Description" + :widths: 6, 4, 40 + + "``$matTag``", integer, "integer tag identifying material" + "``$fc``", float, "concrete compressive strength (compression is negative)" + "``$fct``", float, "concrete tensile strength (tension is positive)" + "``$Ec``", float, "concrete modulus of elasticity" + "``$beta``", float, "tension softening parameter (tension softening exponent)" + "``$tD``", float, "analysis time at initiation of drying (in days)" + "``$epsshu``", float, "ultimate shrinkage strain as per ACI 209R-92 (shrinkage is negative)" + "``$psish``", float, "fitting parameter of the shrinkage time evolution function as per ACI 209R-92" + "``$Tcr``", float, "creep model age (in days)" + "``$epscru``", float, "ultimate creep strain (e.g., taken from experimental measurements)" + "``$sigCr``", float, "concrete compressive stress (input as negative) associated with $epscru (e.g., experimentally applied)" + "``$psicr1``", float, "fitting parameter of the creep time evolution function as per ACI 209R-92" + "``$psicr2``", float, "fitting parameter of the creep time evolution function as per ACI 209R-92" + "``$tcast``", float, "analysis time corresponding to concrete casting (in days; minimum value 2.0)" + +.. note:: + + #. Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + #. Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + + +.. seealso:: + + + `Detailed descriptions of the model and its implementation can be found in the following:` + `(1) Knaack, A.M., Kurama, Y.C. 2018. Modeling Time-Dependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175-190. doi:10.14359/51701153` + `(2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: short-term and long-term behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp` + `A manual describing the use of the model and sample files can be found at:` + ``_ diff --git a/source/user/manual/material/uniaxialMaterials/TDConcreteMC10.rst b/source/user/manual/material/uniaxialMaterials/TDConcreteMC10.rst new file mode 100644 index 00000000..95363d65 --- /dev/null +++ b/source/user/manual/material/uniaxialMaterials/TDConcreteMC10.rst @@ -0,0 +1,43 @@ +TDConcreteMC10 +^^^^^^^^^^^^^^ + +This command is used to construct a uniaxial time-dependent concrete material object with linear behavior in compression, nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to fib Model Code 2010. + +.. function:: uniaxialMaterial TDConcreteMC10 $matTag $fc $fct $Ec $Ecm $beta $tD $epsba $epsbb $epsda $epsdb $phiba $phibb $phida $phidb $tcast $cem + +.. csv-table:: + :header: "Argument", "Type", "Description" + :widths: 6, 4, 40 + + "``$matTag``", integer, "integer tag identifying material" + "``$fc``", float, "concrete compressive strength (compression is negative)" + "``$fct``", float, "concrete tensile strength (tension is positive)" + "``$Ec``", float, "concrete modulus of elasticity at loading age" + "``$Ecm``", float, "concrete modulus of elasticity at 28 days" + "``$beta``", float, "tension softening parameter (tension softening exponent)" + "``$tD``", float, "analysis time at initiation of drying (in days)" + "``$epsba``", float, "ultimate basic shrinkage strain (input as negative) as per fib Model Code 2010" + "``$epsbb``", float, "fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010" + "``$epsda``", float, "product of ultimate drying shrinkage strain and relative humidity function as per fib Model Code 2010" + "``$epsdb``", float, "fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010" + "``$phiba``", float, "parameter for the effect of compressive strength on basic creep as per fib Model Code 2010" + "``$phibb``", float, "fitting parameter of the basic creep time evolution function as per fib Model Code 2010" + "``$phida``", float, "product of the effect of compressive strength and relative humidity on drying creep as per fib Model Code 2010" + "``$phidb``", float, "fitting parameter of the drying creep time evolution function as per fib Model Code 2010" + "``$tcast``", float, "analysis time corresponding to concrete casting (in days; minimum value 2.0)" + "``$cem``", float, "coefficient dependent on the type of cement as per fib Model Code 2010" + +.. note:: + + #. Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + #. Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + + +.. seealso:: + + + `Detailed descriptions of the model and its implementation can be found in the following:` + `(1) Knaack, A.M., Kurama, Y.C. 2018. Modeling Time-Dependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175-190. doi:10.14359/51701153` + `(2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: short-term and long-term behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp` + `A manual describing the use of the model and sample files can be found at:` + ``_ diff --git a/source/user/manual/material/uniaxialMaterials/TDConcreteMC10NL.rst b/source/user/manual/material/uniaxialMaterials/TDConcreteMC10NL.rst new file mode 100644 index 00000000..a1b1f1ce --- /dev/null +++ b/source/user/manual/material/uniaxialMaterials/TDConcreteMC10NL.rst @@ -0,0 +1,45 @@ +TDConcreteMC10NL +^^^^^^^^^^^^^^^^ + +This command is used to construct a uniaxial time-dependent concrete material object with non-linear behavior in compression (REF: Concrete02), nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to fib Model Code 2010. + +.. function:: uniaxialMaterial TDConcreteMC10NL $matTag $fc $fcu $epscu $fct $Ec $Ecm $beta $tD $epsba $epsbb $epsda $epsdb $phiba $phibb $phida $phidb $tcast $cem + +.. csv-table:: + :header: "Argument", "Type", "Description" + :widths: 6, 4, 40 + + "``$matTag``", integer, "integer tag identifying material" + "``$fc``", float, "concrete compressive strength (compression is negative)" + "``$fcu``", float, "concrete crushing strength (compression is negative)" + "``$epscu``", float, "concrete strain at crushing strength (input as negative)" + "``$fct``", float, "concrete tensile strength (tension is positive)" + "``$Ec``", float, "concrete modulus of elasticity at loading age" + "``$Ecm``", float, "concrete modulus of elasticity at 28 days" + "``$beta``", float, "tension softening parameter (tension softening exponent)" + "``$tD``", float, "analysis time at initiation of drying (in days)" + "``$epsba``", float, "ultimate basic shrinkage strain (input as negative) as per fib Model Code 2010" + "``$epsbb``", float, "fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010" + "``$epsda``", float, "product of ultimate drying shrinkage strain and relative humidity function as per fib Model Code 2010" + "``$epsdb``", float, "fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010" + "``$phiba``", float, "parameter for the effect of compressive strength on basic creep as per fib Model Code 2010" + "``$phibb``", float, "fitting parameter of the basic creep time evolution function as per fib Model Code 2010" + "``$phida``", float, "product of the effect of compressive strength and relative humidity on drying creep as per fib Model Code 2010" + "``$phidb``", float, "fitting parameter of the drying creep time evolution function as per fib Model Code 2010" + "``$tcast``", float, "analysis time corresponding to concrete casting (in days; minimum value 2.0)" + "``$cem``", float, "coefficient dependent on the type of cement as per fib Model Code 2010" + +.. note:: + + #. Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + #. Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally). + + +.. seealso:: + + + `Detailed descriptions of the model and its implementation can be found in the following:` + `(1) Knaack, A.M., Kurama, Y.C. 2018. Modeling Time-Dependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175-190. doi:10.14359/51701153` + `(2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: short-term and long-term behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp` + `A manual describing the use of the model and sample files can be found at:` + ``_