Cable Response to 

Live Fire (CAROLFIRE) 

Volume 3: Thermally-Induced 

Electrical Failure (THIEF) 

Model 

Office of Nuclear Regulatory Research 

NUREG/CR-6931, Vol. 3 

NISTIR 7472
Cable Response to 

Live Fire (CAROLFIRE) 

Volume 3: Thermally-Induced 

Electrical Failure (THIEF) 

Model 

Manuscript Completed: January 2008 

Date Published: April 2008 

Prepared by 

K. McGrattan 

National Institute of Standards and Technology 

Building and Fire Research Laboratory 

Gaithersburg, MD 20899-1070 

J. Dreisbach, NRC Project Manager 

NRC Job Code N6414 

Office of Nuclear Regulatory Research 

NUREG/CR-6931, Vol. 3 

NISTIR 7472 
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iii

ABSTRACT 

This report describes a thermally-induced electrical failure (THIEF) model’s ability to predict 

the behavior of power, instrument, and control cables during a fire. The model is intended to be 

incorporated as a subroutine for deterministic fire models, and it is of comparable accuracy and 

simplicity to the activation algorithms for various other fire protection devices (e.g., sprinklers, 

heat and smoke detectors). THIEF model predictions are compared to experimental 

measurements of instrumented cables in a variety of configurations, and the results indicate that 

the model is an appropriate analysis tool for nuclear power plant applications. This work was 

performed as part of the CAROLFIRE (Cable Response to Live Fire) program sponsored by the 

U.S. Nuclear Regulatory Commission. The experiments for CAROLFIRE were conducted at 

Sandia National Laboratories, Albuquerque, New Mexico. Details of the CAROLFIRE 

experimental program are contained in Volumes 1 and 2 of this three-volume series. 
v

FOREWORD 

The Browns Ferry fire in 1975 demonstrated that instrument, control and power cables are 

susceptible to fire damage. At Browns Ferry, over 1,600 cables were damaged by the fire and 

caused short circuits between energized conductors. These short circuits (i.e., “hot-shorts”) 

caused certain systems to operate in an unexpected manner. Additionally, recent advances in the 

use of risk-informed methods indicate that hot-shorts, under certain circumstances, can pose a 

significant risk, and that plant risk analyses should account for those additional risks. 

In order to better understand the issue of cable hot-shorts, the nuclear industry (Nuclear Energy 

Institute/Electric Power Research Institute) conducted a series of cable fire tests that were 

witnessed by the NRC staff in 2001. Based on the results of those tests, and data from previous 

tests available in the literature, the NRC facilitated a workshop on February 19, 2003. The 

workshop led the NRC to issue Regulatory Issue Summary (RIS) 2004-03, Revision 1, “RiskInformed Approach for Post-Fire Safe Shutdown Circuit Inspections,” December 29, 2004 

(ADAMS Accession No. ML042440791), which describes the guidance NRC inspectors 

currently follow in deciding which causes of fire-induced hot-shorts are important to safety and 

should be considered during inspections. The RIS also describes “Bin 2" items, which are 

scenarios where the importance to safety of cable hot shots was unknown at the time of the 

workshop. 

This report describes the CAROLFIRE (CAble Response tO Live FIRE) testing program. The 

primary objective of this program was to determine the safety importance of these Bin 2 items. A 

secondary objective of CAROLFIRE was to foster the development of cable thermal response 

and electrical failure fire modeling tools. To achieve these objectives, Sandia National 

Laboratories conducted a variety of fire experiments designed to examine the “Bin 2” items, and 

designed to capture cable thermal response and failure data. The cable thermal response data has 

been provided to the National Institute of Standards and Technology and the University of 

Maryland for use as the basis of development and initial validation of cable target response 

models. 

The results presented in this report were from a series of both small- and intermediate-scale 

cable fire tests. The combined test matrices comprised 96 individual experiments of varying 

complexity. The tests involved a variety of common cable constructions and variations in test 

conditions like thermal exposure, raceway type, and bundling of similar and dissimilar cable 

types. The results provide the most extensive set of cable thermal response and failure data to 

date. This research provides valuable information and insights that may be used to evaluate the 

risk of fire-induced cable hot-shorts. 

Christiana H. Lui, Director 

Division of Risk Analysis 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 
vii

CONTENTS 

Abstract..........................................................................................................................................iii

Foreword......................................................................................................................................... v

Contents ........................................................................................................................................ vii

List of Figures................................................................................................................................ ix

List of Tables ................................................................................................................................. xi

Executive Summary.....................................................................................................................xiii

Acknowledgements....................................................................................................................... xv

Abbreviation ............................................................................................................................... xvii

1 Background............................................................................................................................. 1

1.1 Introduction and Purpose ................................................................................................. 1

1.2 A Brief History of Cable Modeling ................................................................................. 1

2 Model Development................................................................................................................ 5

2.1 Model Assumptions and Governing Equations................................................................ 5

2.2 Cable Properties ............................................................................................................... 6

2.3 Numerical Algorithm............................................................................................................ 9

Finite Difference Scheme ....................................................................................................... 9

External Heat Flux ................................................................................................................ 10

Conduits ................................................................................................................................ 10

3 Bench-Scale “Penlight” Experiments ................................................................................... 13

3.1 Experimental Description............................................................................................... 13

3.2 Experimental Results ..................................................................................................... 14

3.3 Modeling Considerations ............................................................................................... 17

3.4 Modeling Results ........................................................................................................... 18

Thermoset Cables.................................................................................................................. 19

Thermoplastic Cables ........................................................................................................... 23

Special Cables....................................................................................................................... 27

3.5 Summary of Penlight Analysis....................................................................................... 28

3.6 Why Does the THIEF Model Work? ............................................................................. 32

4 Intermediate Scale Experiments ........................................................................................... 35

4.1 Experimental Description............................................................................................... 35

4.2 Modeling Considerations ............................................................................................... 35

4.3 Model Results................................................................................................................. 38

Single Cables within Trays ................................................................................................... 38

Cables in Conduits ................................................................................................................ 40

Random Fill Cable Trays...................................................................................................... 43

Air Drops .............................................................................................................................. 45

Six Cable Bundles................................................................................................................. 46

Twelve Cable Bundles .......................................................................................................... 51

4.4 Summary of the Intermediate Scale Tests...................................................................... 53

5. Lessons Learned from CAROLFIRE.................................................................................... 57

5.1 Characterizing the thermal environment........................................................................ 57

5.2 Specifying a “failure temperature”................................................................................. 57

5.3 Defining the cable within the fire model........................................................................ 57

5.4 Modeling cable burning ................................................................................................. 58
viii

6 Conclusion ............................................................................................................................ 59

7 References............................................................................................................................. 61
ix

LIST OF FIGURES 

Figure Title: Page

Figure 1. Curves representing the current guidance given in NUREG-1805 for estimating the 

time to cable electrical failure for a particular exposing temperature. Also shown are the 

results of the CAROLFIRE bench-scale (Penlight) experiments for single cables (Nowlen 

and Wyant 2007b)................................................................................................................... 3 

Figure 2. Schematic diagram of Penlight apparatus, courtesy Sandia National Laboratory. 

Details can be found in Nowlen and Wyant (2007b)............................................................ 13

Figure 3. Thermocouple locations for a 7/C cable. ..................................................................... 14 

Figure 4. The results of Penlight Test 2 where it is observed that the inner cable temperatures 

(solid and dashed red lines) increase significantly about 1 min prior to the first recorded 

electrical short. The dotted lines are results of the THIEF model. ...................................... 15 

Figure 5. (Left) Photograph of a conduit within the penlight apparatus, with end caps installed, 

courtesy Frank Wyant, Sandia National Laboratories. (Right) Predicted (dotted line) and 

measured (solid line) temperatures of the conduit when exposed to the shroud temperature 

profile. This example is part of penlight experiment number 7........................................... 17 

Figure 6. Key to graphs showing results of penlight tests. Note that the term “First Short” 

indicates the first observed electrical failure, regardless of the specific type. In the 

experiments, subsequent shorts were observed, but are not relevant here. .......................... 18 

Figure 7. Results for Cable #14 (XLPE/CSPE, 3 conductor). The upper-most black curves 

depict the measured (solid) and specified (dotted) shroud temperature. The solid and 

dashed red lines are the measured temperatures inside the cable jacket, at opposite sides. 

The dotted red curve is the predicted inner cable temperature. The vertical dashed line 

indicates the first observed electrical short in the experiment. For Test 7, the solid blue and 

dotted blue curves represent the measured and predicted conduit temperatures, respectively.

