Legacy · Thermal validation

UHE São Manoel piers

Back-analysis of the spillway monitoring, 21–25 September 2015 on the instrumented stretch. Pier P4 is the reference case. The other four piers use the same geometric idealisation.

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

Input data

The member is read as an infinite slab: in a tall pier with sliding formwork, loss through the lateral faces dominates over the placement horizon. The effective thickness is the distance between those faces.

Item	Value
Model	infinite slab, $L=5.0\,\mathrm{m}$
Thermometer	$x=2.5\,\mathrm{m}$
$E_a/R$ in the back-analysis	$0$
Parametrisation	two-term Hill law for $\partial T^{Q}/\partial t$
$T_{\infty}$ adopted for P4	$25.0\,^{\circ}\mathrm{C}$

Placement of each pier:

Pier	Placement	$T_0$ (°C)	$t_f$ (h)	$n$	Measured $T_{\max}$ (°C)
P1	2015-09-10 22:00	26.8	319	75	57.9
P2	2015-09-11 06:00	22.9	311	73	71.5
P3	2015-09-11 22:00	22.8	295	69	67.5
P4	2015-09-15 06:00	21.5	215	49	69.8
P5	2015-09-16 06:00	21.2	191	43	70.2

Mean ambient temperature in the placement table of the report lies between $25.7$ and $26.1\,^{\circ}\mathrm{C}$ . The P4 back-analysis uses $25.0\,^{\circ}\mathrm{C}$ .

Reference result — P4

Two scenarios for $h^{2}$ .

Quantity	$h^{2}$ fixed at $0.0045\,\mathrm{m^2/h}$	$h^{2}$ free
$\Delta T_1$ (°C)	44.73	41.56
$\tau_1$ (h)	16.68	16.66
$\beta_1$	5.50	5.53
$\Delta T_2$ (°C)	2.36	7.19
$\tau_2$ (h)	5.00	15.65
$\beta_2$	3.37	1.64
$h^{2}$ ( $\mathrm{m^2/h}$ )	0.00450	0.00562
RMSE (°C)	0.76	0.27

Reference result — P1 to P5

Prescribed diffusivity $h^{2}=0.0057\,\mathrm{m^2/h}$ , or free.

Pier	RMSE, fixed $h^{2}$ (°C)	RMSE, free $h^{2}$ (°C)	free $h^{2}$ ( $\mathrm{m^2/h}$ )	Measured $T_{\max}$ (°C)
P1	1.11	0.71	0.01160	57.9
P2	0.89	0.18	0.00698	71.5
P3	1.95	1.66	0.00477	67.5
P4	0.27	0.27	0.00571	69.8
P5	0.56	0.54	0.00541	70.2

P2, P4 and P5 close with RMSE below $0.6\,^{\circ}\mathrm{C}$ when $h^{2}$ is free. P3 stays at $1.66\,^{\circ}\mathrm{C}$ . P1 measures $57.9\,^{\circ}\mathrm{C}$ and asks for nearly twice the typical $h^{2}$ . The report keeps P1 out of the global fit until the site record is confirmed.

Reducing P2–P5 to one isothermal curve, with $E_a/R=4000\,\mathrm{K}$ held fixed, gives $\Delta T_1=39.02\,^{\circ}\mathrm{C}$ , $\tau_1=23.87\,\mathrm{h}$ , $\beta_1=2.695$ , $\Delta T_2=7.30\,^{\circ}\mathrm{C}$ , $\tau_2=81.11\,\mathrm{h}$ , $\beta_2=3.827$ , joint RMSE $3.21\,^{\circ}\mathrm{C}$ . The error profile versus $E_a/R$ is nearly flat: these histories do not separate the activation energy.

Series t × Tmax × teq × Q(t)

Tmax_C is the measured temperature. Because the back-analysis uses $E_a/R=0$ , teq_h $=t$ . Q_kJ_kg converts the particular rise with $\rho=2400\,\mathrm{kg/m^3}$ , $c_e=0.75\,\mathrm{kJ/(kg\cdot^{\circ}C)}$ and $C=300\,\mathrm{kg/m^3}$ . That conversion is not part of the fit. The fit works with the rise in °C. The column is there so the series has the same form as the other cases.

The particular generation in these files is the free- $h^{2}$ scenario of the processed monitoring file.

Report figures

P4, monitoring and analytical solution, fixed and free $h^{2}$ .