Legacy · Thermal validation

Slab on foundation

Same isothermal calibration as the shaft and the infinite slab of this campaign. Geometry and soil change.

Paper: Analytical and numerical validation of the thermochemical problem of early-age concrete · DOI 10.70271/rirc.v1n2a008

Input data

Item	Value
Slab	thickness $L_Y=2.0\,\mathrm{m}$ ; half-width $L_X=1.0\,\mathrm{m}$
Soil	semi-infinite
$T_{\max}$ point	$(0,\ L_Y/2)=(0,\ 1\,\mathrm{m})$
$Q(t_{eq})$	$\Delta T=50\,^{\circ}\mathrm{C}$ , $a_1=40.10873\,\mathrm{h}$ , $c_1=1.54782$
$E_a/R$	$4000\,\mathrm{K}$
$T_{\mathrm{ref}}$	$20\,^{\circ}\mathrm{C}$
$T_0$	$20$ , $30$ or $40\,^{\circ}\mathrm{C}$
$T_{\infty}$	$20\,^{\circ}\mathrm{C}$
Concrete	$k=9$ ; $\rho=2400\,\mathrm{kg/m^3}$ ; $c_e=0.75\,\mathrm{kJ/(kg\cdot^{\circ}C)}$ ; $h^{2}=0.005\,\mathrm{m^2/h}$
Soil	$k=3\,\mathrm{kJ/(m\cdot h\cdot^{\circ}C)}$ ; $\rho=1500\,\mathrm{kg/m^3}$ ; $c_e=0.5\,\mathrm{kJ/(kg\cdot^{\circ}C)}$ ; $h^{2}=0.004\,\mathrm{m^2/h}$
Horizon	$t_f=480\,\mathrm{h}$
$C$ in the $Q$ column	$300\,\mathrm{kg/m^3}$

Concrete $k$ is in $\mathrm{kJ/(m\cdot h\cdot^{\circ}C)}$ , as on the soil line. The conversion of $Q$ to kJ/kg is the same as for the shaft: the report works with $\Delta T^{Q}$ in °C.

Reference result

Regressed $\Delta T=50.00\,^{\circ}\mathrm{C}$ . $\beta=1.548$ .

$T_0$ (°C)	$\tau$ (h)	RMSE of $T(t)$ (°C)	$T_{\max}$ FEM / analytical (°C)
20	13.73	0.044	59.0 / 59.0
30	12.69	0.071	68.0 / 68.1
40	10.40	0.091	78.5 / 78.6

On the series, FEM peaks are $58.95\,^{\circ}\mathrm{C}$ ( $41.58\,\mathrm{h}$ ), $68.00\,^{\circ}\mathrm{C}$ ( $38.06\,\mathrm{h}$ ) and $78.46\,^{\circ}\mathrm{C}$ ( $31.96\,\mathrm{h}$ ).

Series t × Tmax × teq × Q(t)

No suffix: isothermal source at $t_{eq}$ ( $E_a/R=4000\,\mathrm{K}$ , $T_{\mathrm{ref}}=20\,^{\circ}\mathrm{C}$ ) and Tmax_C at $(0,\ 1\,\mathrm{m})$ .

Suffix _particular: $t_{eq}=t$ and the particular generation stored in the FEM history ( $E_a/R=0$ ).

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