............................................................................................................................................... 20 

Figure 8. Results for Cable #10 (XLPE/CSPE, 7 conductor). The color scheme is the same as in 

Figure 7. ................................................................................................................................ 21 

Figure 9. Results for various thermoset cables. The upper-most black curves depict the 

measured (solid) and specified (dotted) shroud temperature. The solid and dashed red lines 

are the measured temperatures inside the cable jacket, at opposite sides. The dotted red 

curve is the predicted inner cable temperature. The vertical dashed line indicates the first 

observed electrical short in the experiment. ......................................................................... 22 

Figure 10. Results for Cable #5 (PVC/PVC, 3 conductor). The upper-most black curves depict 

the measured (solid) and specified (dotted) shroud temperature. The solid and dashed red 

lines are the measured temperatures inside the cable jacket, at opposite sides. The dotted 

red curve is the predicted inner cable temperature. The vertical dashed line indicates the 

first observed electrical short in the experiment. For Test 8, the solid blue and dotted blue 

curves represent the measured and predicted conduit temperatures, respectively. .............. 24 

Figure 11. Results for Cable #15 (PE/PVC, 7 conductor). The color scheme is the same as in 

Figure 10. .............................................................................................................................. 25 

Figure 12. Results for 2, 7, and 12 conductor PVC/PVC (thermoplastic) cables. The upper-most 

black curves depict the measured (solid) and specified (dotted) shroud temperature. The 

solid and dashed red lines are the measured temperatures inside the cable jacket, at opposite 
x

sides. The dotted red curve is the predicted inner cable temperature. The vertical dashed 

line indicates the first observed electrical short in the experiment....................................... 26 

Figure 13. Results for Cable #9 (Silicone Rubber/Aramid Braid, 7 conductor) and Cable #11 

(VITA-LINK, 7 conductor). The upper-most black curves depict the measured (solid) and 

model-specified (dotted) shroud temperature. The solid red line is the measured 

temperature inside the cable jacket. The dotted red line is the predicted inner cable 

temperature. Ignition and burning are not included in the THIEF model, and electrical 

shorting did not occur in these two experiments. Note that neither cable failed electrically 

until the introduction of a water spray. See Nowlen and Wyant (2007b) for details. ......... 27 

Figure 14. Comparison of THIEF model and experiment for the Penlight series. Point A and B 

refer to the thermocouple measurements made on opposite sides of the cable, just under the 

jacket. The “Threshold Temperature” is 400 °C (752 °F) for thermoset cables and 200 °C 

(392 °F) for thermoplastics. The dashed lines represent the average (-3 %) and standard 

deviation (20 %) of the data.................................................................................................. 29 

Figure 15. Sensitivity of the THIEF model predictions to various cable properties. The Relative 

Difference refers to the predicted vs measured times to reach the threshold temperature. 

The horizontal dashed line is the average Relative Difference for all the Penlight 

comparisons. ......................................................................................................................... 31 

Figure 16. Results of an alternative thermal model (short dashes) and the THIEF model (dotted 

line), compared to measurements (solid and long dashed lines). ......................................... 32 

Figure 17. Side view of the Intermediate Scale Test rig. Courtesy Sandia National Laboratories.

............................................................................................................................................... 35 

Figure 18. Key to Intermediate Scale graphs............................................................................... 36 

Figure 19. Example of an experiment where the temperature measurement (TC-1) may not 

coincide with the location of the first electrical short........................................................... 37 

Figure 20. Summary of results for single, isolated cables in the Intermediate scale tests. Black 

indicates the exposing temperature; red the cable. Solid lines for experiment, dotted for 

model..................................................................................................................................... 39 

Figure 21. Summary of results for the cables in the conduit at Location E. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model............ 41 

Figure 22. Summary of results for cables in conduits at Location D and G. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model............ 42 

Figure 23. Cable tray configuration for Intermediate Test 1. ...................................................... 43 

Figure 24. Cable tray configuration for Intermediate Tests 13 and 14........................................ 43 

Figure 25. Summary of results for trays filled with random cable. Black indicates the exposing 

temperature; red the cable. Solid lines for experiment, dotted for model. The measured 

temperature at Location A in Test 13 (middle left graph) is inconsistent with that at 

Location C (middle right graph). .......................................................................................... 44 

Figure 26. Summary of results for air drop cables in the Intermediate scale tests. Black 

indicates the exposing temperature; red the cable. Solid lines for experiment, dotted for 

model..................................................................................................................................... 45 

Figure 27. Summary of results for 6 cable bundles, Location A. Black indicates the exposing 

temperature; red the cable. Solid lines for experiment, dotted for model. .......................... 47 

Figure 28. Summary of results for 6 cable bundles, Locations A and C. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model............ 48 

Figure 29. Summary of results for 6 cable bundles, Locations C and F. Black indicates the 
xi

exposing temperature; red the cable. Solid lines for experiment, dotted for model............ 49 

Figure 30. Summary of results for the 6 cable bundles, Location G. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model............ 50 

Figure 31. Summary of results for the 12 cable bundles. Black indicates the exposing 

temperature; red the cable. Solid lines for experiment, dotted for model. .......................... 52 

Figure 32. Summary of the Intermediate Scale Test predictions. The dashed lines indicate the 

average (-15 %) and standard deviation (33 %) of the data. Also note that the description 

“Inside Fire Plume” refers to locations A and C, which were within the flaming region of 

the fire. .................................................................................................................................. 54 

LIST OF TABLES 

Table Title: Page

Table 1. Physical properties of the cables that are relevant to the modeling study. Additional 

information is included in Nowlen and Wyant (2007a). Note that the “Cable Number” is 

used only to identify the cables used in the study................................................................... 8

Table 2. Summary of the Sandia Penlight experiments that involved only single cables. 

Measurement uncertainties are reported in Nowlen and Wyant (2007b). Note that the 

thermoplastic cable (TEF/TEF) in Test 22 was tested like a thermoset. .............................. 16

Table 3. Summary of the THIEF Model Predictions of the Penlight Experiments. .................... 30

Table 4. Results of the Intermediate Scale THIEF Model Predictions. See Nowlen and Wyant 

(2007b) for details about each configuration........................................................................ 55
xiii

EXECUTIVE SUMMARY 

This report documents the numerical modeling results from the Cable Response to Live Fire

(CAROLFIRE) project. CAROLFIRE is a U.S. Nuclear Regulatory Commission (US NRC) 

Office of Nuclear Regulatory Research (RES) initiated effort to study the fire-induced thermal 

response and functional behavior of electrical cables. The project is a collaborative effort that 

includes the NRC Office of Nuclear Reactor Regulation (NRR) as peer reviewers, Sandia 

National Laboratories (SNL) as the primary testing laboratory, and both the University of 

Maryland and the National Institute of Standards and Technology (NIST) as general 

collaborative partners to develop a better predictive model for cable thermal response in 

deterministic fire models. 

The primary project objective of CAROLFIRE is to characterize the various modes of electrical 

failure (e.g. hot shorts, shorts to ground) within bundles of power, control and instrument cables. 

A secondary objective of the project is to develop a simple model to predict Thermally-Induced 

Electrical Failure (THIEF) when a given interior region of the cable reaches an empirically 

determined threshold temperature. The measurements used for these purposes are described in 

Volume II of the CAROLFIRE test report (Nowlen and Wyant 2007b). 

The THIEF model for cables has been shown to work effectively in realistic fire environments. 

The THIEF model is essentially nothing more than the numerical solution of the onedimensional heat conduction equation within a homogenous cylinder with fixed, temperatureindependent properties. The model was used to predict the inner cable temperature of 100 

instrumented cables from the CAROLFIRE Penlight (35 single cable experiments; 66 point to 

point comparisons) and Intermediate Scale Test Series (14 experiments; 65 point to point 

comparisons). Because the Penlight experiments tested single cables that were heated uniformly 

on all sides, the one-dimensional THIEF model accurately predicted the times for the 

temperature inside the cable jacket to reach “threshold” values that are typically observed when 

the cable fails electrically. For 66 measurements, the model under-predicted the time to reach 

threshold temperature by 3 %, on average. In the Intermediate Scale experiments, where the 

cable configurations were more typical of actual installations, the model under-predicted the 

times to reach threshold temperature by 15 %, on average. This latter result is realistically 

conservative – the THIEF model does not account for the shielding effects of cable bundles, and 

thus over-predicts cable temperatures and under-predicts “failure” times. 
xv

ACKNOWLEDGEMENTS 

The work described in this report was supported by the Office of Nuclear Regulatory Research 

(RES) of the US Nuclear Regulatory Commission (USNRC). The CAROLFIRE program was 

directed by H.W (Roy) Woods and Mark Henry Salley, with assistance from Jason Dreisbach 

and Felix Gonzalez. The experiments described in this report were conducted by Steve Nowlen 

and Frank Wyant of Sandia National Laboratories. 

Special thanks to Petra Andersson and Patrick Van Hees at SP, Sweden, for their development of 

the thermally-induced electrical failure (THIEF) model that is described in this report. 
xvii

ABBREVIATION 

AWG American Wire Gauge 

CAROLFIRE Cable Response to Live Fire 

CPE Chlorinated Polyethylene 

CSPE Chloro-Sulfanated Polyethylene 

EPR Ethylene-Propylene Rubber 

EPRI Electric Power Research Institute 

NFPA National Fire Protection Association 

NIST National Institute of Standards and Technology 

NRC Nuclear Regulatory Commission 

NRR NRC Office of Nuclear Reactor Regulation 

PE Polyethylene 

PVC Poly-vinyl Chloride 

RES NRC Office of Nuclear Regulatory Research 

SNL Sandia National Laboratories 

SR Silicone Rubber 

TC Thermocouple 

THIEF Thermally-Induced Electrical Failure 

TP Thermoplastic 

TS Thermoset 

XLPE Cross-Linked Polyethylene 

XLPO Cross-Linked Polyolefin 
1

1 BACKGROUND 

1.1 Introduction and Purpose 

The Cable Response to Live Fire (CAROLFIRE) project is a U.S. Nuclear Regulatory 

Commission (US NRC) Office of Nuclear Regulatory Research (RES) initiated effort to study 

the fire-induced thermal response and functional behavior of electrical cables. The project is a 

collaborative effort that includes the NRC Office of Nuclear Reactor Regulation (NRR) as peer 

reviewers, Sandia National Laboratories (SNL) as the primary testing laboratory, and both the 

University of Maryland and the National Institute of Standards and Technology (NIST) as 

general collaborative partners to develop a better predictive model for cable thermal response in 

deterministic fire models. 

The primary project objective of CAROLFIRE is to characterize the various modes of electrical 

failure (e.g. hot shorts, shorts to ground) within bundles of power, control and instrument cables. 

 Details can be found in Volume 1 of the CAROLFIRE test report (Nowlen and Wyant 2007a). 

A secondary objective of the project is to develop a simple model to predict Thermally-Induced 

Electrical Failure (THIEF) when a given interior region of the cable reaches an empirically 

determined threshold temperature. The measurements used for these purposes are described in 

Volume II of the CAROLFIRE test report (Nowlen and Wyant 2007b). 

