Heat Soak Model

Overview

FRI3D employs two methodologies to estimate cable failure from the fire simulation results: the heat-soak and THIEF methods. The heat-soak method is the simpler of the two. It uses a lookup table for time-to-damage as a function of constant exposure, and considers the cumulative effect of preheating that may occur at temperatures lower than the damage-threshold temperatures.

Damage Integral

Heat soak calculates a variable called the damage integral based on a time-dependent reaction rate. Damage occurs when this damage integral is greater than or equal to 1. The damage integral is given by:

$$\Omega={\int_{0}^{t}RR\left(t\right)dt}$$

Where $\Omega$ is the damage integral and $RR\left(t\right)$ is a time-dependent reaction rate, which is assumed to be the inverse of the exposure duration as follows:

$$RR\left(t\right)=\frac{1}{t_{dam}^\prime\left(T\left(t\right)\right)}$$

Where $T(t)$ is the exposure temperature at time t, and $t_{dam}^\prime$ is the time until damage for that temperature. Cable failure occurs when the damage integral reaches 1:

$$\Omega=\int_{0}^{t_{dam}}{\frac{1}{t_{dam}^\prime\left(T\left(t\right)\right)}dt=1}$$

The table below illustrates the calculation for a sample exposure history:

Time (min)	Temperature (C)	Time-to-damage (from NUREG 6850)	Damage rate (min-1)	Damage integral
0	210	30	0.033	0
1	320	5	0.2	0.12
2	350	3	0.33	0.38
3	320	5	0.2	0.65
4	320	5	0.2	0.85
5	320	5	0.2	1.05 (Failure)

Using Heat Soak in FRI3D

The main variable in determining the damage integral is the cable's type — thermoset or thermoplastic. For that reason, FRI3D uses the heat-soak method by default, selecting the conservative setting, when detailed cable data is not provided by the modeler in the FRI3D model. To use this method, simply add a "Cable" in FRI3D and leave the material properties at "Null" as shown in the figure below.

Cables carried by a raceway that is assigned directly to a fire source fail at time zero with the Source Location method, regardless of the heat-soak/THIEF results — see Assigning Equipment and Raceways to a Fire Source. Thermal raceway failures do not propagate to their cables; each cable is evaluated individually by the methods described here.

What's next?

• THIEF Model — the more detailed cable-failure calculation used when cable dimension and thermal data are provided.
• FLASH-CAT Methodology — how burning cables become secondary fire sources.