IRC Instituto Roy Carlson

Legacy · Mechanical validation · Material

Itumbiara material — creep compliance

Shared mechanical anchor for the cases with aging (Fig. 6, slabs, plane ΔT, torsion, Hiramatsu on strains). The Zocher/SLS cases use another material — see each Zocher case page.

Article: Part I · DOI 10.70271/rirc.v1n2a007.

Creep and relaxation

Itumbiara — E(z), creep and relaxation

Fitting report and property summary (origin of the coefficients used on the portal): itumbiara_relatorio.pdf.

Notation

Symbol Quantity
h2h^{2} Thermal diffusivity k/(ρc)k/(\rho c)
α\alpha Degree of hydration
αT\alpha_{T} Thermal expansion
aTa_{T} Shift factor (Arrhenius) — not diffusivity
J(t,z)J(t,z) Creep compliance

Two layers of the same concrete

1) Empirical model (Table 1)

Quantity Form
Modulus E(z)=z/(aEz+bE)E(z)=z/(a_E z+b_E) with aE=3.619×10−5a_E=3.619\times10^{-5}, bE=7.750×10−5b_E=7.750\times10^{-5}
Creep coefficient φ(z)=exp⁡(A+B/z)\varphi(z)=\exp(A+B/z) with A=−12.420A=-12.420, B=1.556B=1.556
Compliance J(t,z)=1/E(z)+φ(z)ln⁡(t−z+1)J(t,z)=1/E(z)+\varphi(z)\,\ln(t-z+1)

Useful to situate the origin; not the form discretized by the incremental algorithm.

2) Rheological model (Tables 3–4) — anchor

J(t,z)=D0(z)+D1(z)∑j=1Mφj[1−e−(t−z)/τj],E(z)=1D0(z), J(t,z)=D_0(z)+D_1(z)\sum_{j=1}^{M}\varphi_j\bigl[1-e^{-(t-z)/\tau_j}\bigr], \qquad E(z)=\frac{1}{D_0(z)},

with M=11M=11 Kelvin units and Dp(z)=ap+bpe−z/cp+dpe−z/cp2D_p(z)=a_p+b_p\,e^{-z/c_p}+d_p\,e^{-z/c_{p2}}.

Term apa_p bpb_p dpd_p cpc_p cp2c_{p2}
D0D_0 3.700×10−53.700\times10^{-5} 5.479×10−55.479\times10^{-5} 1.110×10−51.110\times10^{-5} 2.416 16.063
D1D_1 2.838×10−52.838\times10^{-5} 4.624×10−54.624\times10^{-5} 6.117×10−66.117\times10^{-6} 2.416 16.063

With these coefficients, D0(3d)=6.204×10−5MPa−1D_0(3\,\mathrm{d})=6.204\times10^{-5}\,\mathrm{MPa}^{-1} and E(3)=16119MPaE(3)=16\,119\,\mathrm{MPa}.

Spectrum — ref_itumbiara_espectro_kelvin.csv:

jj τj\tau_j (d) φj\varphi_j
1 0.3099 5.299×10−35.299\times10^{-3}
2 0.7619 3.488×10−23.488\times10^{-2}
3 1.873 7.646×10−27.646\times10^{-2}
4 4.604 1.047×10−11.047\times10^{-1}
5 11.32 1.193×10−11.193\times10^{-1}
6 27.82 1.255×10−11.255\times10^{-1}
7 68.39 1.286×10−11.286\times10^{-1}
8 168.1 1.280×10−11.280\times10^{-1}
9 413.3 1.401×10−11.401\times10^{-1}
10 1016 6.710×10−26.710\times10^{-2}
11 2497 3.274×10−13.274\times10^{-1}

Constants: ν=0.20\nu=0.20; αT=10×10−6∘C−1\alpha_{T}=10\times10^{-6}\,^{\circ}\mathrm{C}^{-1}.

Public files

Anchor: Table 3 in MPa−1^{-1} (and tabulated E(z)E(z)). “First-hand” conversions from the Itumbiara book may differ by ~2 %.

Package

itumbiara_material() in irc-creep.