The description and validation of the THIEF model are reported here. Current nuclear power 

plant probabilistic risk assessment (PRA) methods employ simple linear regression techniques to 

predict cable performance in a fire. These methods take into account the general composition of 

the cable, but not other information, like its mass or diameter. The THIEF model described in 

this report uses the general cable construction and bulk properties, but does not require more 

detailed thermo-physical properties. For example, the mass per unit length and diameter are 

needed, but the thermal conductivity, specific heat, and emissivity are assumed, based on the 

current generation of cables in existing plants. This latter detailed information is not always 

readily available for the wide variety of often proprietary cable materials, and bench-scale 

experiments to measure the properties can be expensive and difficult to perform for all existing 

and future cable materials. 

1.2 A Brief History of Cable Modeling 

The thermal decomposition and electrical failure1 of multi-conductor cables in a fire have been 

of interest to the nuclear power industry dating back to the Browns Ferry fire of 1975 (US NRC 

1975). However, the development of a predictive model of cable failure has been elusive for a 

number of reasons. First, cables are a fairly complex combination of insulating plastics, metal 

conductors, protective armors, and a variety of filler materials. The availability of 

comprehensive thermo-physical properties of these materials is limited. Even when the material 

 

1

 Throughout this report, the term “electrical failure” applies to any situation where a cable no longer functions as 

designed due to the heating by a fire. Most often, these failures come in the form of hot shorts or shorts to ground that 

can result in spurious actuations of system and components. See Nowlen and Wyant (2007a) for a more detailed 

discussion. 
2

properties for a particular cable are available, it is still a challenge to calculate the heat 

penetration through a bundle of the cables lying in a tray or run through a conduit. 

Rather than try to develop detailed models, engineers have looked for a practical correspondence 

between electrical failure and the compartment temperature in a fire. A simple approach is to 

develop an empirical relationship between the time to electrical failure and the “exposing” 

temperature; that is, the temperature of the hot gases in the vicinity of the cable. NUREG-1805 

(Iqbal and Salley 2004), a set of engineering calculation methods specifically designed for 

nuclear power plant applications, suggests that the time to electrical failure is inversely 

proportional to the exposing temperature. For the two major classes of cables, thermosets and 

thermoplastics,2 it provides an estimated failure time (in seconds) for a given exposing 

temperature (in °C): 

3.343 10 0.01044 1 5 = × − − T

t

 for thermoset cables (1.1) 

3.488 10 0.007467 1 5 = × − − T

t

 for thermoplastic cables (1.2) 

These two curves are shown in Figure 1, along with some results from the CAROLFIRE 

experimental program (Nowlen and Wyant 2007b). While Eqs. (1.1) and (1.2) are useful 

screening methods, they are somewhat limited in application. First, they are based on constant 

temperature exposures, which is unrealistic in fire. For example, the CAROLFIRE results 

shown in Figure 1 are only from the small-scale experiments in which individual cables were 

exposed to a uniform temperature. The larger-scale test results from CAROLFIRE cannot be 

characterized in terms of a single exposing temperature or heat flux. Second, Eqs. (1.1) and 

(1.2) do not account for different cable installations or configurations. For example, suppose the 

cable is routed through a conduit, or has a protective armor jacket. What if the cable is 

considerably different in size and composition to those that were tested? The formulae only 

distinguish between a thermoset and thermoplastic cable, based on the fact that the latter have 

been shown to fail at lower temperatures than the former. The formulae do not take into account 

size, mass, protective barriers, or site-specific conditions. For several of the CAROLFIRE test 

configurations, neither Eqs. (1.1) nor (1.2) could be applied directly. 

Because of these limitations, a more flexible predictive model must have some consideration for 

the thermal mass of the cable, and it must infer electrical failure from the attainment of a given 

“failure” temperature somewhere within the cable. Over the past 30 years, a number of studies 

on electrical cable performance in fires have suggested various “failure” temperatures for 

different classes of cables. A review of these studies is included in NUREG-1805 (Iqbal and 

Salley 2004). The intent of this report is to demonstrate that a simple heat conduction 

calculation, along with an empirically-based “failure” temperature, is sufficient to predict cable 

 

2

 Plastics can be classified into two major categories: thermoplastics and thermosets. In general, thermoplastics can be 

heated, melted and cooled to solid form. Thermosets will reach decomposition temperature before melting temperature 

and will degrade irreversibly if exposed to high temperatures. 
3

failure times to an accuracy that is consistent with that of current generation fire models (US 

NRC and EPRI 2007). The calculation is described in the next section. 

Time to First Electrical Short (s)

0 600 1200 1800 2400 3000 3600

Exposing Temperature (°C)

0

200

400

600

800

1000

NUREG-1805 Thermosets

NUREG-1805 Thermoplastics

CAROLFIRE Penlight TS in Tray

CAROLFIRE Penlight TP in Tray

CAROLFIRE Penlight TS in Conduit

CAROLFIRE Penlight TP in Conduit

Figure 1. Curves representing the current guidance given in NUREG-1805 for estimating 

the time to cable electrical failure for a particular exposing temperature. Also shown are 

the results of the CAROLFIRE bench-scale (Penlight) experiments for single cables 

(Nowlen and Wyant 2007b). 
5

2 MODEL DEVELOPMENT 

Petra Andersson and Patrick Van Hees of the Swedish National Testing and Research Institute 

(SP) have proposed that a cable’s thermally-induced electrical failure (THIEF) can be predicted 

via a simple one-dimensional heat transfer calculation, under the assumption that the cable can 

be treated as a homogenous cylinder (Andersson and Van Hees 2005). Their results for PVC 

cables were encouraging and suggested that the simplification of the analysis is reasonable and 

that it should extend to other types of cables. In the section, the model is described. 

2.1 Model Assumptions and Governing Equations 

The assumptions underlying the THIEF model are as follows: 

1. The heat penetration into a cable of circular cross section is largely in the radial direction. 

This greatly simplifies the analysis, and it is also conservative because it is assumed that 

the cable is completely surrounded by the heat source. 

2. The cable is homogenous in composition. In reality, a cable is constructed of several 

different types of polymeric materials, cellulosic fillers, and a conducting metal, most 

often copper. 

3. The thermal properties – conductivity, specific heat, and density – of the assumed 

homogenous cable are independent of temperature. In reality, both the thermal 

conductivity and specific heat of polymers are temperature-dependent, but this 

information is very difficult to obtain from manufacturers. More discussion of this 

assumption is found below. 

4. It is assumed that no decomposition reactions occur within the cable during its heating, 

and ignition and burning are not considered in the model. In fact, thermoplastic cables 

melt, thermosets form a char layer, and both off-gas volatiles up to and beyond the point 

of electrical failure. 

5. Electrical failure occurs when the temperature just inside the cable jacket reaches an 

experimentally determined value. 

Given these assumptions, the governing equation for the cable temperature, T(r,t) , is given by: 

r

T k r

t r r

T

c

∂

∂

∂

∂ = ∂∂ 1

ρ (2.1) 

where ρ , c , and k are the effective density, specific heat, and conductivity of the solid, all 

assumed constant. The boundary condition at the exterior boundary, r = R, is given by: 

R t q

r

T k = ′′ ∂∂ ( (2.2) , ) &

where q&′′ is the assumed axially-symmetric heat flux to the exterior surface of the cable. The 

heat flux is provided by the fire model or fire analysis that is being used to assess the overall 
6

thermal environment of the compartment where the cable is located. In most realistic fire 

scenarios, the heat flux to the cable is not axially-symmetric. For the purpose of modeling cable 

failure, it is recommended that the maximum value of the heat flux be used. 

Obviously, there are considerable assumptions inherent in the Andersson and Van Hees THIEF 

model, but their results for various polyvinyl chloride (PVC) cables suggest that it may be 

sufficient for engineering analyses of a wider variety of cables. In this report, the model is 

applied to fifteen different cable samples that have been exposed to a variety of thermal 

exposures. The only difference in the application of the model here is that the 1-D heat transfer 

equation (2.1) is solved numerically rather than analytically. The analytical solution derived by 

the SP researchers, while perfectly correct, is fairly complicated and a simple numerical solution 

is easier to implement in a large-scale fire model. Indeed, most fire models already employ a 1-

D heat transfer algorithm to compute heat losses to walls. The accuracy of either the analytical 

solution or the numerical solution is not of concern, given the much greater uncertainty in the 

material properties of the plastic and the underlying assumption of homogeneity. Moreover, the 

numerical solution is less restricted, which is important if it is found that a particular type of 

cable cannot be described as a homogenous cylinder. 

The THIEF model can only predict the temperature profile within the cable as a function of time, 

given a time-dependent exposing temperature or heat flux. The model does not predict at what 

temperature the cable fails electrically. This information is gathered from experiment. The 

CAROLFIRE experimental program included bench-scale, single cable experiments in which 

temperature measurements were made on the surface of, and at various points within, cables 

subjected to a uniform heat flux. These experiments provided the link between internal cable 

temperature and electrical failure. The model can only predict the interior temperature and infer 

electrical failure when a given “failure” temperature is reached. It is presumed that the 

temperature of the centermost point in the cable is not necessarily the indicator of electrical 

failure. This analysis method uses the temperature just inside the cable jacket rather than the 

centermost temperature, as that is where electrical shorts in a multi-conductor cable are most 

likely to occur first. 

2.2 Cable Properties 

Fifteen types of cable construction were tested in the CAROLFIRE project. A detailed 

description of each can be found in Nowlen and Wyant (2007a). Each cable is typically 

composed of an outer jacket, insulated conductors, and, for certain types, a light weight filler 

material. Various polymers are used for the jacket and insulation, typically classified as either 

thermoset or thermoplastic. The THIEF model does not distinguish between thermosets and 

thermoplastics, but the behavior of each at elevated temperatures is distinctly different, and 

consequently the experimental test parameters depended on the cable type. 

Table 1 provides information about the cables that is relevant to the THIEF model. The material 

names have been abbreviated as follows: 

Aramid Braid ® A synthetic fiber manufactured by DuPont Chemical (Thermoset) 

CPE Chlorinated Polyethylene (Thermoset) 
7

CSPE Chlorosulfonated Polyethylene (Thermoset) 

EPR Ethylene Propylene Rubber (Thermoset) 

PE Polyethylene (Thermoplastic) 

PVC Polyvinyl Chloride (Thermoplastic) 

SR Silicone-Rubber (Thermoset) 

Tefzel ® A fluoropolymer resin manufactured by DuPont (Thermoplastic) 

Vitalink ® A silicone rubber manufactured by Rockbestos-Surprenant (Thermoset) 

XLPE Cross-Linked Polyethylene (Thermoset) 

XLPO Cross-Linked Polyolefin (Thermoset) 

The only information required by the THIEF model for a particular cable is its overall diameter, 

its mass per unit length, its outer jacket thickness, and an experimentally determined “failure” 

temperature. The first two pieces of information are needed to describe the geometry and bulk 

thermal inertia of the cable; the jacket thickness is needed because it is assumed that cables fail 

electrically when the temperature of the insulation material surrounding the first layer of 

conductors just inside the jacket of a multi-conductor cable reaches a particular value which is 

determined experimentally (the last piece of information required as input). The cable diameter, 

mass per unit length and jacket thickness are all easily obtained either from the manufacturer or 

by direct measurement. The insulation thickness itself is not used by the model, but it is 

included in Table 1 because it might provide some insight into the failure mechanism. Generally 

speaking, the insulation is relatively thin, and its thermal penetration time is relatively short, 

compared to the jacket. The copper volume and mass fractions are included only to demonstrate 

the varied make up of the different cables. It will be shown below that the results of the THIEF 

model are insensitive to the relative amounts of copper and plastic, at least for the 15 cable types 

tested. 

One of the challenges in developing a more detailed model of the cable is the difficulty in 

obtaining material properties. The insulation and jacket materials are often complex polymers 

that undergo a number of reactions as they heat. Given the complexity of these processes and 

the expense of obtaining various thermo-physical properties, the THIEF model employs a single 

value for the specific heat and the thermal conductivity, 1.5 kJ/kg/K and 0.2 W/m/K, 

respectively, for both thermoset and thermoplastic cables. The bulk density of the cable, ρ , can 

be calculated by dividing the inputted mass per unit length by the cross sectional area. The 

emissivity of the cable jacket is assumed to be 0.95. These values are typical of several types of 

commonly used cable jacket and insulation materials, as reported by Hamins et al. (2006). Of 

course, each type of polymer is different; the properties are temperature-dependent, other 

decomposition reactions occur, etc. The calculations presented in this report could easily be 

repeated using other values, but it is hardly worthwhile because the predicted “failure” times are, 

to a first approximation, linearly proportional to the jacket thickness, the specific heat, and the 

density, and inversely proportional to the thermal conductivity. 
Table 1. Physical properties of the cables that are relevant to the modeling study. Additional information is included 

in Nowlen and Wyant (2007a). Note that the “Cable Number” is used only to identify the cables used in the study. 

Cable 

Number 

Cable Description 

(Insulation/Jacket/ 

No. Conductors) 

Cable 

Classification 

Insulation

Thickness

(mm) 

Jacket 

Thickness

(mm) 

Outer 

Diameter

(mm) 

Mass 

per 

Length 

(kg/m) 

Bulk 

Density

(kg/m3)

Copper

Volume

Fraction 

Copper 

Mass 

Fraction 

1 PVC/PVC, 7/C Thermoplastic 0.5 1.1 12.4 0.324 2680 0.24 0.80 2 EPR/CPE, 7/C Thermoset 0.8 1.5 15.1 0.400 2232 0.16 0.65 3 XLPE/PVC, 7/C Mixed 0.8 1.5 15.1 0.388 2166 0.16 0.67 4 PVC/PVC, 2/C Thermoplastic 0.7 1.0 7.0 0.076 1668 0.07 0.40 5 PVC/PVC, 3/C Thermoplastic 0.9 1.5 15.2 0.459 2532 0.18 0.63 6 PVC/PVC, 12/C Thermoplastic 0.5 1.1 11.3 0.195 1948 0.13 0.59 7 XLPE/CSPE, 2/C Thermoset 0.6 1.1 7.9 0.097 1993 0.07 0.31 8 XLPO/XLPO, 7/C Thermoset 0.5 0.9 12.2 0.321 2743 0.25 0.81 9 SR/Aramid Braid, 7/C Thermoset 1.3 1.0 14.5 0.358 2168 0.18 0.73 

10 XLPE/CSPE, 7/C Thermoset 0.8 1.5 15.0 0.410 2321 0.16 0.63 11 VITA-LINK, 7/C Thermoset 1.5 2.0 19.0 0.500 1656 0.06 0.34 12 TEF/TEF, 7/C Thermoplastic 0.4 0.5 10.2 0.292 3578 0.36 0.89 13 XLPE/CSPE, 12/C Thermoset 0.6 1.1 12.7 0.231 1825 0.10 0.50 14 XLPE/CSPE, 3/C Thermoset 1.1 1.5 16.3 0.529 2538 0.16 0.55 15 PE/PVC, 12/C Thermoplastic 0.8 1.1 15.0 0.380 2152 0.16 0.68 

8 
9

2.3 Numerical Algorithm 

This section provides details of the numerical solution of the heat conduction equation described 

in Section 2.1. It can be incorporated into any fire model that predicts the thermal environment 

surrounding the cable(s). This can be as simple as a gas temperature predicted by an empirical 

correlation, or as detailed as a spatially-resolved flow field in a computational fluid dynamics 

model. Whatever model is chosen, it must produce an estimate, as a function of time, of the heat 

flux to the cable surface, even if the cable itself is not explicitly included in the fire model. 

Finite Difference Scheme 

To solve Eq. (2.1) numerically, first divide the radius, R, of the cable into N uniformly spaced 

increments of length, δr = R/ N . An appropriate value for δr is about 0.1 mm for cables similar 

to those tested in CAROLFIRE. Next, define a time step that is related to the spatial increment. 

This is known as the time step constraint, which is necessary for accuracy, and sometimes 

numerical stability: 

k

c r

t

2

2 ρ δ δ = (2.3) 

The temperature of the i-th radial increment (or cell) at the n-th time step (t n t n = δ ) is denoted, n Ti . The value of the radius at the forward edge of the i-th cell is denoted, r i r i = δ . Thus, 0 r0 =

and rN = R . 

A finite difference approximation to Eq. (2.1), second order accurate in space and time3

, is 

given by: 

⎥

⎦

⎤ ⎢

⎣

⎡ − − − + − − −

+ = − +

−

+

−

+ +

− +

−

+

+

+

r

T T

r

r

T T

r

r

T T

r

r

T T

r

r r r

k

t

T T

c

n

i

n

i

i

n

i

n

i

i

n

i

n

i

i

n

i

n

i

i

i i

n

i

n

i

δ δ δ δ δ δ ρ

1

1

1

1

1 1

1 1

1

1

1

1

2

1

( )

2 (2.4) 

where ρ , c , and k are the effective density, specific heat, and conductivity of the solid, all 

assumed constant and given in the previous section. The boundary condition (Eq. (2.2)) is 

written in finite difference form as: 

( ) 1 n

n

N

n

N q t

r

T T k = ′′ + − & δ (2.5) 

Note that n Ts,N +1 is a fictitious value of the temperature half a grid increment away from the 

exterior surface. It serves only to define the temperature gradient at the cable surface. 

 

3

 The order of accuracy of the scheme has to do with the finite difference form of the partial derivatives in the original 

equation. The scheme shown here is known as the Crank-Nichsolson Method, and it was used to produce the results 

shown in this report. A simpler implementation, which is first order accurate in time instead of second, can be derived 

simply by replacing the superscripts n+1 by n on the right side of the equation. This has the effect of making the scheme 

explicit, meaning that the solution can be advanced in time by just moving all the terms defined at the n-th time step to 

the right hand side of the equation and solving for the temperature at the next (n+1) time step directly. The CrankNicholson Method requires the solution of a tri-diagonal system of linear equations. 
10

External Heat Flux 

The net4 heat flux at the surface is determined from the exposing gas temperature surrounding 

the cable at the n-th time step, ( )

n

g T t : 

( ) ( ) n

s

n

g

n

s

n

g

n q′′(t ) = T (t ) − (T ) + h T (t ) −T 4 4 & εσ (2.6) 

Here, ε is the emissivity of the cable surface (assumed to be 0.95 by THIEF), σ is the StefanBoltzmann constant ( 8 5.67 10− × W/m2

/K4), h is the convective heat transfer coefficient 

(assumed to be 10 W/m2

/K, typical of free convection (Incropera and DeWitt 1990)), and ( )

n

g T t

is the effective5

 gas temperature at the n-th time step, which is calculated by the fire model in 

which THIEF is embedded. The surface temperature of the cable, n Ts , can be taken as n TN , the 

temperature one half of a cell width inside the cable surface. Typically, the cell width is chosen 

to be about 0.1 mm, a very small length, and this minor approximation has very little influence 

on the solution. 

The fire model, in which THIEF is embedded as a target sub-model, may or may not produce the 

heat flux directly. At the very least, the fire model predicts an upper layer temperature, which 

for this application can be taken as the effective gas temperature, Tg , to which the cable is 

exposed. Depending on the application, the cable(s) might be exposed directly to the fire, in 

which case the required net radiative heat flux to the cable is taken as the incident heat flux 

determined by the fire model (point source method, for example) minus the radiative loss of the 

cable: 

4 ( ) ( )n

inc N

n q&′′ t = ε q&′′ − εσ T (2.7) 

Further discussion of the heat flux is included in Section 5, “Lessons Learned from 

CAROLFIRE,” in which various issues related to the implementation of THIEF in a fire are 

discussed. 

Conduits 

A slight complication of the solution methodology described above is in situations where the 

cable is surrounded by a protective layer like a conduit, armor jacket, or tray covering. In 

CAROLFIRE, only conduits were considered in the modeling, but other protective measures can 

be handled in similar fashion, assuming test data is available to validate the various physical 

assumptions. 

A conduit forms a thermal barrier between the hot gases of a fire and the cable itself. A simple 

way to incorporate its effect into the THIEF model is to replace the “exposing” gas temperature, 

Tg , in Eq. (2.6) by the conduit’s temperature, Tc . In other words, the cable no longer “sees” the 

hot gases from the fire, but rather the interior surface of the conduit. A steel conduit may be 

 

4

 The net flux implies the incident minus the re-radiated radiation heat flux. 5

 It is assumed that in most applications of the THIEF model, the cables are to be surrounded by hot, smoke-filled gases 

from a fire, and that these gases are optically-thick, or “black.” 
11

assumed thermally-thin; that is, its conductivity is so large that for all practical purposes it can be 

assumed that its exterior and interior surface temperatures are equal. Its temperature increases 

due to the heat flux from the hot gases at its exterior surface: 

( ) ( ) n

c

n

g

n

c

n

c g

n q′′ (t ) = T (t ) − (T ) + h T (t ) − T 4 4 &ext ε σ (2.8) 

Here, n Tc is the conduit temperature at the n-th time step and c ε is the emissivity of its surface, 

taken as 0.85, typical of non-polished steel (Weast 1982). Heat is transferred from the interior 

surface of the conduit to the cable surface via: 

( )( )

1

4 4

int

1 1 ( ) ( ) ( ) ; 

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎟ + ⎠

⎞ ⎜

⎝

⎛ ′′ = − + − =

c

n c c

N

n

c

n

N

n

c

n

R

R

q t F T T h T T F

ε

ε

ε & σ (2.9) 

Here, Rc is the inner radius of the conduit. The view factor, F, is based on the assumption that 

the conduit and cable are concentric cylinders (Incropera and DeWitt 1990). The temperature of 

the conduit is raised by the net heat fluxes to its exterior and from its interior surfaces: 

c c c

n

c

n

c c

q q T T t

ρ δ

δ 1 ext int ′′ − ′′ = + + & & (2.10) 

Here, the subscript, c, stands for conduit, and the density and specific heat are that of steel 

(7850 kg/m3

 and 0.46 kJ/kg/K). The thickness of the conduit, δ c , used in the CAROLFIRE 

experiments was 4.9 mm (0.19 in). 
13

3 BENCH-SCALE “PENLIGHT” EXPERIMENTS 

The CAROLFIRE test program consisted of small-scale and intermediate-scale experiments, all 

conducted at Sandia National Laboratories. The experiments are described briefly below. 

Details can be found in Nowlen and Wyant (2007b). The information included in this report is 

that which is relevant to explain how the THIEF model of cable failure outlined above was 

applied for all 15 different cable construction samples for the various test configurations. This 

chapter describes the small-scale experiments in what is referred to as the “penlight’’ apparatus. 

3.1 Experimental Description 

The penlight is a cylinder formed by heating elements, 0.60 m (2 ft) long and 0.45 m (1.5 ft) in 

diameter, usually oriented horizontally, as shown in Figure 2. In the experiments, the 

temperature of the cylindrical “shroud” was controlled according to a specified function of time, 

while pairs of cables were monitored, one for thermal and the other for electrical response. 

Figure 2. Schematic diagram of Penlight apparatus, courtesy Sandia National Laboratory. 

 Details can be found in Nowlen and Wyant (2007b). 
14

The figure at left shows the thermocouple 

locations for a seven conductor (7/C) cable. 

The thermocouples were affixed to the cable 

surface and inserted inside the cable, just 

under the jacket, at various locations, 

depending on the number of conductors. 

For comparison to the THIEF model, only 

the two measurements just inside the jacket 

(TC 1 and TC 4) were used. These 

measurements were made very near the 

center of the penlight apparatus, where the 

heat flux was expected to be greatest. 

There were 35 Penlight experiments in 

which single cables were monitored for 

thermal and electrical response, designated 

in Nowlen and Wyant (2007b) as PT-1 

through PT-31 and PT-62 through PT-65. There were three ways in which the cables were 

supported within the penlight apparatus: on a tray, in a conduit, or merely suspended midway 

through the penlight tunnel, commonly referred to as an “air drop”. Other penlight experiments 

were conducted with multiple cables bundled together and monitored electrically. The primary 

purpose of these experiments was to address the various modes of electrical cable failure; they 

were not designed to assess the thermal response of a set of bundled cables. Consequently, the 

issue of predicting the temperatures of bundled cables is addressed in the chapter describing the 

Intermediate Scale Test Series. 

3.2 Experimental Results 

The results of 35 penlight experiments involving single (non-bundled) cables are summarized in 

Table 2. From the measurements of the temperatures just below the jacket, it is fairly evident 

that the tested thermoplastic cables failed electrically when their inner (under the jacket) 

temperatures reached somewhere between 200 °C and 250 °C (392 °F and 482 °F). For 

thermosets, the range was about 400 °C to 450 °C (752 °F to 842 °F). It is not possible to be 

more precise for several reasons. First, there were a limited number of replicate tests for most of 

the cable samples. Second, the electrical monitoring and thermal measurements were never 

made on the same cable, but rather on identical cables separated by a few centimeters in the tray 

or conduit. This was done to prevent interference between the thermocouple wire and the live 

cable conductors. Finally, as seen in Figure 4, the measured inner cable temperatures often 

increased dramatically just before the first electrical short because typically these types of cables 

ignite and fail electrically at about the same temperature (Nowlen and Wyant 2007b). 

Figure 3. Thermocouple locations for a 7/C 

cable. 
15

Penlight Test 2

XLPE/CSPE

3/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

864 s

Figure 4. The results of Penlight Test 2 where it is observed that the inner cable 

temperatures (solid and dashed red lines) increase significantly about 1 min prior to the 

first recorded electrical short. The dotted lines are results of the THIEF model. 
16

Table 2. Summary of the Sandia Penlight experiments that involved only single cables. 

Measurement uncertainties are reported in Nowlen and Wyant (2007b). Note that the 

thermoplastic cable (TEF/TEF) in Test 22 was tested like a thermoset. 

Test Cable 

No. 

Cable 

Composition Raceway 

Exposing 

Temp. 

(°C) 

Inner Cable 

Temperature 

(°C) 

Time to 

First 

Short 

(s) 

Thermosets 

PT-1 14 XLPE/CSPE Tray 475 393 396 771 

PT-2 14 XLPE/CSPE Tray 470 393 410 864 

PT-3 14 XLPE/CSPE Tray 470 N/A N/A 790 

PT-7 14 XLPE/CSPE Conduit 470 403 424 2334 

PT-9 14 XLPE/CSPE Air Drop 470 413 418 1531 

PT-11 10 XLPE/CSPE Tray 470 415 425 1225 

PT-12 10 XLPE/CSPE Tray 470 420 425 1273 

PT-13 10 XLPE/CSPE Tray 470 419 434 1198 

PT-17 2 EPR/CPE Tray 470 447 448 613 

PT-18 9 SR/ Aramid Braid Tray 700 N/A N/A DNF 

PT-19 8 XLPO/XLPO Tray 470 419 436 935 

PT-20 3 XLPE/PVC Tray 470 413 421 612 

PT-22 12 TEF/TEF Tray 470 382 384 445 

PT-23 10 XLPE/CSPE Conduit 470 425 429 1803 

PT-24 10 XLPE/CSPE Conduit 470 422 433 2006 

PT-27 10 XLPE/CSPE Air Drop 470 423 426 1356 

PT-28 10 XLPE/CSPE Air Drop 470 421 430 1314 

PT-31 11 VITA-LINK Tray 700 N/A N/A DNF 

PT-62 13 XLPE/CSPE Tray 470 N/A N/A 502 

PT-64 7 XLPE/CSPE Tray 470 N/A N/A 348 

Thermoplastics 

PT-4 5 PVC/PVC Tray 300 195 200 590 

PT-5 5 PVC/PVC Tray 300 211 213 766 

PT-6 5 PVC/PVC Tray 300 206 216 776 

PT-8 5 PVC/PVC Conduit 300 164 174 1245 

PT-10 5 PVC/PVC Air Drop 300 228 N/A 1173 

PT-14 15 PE/PVC Tray 300 237 238 1464 

PT-15 15 PE/PVC Tray 325 246 266 806 

PT-16 15 PE/PVC Tray 325 236 244 824 

PT-21 1 PVC/PVC Tray 300 196 229 560 

PT-25 15 PE/PVC Conduit 325 N/A N/A 2924 

PT-26 15 PE/PVC Conduit 325 N/A N/A DNF 

PT-29 15 PE/PVC Air Drop 325 232 239 845 

PT-30 15 PE/PVC Air Drop 325 243 256 599 

PT-63 6 PVC/PVC Tray 325 205 208 333 

PT-65 4 PVC/PVC Tray 325 225 N/A 258 

DNF Cable Did Not Fail electrically 
17

3.3 Modeling Considerations 

The thermally-induced electrical failure (THIEF) model has been incorporated into a 

computational fluid dynamics model called the Fire Dynamics Simulator or FDS (McGrattan et 

al. 2007). For the purpose of testing the THIEF model, the penlight apparatus was crudely 

modeled as a rectangular cavity, 0.6 m (2 ft) in length and 0.45 m (1.5 ft) in each transverse 

direction. The cable was modeled as a rectangular obstruction running the length of the cavity. 

Even though the obstruction is rectangular and much larger than the actual cable (to conform to 

the uniform, gas phase numerical grid), the one-dimensional heat conduction calculation within 

the “cable” is performed in cylindrical coordinates with appropriate dimensions. The rectangular 

obstruction is merely a convenient “target” for calculating the radiative and convective heat flux 

boundary condition for the solid phase heat conduction solver. The radiative heat flux is based 

on the solution of the radiative transport equation; the convective heat flux is based on empirical 

correlations. See McGrattan et al. (2007) for details. 

It is certainly possible to model the penlight apparatus with greater spatial refinement, using FDS 

or another model of comparable capabilities. However, in practice the THIEF model is designed 

to work within a larger model that is to be used to assess the impact of a fire on an entire 

compartment. Resolution of such calculations is currently at best on the order of 5 cm (2 in) to 

10 cm (4 in), making the cable essentially a “subgrid-scale” target. The ability of FDS to 

reproduce the thermal environment of the penlight apparatus is demonstrated in Figure 5. In 

Penlight Test 7 (PT-7), two cables were run through a conduit that was routed through the 

penlight. The conduit was modeled in FDS as a steel box with an assumed wall thickness of 

4.9 mm, conductivity 45.8 W/m/K, density 7850 kg/m3

, specific heat 0.46 kJ/kg/K, and 

emissivity 0.85. The shroud temperature was reported by Nowlen and Wyant (2007b) as rising 

linearly to 478 °C. The prediction of the conduit temperature is within a few percentage points 

of the measurement, almost certainly within experimental uncertainty. However, the point of 

this exercise is not necessarily to validate the radiation and convection heat transfer algorithms 

within FDS, but rather to demonstrate that FDS can reproduce the thermal environment of the 

penlight apparatus. FDS is merely a convenient test bed for the cable failure algorithm. 

Penlight Test 7

Shroud and 

Conduit

Temperatures

Time (s)

0 600 1200 1800 2400

Temperature (°C)

0

200

400

600

Shroud

Conduit

Figure 5. (Left) Photograph of a conduit within the penlight apparatus, with end caps 

installed, courtesy Frank Wyant, Sandia National Laboratories. (Right) Predicted (dotted 

line) and measured (solid line) temperatures of the conduit when exposed to the shroud 

temperature profile. This example is part of penlight experiment number 7. 
18

3.4 Modeling Results 

The THIEF model predictions of each of the 35 penlight experiments are presented in the 

following sections. Each experiment is summarized by a single graph, an example of which is 

shown in Figure 6. 

Penlight Test 1

XLPE/CSPE

3/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (°C)

0

200

400

600

First Short

771 s

Shroud temperature in experiment (solid, black line);

Specified exposure temperature in model (dotted, black line)

Measured inner cable temperatures

on opposite sides of the cable 

(solid and dashed red lines).

These temperatures sometimes

noticeably increase following the

first short and subsequent ignition.

Predicted inner cable temperature (dotted, red line).

No ignition included in the model.

Figure 6. Key to graphs showing results of penlight tests. Note that the term “First Short” 

indicates the first observed electrical failure, regardless of the specific type. In the 

experiments, subsequent shorts were observed, but are not relevant here. 
19

Thermoset Cables 

Thermoset cables, in general, have been observed to short at higher temperatures than 

thermoplastics (Iqbal and Salley 2004). For this reason, the thermoset cables included in the 

CAROLFIRE program were exposed to higher temperatures in the Penlight Test Series. Even 

though the THIEF model does not distinguish between thermosets and thermoplastics, it is 

convenient to present the results according to this classification scheme. 

Figure 7 through Figure 9 contain THIEF model predictions of the temperatures of various 

thermoset cables within the penlight apparatus. 
20

Penlight Test 1

XLPE/CSPE

3/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

771 s

Penlight Test 7

XLPE/CSPE

3/C

Conduit

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

2334 s

Shroud

Conduit

Cable

Penlight Test 2

XLPE/CSPE

3/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

864 s

Penlight Test 9

XLPE/CSPE

3/C

Air Drop

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First

Short

1531 s

Penlight Test 3

XLPE/CSPE

3/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

790 s

Figure 7. Results for Cable #14 (XLPE/CSPE, 3 conductor). The upper-most black curves 

depict the measured (solid) and specified (dotted) shroud temperature. The solid and 

dashed red lines are the measured temperatures inside the cable jacket, at opposite sides. 

The dotted red curve is the predicted inner cable temperature. The vertical dashed line 

indicates the first observed electrical short in the experiment. For Test 7, the solid blue 

and dotted blue curves represent the measured and predicted conduit temperatures, 

respectively.
21

Penlight Test 11

XLPE/CSPE

7/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

1225 s

Penlight Test 23

XLPE/CSPE

7/C

Conduit

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

1803 s

Shroud

Conduit

Cable

Penlight Test 12

XLPE/CSPE

7/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

1273 s

Penlight Test 24

XLPE/CSPE

7/C

Conduit

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

2006 s

Shroud

Conduit

Cable

Penlight Test 13

XLPE/CSPE

7/C

Tray

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

1198 s

Penlight Test 27

XLPE/CSPE

7/C

Air Drop

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

1356 s

Penlight Test 28

XLPE/CSPE

7/C

Air Drop

Time (s)

0 600 1200 1800 2400

Temperature (C)

0

200

400

600

First Short

1314 s

Figure 8. Results for Cable #10 (XLPE/CSPE, 7 conductor). The color scheme is the same as in 

Figure 7. 
22

Penlight Test 17

EPR/CPE 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

First Short

613 s

Penlight Test 22

TEF/TEF 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

First

Short

445 s

Penlight Test 19

XLPO/XLPO 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

First

Short

935 s

Penlight Test 62

XLPE/CSPE 12/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

Cable 

Ignites

257 s

First

Short

502 s

Penlight Test 20

XLPE/PVC 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

First Short

612 s

Penlight Test 64

XLPE/CSPE 2/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

First 

Short

348 s

Cable

Ignites

218 s

Figure 9. Results for various thermoset cables. The upper-most black curves depict the 

measured (solid) and specified (dotted) shroud temperature. The solid and dashed red 

lines are the measured temperatures inside the cable jacket, at opposite sides. The dotted 

red curve is the predicted inner cable temperature. The vertical dashed line indicates the 

first observed electrical short in the experiment. 
23

Thermoplastic Cables 

The shroud temperature for the single cable thermoplastic penlight tests was set to just over 

300 °C (572 °F). For the THIEF model predictions, the same thermal conductivity and specific 

heats that are used for the thermosets are also used for the thermoplastics. Thus, no distinction is 

made in the THIEF model between thermosets and thermoplastics. 

Figure 10 through Figure 12 contain THIEF model predictions of the temperatures of various 

thermoplastic cables within the penlight apparatus. 
24

Penlight Test 4

PVC/PVC 3/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

590 s

Penlight Test 8

PVC/PVC 3/C

Conduit

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

1245 s

Conduit

Penlight Test 5

PVC/PVC 3/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

766 s

Penlight Test 10

PVC/PVC 3/C

Air Drop

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

1173 s

Penlight Test 6

PVC/PVC 3/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

776 s

Figure 10. Results for Cable #5 (PVC/PVC, 3 conductor). The upper-most black curves 

depict the measured (solid) and specified (dotted) shroud temperature. The solid and 

dashed red lines are the measured temperatures inside the cable jacket, at opposite sides. 

The dotted red curve is the predicted inner cable temperature. The vertical dashed line 

indicates the first observed electrical short in the experiment. For Test 8, the solid blue 

and dotted blue curves represent the measured and predicted conduit temperatures, 

respectively.
25

Penlight Test 14

PE/PVC 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

1464 s

Penlight

Test 25

PE/PVC

7/C

Conduit

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (C)

0

100

200

300

400

First Short

2918 s

Shroud

Conduit

Cable

TCs Fail

Penlight Test 15

PE/PVC 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

806 s

Penlight

Test 26

PE/PVC

7/C

Conduit

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (C)

0

100

200

300

400

No Shorts

Shroud

Conduit

Cable

Penlight Test 16

PE/PVC 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

824 s

Penlight Test 29

PE/PVC 7/C

Air Drop

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

845 s

Penlight Test 30

PE/PVC 7/C

Air Drop

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

599 s

Figure 11. Results for Cable #15 (PE/PVC, 7 conductor). The color scheme is the same as in 

Figure 10. 
26

Penlight Test 21

PVC/PVC 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First Short

560 s

Penlight Test 63

PVC/PVC 12/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First 

Short

333 s

Penlight Test 65

PVC/PVC 2/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

100

200

300

400

First 

Short

258 s

Figure 12. Results for 2, 7, and 12 conductor PVC/PVC (thermoplastic) cables. The 

upper-most black curves depict the measured (solid) and specified (dotted) shroud 

temperature. The solid and dashed red lines are the measured temperatures inside the 

cable jacket, at opposite sides. The dotted red curve is the predicted inner cable 

temperature. The vertical dashed line indicates the first observed electrical short in the 

experiment. 
27

Special Cables 

Two of the fifteen cable samples were observed during preliminary experiments to withstand 

significantly higher temperatures than the others without any observed electrical shorting. Thus, 

these two cables were tested at higher temperatures during the Penlight test series. Figure 13 

presents the results of the experiments and THIEF model predictions. Note that the cables were 

not observed to fail electrically during the experiments, even though they did ignite and burn. 

This same behavior was observed during the Intermediate Scale experiments, but the cables did 

fail electrically when a water spray was applied. See Nowlen and Wyant (2007b) for details. 

Penlight Test 18

SR/Aramid Braid 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

800

Cable Ignites

114 s

Penlight Test 31

VITA-LINK 7/C

Tray

Time (s)

0 600 1200 1800

Temperature (C)

0

200

400

600

800

Cable Ignites

208 s

Figure 13. Results for Cable #9 (Silicone Rubber/Aramid Braid, 7 conductor) and Cable 

#11 (VITA-LINK, 7 conductor). The upper-most black curves depict the measured (solid) 

and model-specified (dotted) shroud temperature. The solid red line is the measured 

temperature inside the cable jacket. The dotted red line is the predicted inner cable 

temperature. Ignition and burning are not included in the THIEF model, and electrical 

shorting did not occur in these two experiments. Note that neither cable failed electrically 

until the introduction of a water spray. See Nowlen and Wyant (2007b) for details. 
28

3.5 Summary of Penlight Analysis 

For the purpose of evaluating the THIEF model, it is sufficient to simply choose a “threshold 

temperature” for each class of cable to serve as a surrogate for a true failure temperature that 

would have to be determined from a more extensive set of measurements. For this exercise, 

400 °C (752 °F) was chosen for the thermosets; 200 °C (392 °F) for the thermoplastics. Figure 

14 compares the predicted time to the threshold temperature versus the measured times for the 35 

single cable tests chosen from the Penlight series. The data for this graph are included in Table 

3. There are two inner-cable measurements considered, made on opposite sides of the cable, just 

beneath the jacket. In all, 66 THIEF model predictions of time to “threshold” temperature were 

compared to the measured counterparts (in 4 tests, the Point B measurement was not made). The 

THIEF model under-predicted the times by 3 %, on average, and the standard deviation was 

20 %. 

Overall, there is only a slight bias in the THIEF model towards under-predicting the time to 

reach the threshold temperature in the ideal environment of the Penlight apparatus. To test 

whether the model has a particular bias related to the various cable properties, the relative 

differences6

 between the predicted and measured “failure” times were plotted as functions of the 

various cable properties and shown in Figure 15. From the plots, the accuracy of the model does 

not appear to be related to the various bulk properties of the cable, as there is no discernable 

pattern in the various graphs. If, for example, the model were to over-predict the “failure” time 

for thin cables, one would expect to see that reflected in the graph. 

 

6

 The relative difference was calculated as the difference between the predicted and the measured time divided by the 

measured time. A positive value of the relative difference means that the model over-predicted that particular threshold 

time. 
29

Measured Time to Threshold Temperature (s)

0 600 1200 1800 2400

Predicted Time to Threshold Temperature (s)

0

600

1200

1800

2400

Thermoset, Point A

Thermoset, Point B

Thermoplastic, Point A

Thermoplastic, Point B

μ−σ

μ+σ

μ

Figure 14. Comparison of THIEF model and experiment for the Penlight series. Point A 

and B refer to the thermocouple measurements made on opposite sides of the cable, just 

under the jacket. The “Threshold Temperature” is 400 °C (752 °F) for thermoset cables 

and 200 °C (392 °F) for thermoplastics. The dashed lines represent the average (-3 %) and 

standard deviation (20 %) of the data. 
30

Table 3. Summary of the THIEF Model Predictions of the Penlight Experiments. 

Test Cable 

No. 

Cable 

Composition 

(Insulation/Jacket)

Threshold 

Temperature

(°C) 

Measured 

Time to 

Threshold 

(s) 

Predicted 

Time to 

Threshold

(s) 

Thermosets 

PT-1 14 XLPE/CSPE 400 800 800 712 

PT-2 14 XLPE/CSPE 400 761 747 712 

PT-3 14 XLPE/CSPE 400 694 671 712 

PT-7 14 XLPE/CSPE 400 1660 2196 1735 

PT-9 14 XLPE/CSPE 400 1009 1115 920 

PT-11 10 XLPE/CSPE 400 835 993 700 

PT-12 10 XLPE/CSPE 400 740 887 700 

PT-13 10 XLPE/CSPE 400 761 885 700 

PT-17 2 EPR/CPE 400 545 533 600 

PT-18 9 SR/ Aramid Braid 400 157 -- 216 

PT-19 8 XLPO/XLPO 400 710 810 516 

PT-20 3 XLPE/PVC 400 585 575 562 

PT-22 12 TEF/TEF 400 518 530 564 

PT-23 10 XLPE/CSPE 400 1488 1434 1608 

PT-24 10 XLPE/CSPE 400 1532 1608 1608 

PT-27 10 XLPE/CSPE 400 883 975 766 

PT-28 10 XLPE/CSPE 400 785 961 768 

PT-31 11 VITA-LINK 200 322 -- 247 

PT-62 13 XLPE/CSPE 400 349 365 387 

PT-64 7 XLPE/CSPE 400 265 -- 284 

Thermoplastics 

PT-4 5 PVC/PVC 200 588 631 625 

PT-5 5 PVC/PVC 200 639 649 625 

PT-6 5 PVC/PVC 200 693 571 625 

PT-8 5 PVC/PVC 200 1570 1692 1775 

PT-10 5 PVC/PVC 200 599 807 720 

PT-14 15 PE/PVC 200 715 750 525 

PT-15 15 PE/PVC 200 378 471 371 

PT-16 15 PE/PVC 200 532 566 371 

PT-21 1 PVC/PVC 200 342 598 530 

PT-25 15 PE/PVC 200 1382 1467 1362 

PT-26 15 PE/PVC 200 1439 1388 1362 

PT-29 15 PE/PVC 200 509 570 453 

PT-30 15 PE/PVC 200 397 246 453 

PT-63 6 PVC/PVC 200 316 302 294 

PT-65 4 PVC/PVC 400 206 -- 215 
31

Copper Mass Fraction

0.0 0.2 0.4 0.6 0.8 1.0

Relative Difference (%)

-100

-50

0

50

100

Bulk Density (kg/m3)

1000 1500 2000 2500 3000 3500 4000

Relative Difference (%)

-100

-50

0

50

100

Cable Diameter (mm)

6 8 10 12 14 16 18 20

Relative Difference (%)

-100

-50

0

50

100

Mass Per Unit Length (kg/m)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Relative Difference (%)

-100

-50

0

50

100

Insulation Thickness (mm)

0.0 0.5 1.0 1.5 2.0

Relative Difference (%)

-100

-50

0

50

100

Jacket Thickness (mm)

0.0 0.5 1.0 1.5 2.0

Relative Difference (%)

-100

-50

0

50

100

Figure 15. Sensitivity of the THIEF model predictions to various cable properties. The 

Relative Difference refers to the predicted vs measured times to reach the threshold 

temperature. The horizontal dashed line is the average Relative Difference for all the 

Penlight comparisons. 
32

3.6 Why Does the THIEF Model Work? 

Given the complexity and variety of composition among the 15 different cable types that were 

tested in the CAROLFIRE Penlight series, it is reasonable to ask why the simplest of 

mathematical models could have predicted the results of the experiments so well. The answer 

lies in the fact that simple “lumped parameter” models often take advantage of off-setting errors. 

That is, the errors associated with the various modeling assumptions often act to partially cancel 

each other out. The most important assumption in the THIEF model is that the cable is a 

homogenous cylinder with temperature-independent thermal properties. The thermal 

conductivity and specific heat are fixed for all cable types, with values typical of both thermoset 

and thermoplastic materials (Hamins et al. 2006). The density is an effective value, based on the 

overall mass per unit length and cross sectional area of the cable. Even though the mass fraction 

of copper in the cables tested is in the range of 0.3 to 0.9, its contribution is only through the 

bulk density. Neither the conductivity nor specific heat of copper plays a role in the model. 

Suppose, however, that a slightly more detailed model of the cable is formulated. Assume that 

instead of a homogenous cylinder, the cable is idealized as a polymeric/copper mixture, 

surrounded by a purely polymeric jacket. The thermal properties of the mixture are calculated 

based on the measured mass and volume fractions of the respective materials within a particular 

cable. The thermal conductivity, specific heat and density of the polymer are assumed to be 

0.2 W/m/K, 1.5 kJ/kg/K, and 1380 kg/m3

, respectively, all based on measurements of several 

cables and reported in Hamins et al. (2006). The properties of copper are 400 W/m/K, 

0.385 kJ/kg/K, and 8960 kg/m3

, respectively (Weast 1982). The temperature prediction of this 

two-layer model is shown in Figure 16 for Penlight Test 1, along with the THIEF prediction. 

Penlight Test 1

XLPE/CSPE

3/C

Tray

Time (s)

0 300 600 900 1200

Temperature (°C)

0

200

400

600

First Short

771 s

THIEF

Model

Two-Layer

Model

Shroud

Temperature

Measured

Interior 

Temperatures

Figure 16. Results of an alternative thermal model (short dashes) and the THIEF model 

(dotted line), compared to measurements (solid and long dashed lines). 

The prediction of the more detailed model is, at least in this case, less accurate than the THIEF 

model. Why? Consider the noticeable shift in the two measured interior temperatures at about 

200 s and 200 °C. Neither the THIEF nor the two-layer model captures this abrupt shift in 
33

temperature because neither model accounts for decomposition reactions or evaporation which 

inevitably occurs as the polymers heat up and produce this characteristic pattern in the 

temperature plot. The two-layer model is a better description of the cable structure and 

composition, as is apparent from its closer match to the measurement in the first 200 s. 

However, the rise of the measured temperatures inside the cable noticeably slows at this point, 

most likely caused by some endothermic process that draws energy from the system and slows 

the temperature rise. The THIEF model uses the specific heat of the polymer (1.5 kJ/kg/K) 

throughout the cable cross section, whereas the two-layer model uses this value only for the 

jacket layer, and 0.75 kJ/kg/K for the interior mixture. Also, the two-layer model uses the 

density of the polymer (1380 kg/m3

) for the jacket layer, whereas the THIEF model uses the bulk 

density of the entire cable (2538 kg/m3

). In short, the THIEF model uses an upper-bound 

estimate for the thermal inertia (density times specific heat) of the cable, but at the same time 

neglects the endothermic polymeric decomposition reactions. The two-layer model better 

estimates the thermal inertia and overall cable construction, but it too neglects the reactions. 

THIEF works because of the off-setting errors – its upper-bound estimate of the thermal inertia 

counteracts, to some degree, its neglect of the endothermic reactions. The two-layer model has 

no mechanism to counteract its neglect of the reactions. 

A natural question to ask is why not include chemical reactions in the model? Indeed, as part of 

the CAROLFIRE program, a detailed model of a cable -- including multi-component kinetics, 

temperature-dependent thermal properties, and multi-dimensional heat conduction -- was 

developed at the University of Maryland (Chourio 2007). However, the detailed model could 

not be used to predict the measured temperatures because of a lack of property data:

“Given the scarcity of data and the lack of consistency in the characterization of the kinetic 

parameters, it is not possible to assess the endurance limits for this model at this time.” 

As a general rule, a more detailed model requires more detailed inputs. If the thermal and 

chemical properties of the polymers are not available, simplifications have to be made. 

Furthermore, even if the property data were provided or measured, the more detailed model 

would not provide more accurate results, at least for single cables, because of the natural 

variability of the measured failure times. Consider that the replicate Penlight Tests 1, 2 and 3 

had measured failure times of 771 s, 864 s and 790 s, respectively; and that replicate Penlight 

Tests 4, 5 and 6 had measured failure times of 590 s, 766 s and 776 s, respectively. 
35

4 INTERMEDIATE SCALE EXPERIMENTS 

4.1 Experimental Description 

Following the Penlight Test Series, cables in various configurations were exposed to a realistic 

fire environment in what are referred to as the “Intermediate Scale Tests.” In these experiments, 

an ethylene gas burner was centered underneath a 3.6 m (12 ft) by 2.4 m (8 ft) by 1.3 m (4 ft) 

deep enclosure constructed of gypsum board that was suspended about 2 m (6 ft) above the floor 

(see Figure 17). Cable trays, conduits, and “air drop” cables were exposed to fires ranging from 

250 kW to 350 kW. Some cables were monitored for electrical response; some for thermal 

response. 

Figure 17. Side view of the Intermediate Scale Test rig. Courtesy Sandia National 

Laboratories. 

4.2 Modeling Considerations 

Initially, these experiments were simulated using the Fire Dynamics Simulator, and predictions 

were made for the cable failure times based on the THIEF model that was embedded within 

FDS. However, because the heat release rate of the burning cables was not measured, it was not 

possible to predict accurately the gas temperatures in the vicinity of the various cable trays. 

Without sound predictions of the enclosure gas temperatures, it was not possible to test the 
36

THIEF model within a larger simulation of the entire compartment. 

Fortunately, the measured gas temperature from the experiments served as appropriate 

“exposing” temperatures for testing the cable failure algorithm. In other words, the measured 

gas temperatures were used much like the “shroud” temperatures in the Penlight test series. 

Thus, the THIEF model was used to predict the inner temperature of every cable with an 

embedded thermocouple and a gas temperature measurement in its vicinity (usually above or 

below the tray). In the case of conduits, the measured conduit temperature was used as the 

“exposing” temperature. Figure 18 displays the result of a typical comparison of model and 

measurement. 

Intermediate Test 8

Location C, 6 Cable Bundle

PE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

657 s

The type of cable that

was instrumented

The measured gas temperature (solid line);

The specified exposure temperature (dotted line)

All graphs run

out to an hour 

for consistency

The time when the measured cable

temperature exceeds 200 °C (solid, red line)

The time when the predicted cable

temperature exceeds 200 °C (dotted, red line)

All graphs max 

out at 1000 °C 

for consistency

Include first observed electrical

failure in adjacent bundle if 

appropriate

Figure 18. Key to Intermediate Scale graphs. 

Note that the graph in Figure 18 includes a vertical dashed line indicating when the first 

electrical short was observed in the experiment. This is only included for situations when 

comparable cables were instrumented for both thermal and electrical response. This was not 

always the case, and it is noted on the plots when there was no electrical monitoring present. 

Even in cases where two equivalent cables were monitored for thermal and electrical response, it 

is not always appropriate to link the measured temperature with electrical failure. For example, 

Figure 19 shows the measured and predicted inner temperature (TC-1) of a single cable within a 

6-cable bundle. Given the configuration, it is likely that the first short occurs at the bottom of 

Cable E, not the top, where the temperature is measured. The THIEF model cannot distinguish 

the top and bottom of the cable because it only accounts for heat transfer in the radial direction. 
37

Intermediate Test 11

Location G, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

464 s

Figure 19. Example of an experiment where the temperature measurement (TC-1) may 

not coincide with the location of the first electrical short. 
38

4.3 Model Results 

The following sections describe the results of the THIEF predictions for the various cable 

configurations, including single cables within trays, cables within conduit, random fill trays, six 

cable bundles, 12 cable bundles and “air drops.” 

Single Cables within Trays 

In several Intermediate Scale Tests, single cables were laid out in trays in pairs – one 

instrumented for electrical response, the other for thermal. The plots on the following page show 

comparisons of the cable inner temperature measurements and the corresponding predictions by 

the THIEF model. 

Note that for the single cable cases, and only the single cable cases, the measured gas 

temperature was modified to account for the influence of the heat flux from the fire directly on 

the cables. Because the direct impingement of thermal radiation from the fire provided a 

significant fraction of the total heat flux early in the test, the measured gas temperature, Tgas , 

was modified to account for the additional heat flux from the fire, q&′′

(T T ) (T T ) q eff gas − = − + ′′ ∞ ∞ & 4 4 4 4 σ σ (4.1) 

The heat flux from the fire was estimated using a point source approximation, with the origin 

centered above the burner a distance of half the flame height as calculated using Heskestad’s 

correlation (Iqbal and Salley 2004). The “effective” gas temperature, Teff , was used as input in 

the THIEF model as the exposing temperature, rather than the actual measured gas temperature. 

In all other cases, the instrumented cables were shielded from the fire’s direct thermal radiation 

by either a conduit or surrounding cables within a bundle, and no correction to the measured gas 

temperature was needed. 
39

Intermediate Test 2

Location E, Single Cable

PVC/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

Intermediate Test 2

Location G, Single Cable

PVC/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

First Short

580 s

Intermediate Test 3

Location E, Single Cable

PVC/PVC, 3/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

Intermediate Test 3

Location G, Single Cable

PVC/PVC, 3/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

First Short

627 s

Intermediate Test 4

Location E, Single Cable

XLPE/CSPE, 3/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

Intermediate Test 4

Location G, Single Cable

XLPE/CSPE, 3/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

Intermediate Test 5

Location E, Single Cable

EPR/CPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

Intermediate Test 5

Location G, Single Cable

EPR/CPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Effective Gas

Temperature

Figure 20. Summary of results for single, isolated cables in the Intermediate scale tests. Black 

indicates the exposing temperature; red the cable. Solid lines for experiment, dotted for model.
40

Cables in Conduits 

In 10 instances during the Intermediate Scale Test Series, cables were routed through a standard 

heavy wall, galvanized steel conduit in bundles similar to that shown below. The cable labeled 

with the number 1 was instrumented with a thermocouple inside its jacket, while the lettered 

cables were instrumented for electrical response. For the purpose of testing the THIEF model, 

the measured conduit temperature itself was used as the exposing temperature, and the measured 

temperature of Cable 1 was compared to that predicted by the model. 

The results for the conduit at Location E (see Figure 17 for 

locations) are shown in Figure 21; the results for Location D and G 

in Figure 22. These results are most similar to the Penlights 

because the conduit is very much like the “shroud” of the penlight 

apparatus in that it distributes the radiative flux uniformly about 

the instrumented cable. Thus, the one-dimensional heat conduction 

assumption holds. Note that in the Intermediate Scale Tests, no gas 

phase measurements were taken outside the conduit, and no 

attempt was made to predict the conduit temperature, as was the case in the Penlight Tests. 

Rather, the conduit temperature was taken as the specified exposing temperature. From the 

results shown on the following pages, it appears that the conduit provided a fairly uniform 

thermal exposure for the cables inside, much like the cylindrical shroud in the penlight 

apparatus. 
41

Intermediate Test 1

Location E, Conduit

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 6

Location E, Conduit

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 7

Location E, Conduit

PVC/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

1334 s

Intermediate Test 8

Location E, Conduit

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 9

Location E, Conduit

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 10

Location E, Conduit

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 13

Location E, Conduit

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 14

Location E, Conduit

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 21. Summary of results for the cables in the conduit at Location E. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model.
42

Intermediate Test 1

Location D, Conduit

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 6

Location G, Conduit

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 22. Summary of results for cables in conduits at Location D and G. Black indicates 

the exposing temperature; red the cable. Solid lines for experiment, dotted for model. 
43

Random Fill Cable Trays 

In a few of the Intermediate Scale Tests, Trays A and C contained a random mixture of cables, a 

few of which were instrumented with a thermocouple beneath the cable jacket. Figures 22 and 

23 below show the two different configurations. The first is the composition of Tray A during 

Test 1, the second is that of Trays A and C during Tests 13 and 14. 

Figure 23. Cable tray configuration for Intermediate Test 1. 

For Test 1, the exposing temperature corresponding to the instrumented cable in the bottom row 

(TC-1) was measured by TC-2. The exposing temperature for the top row cable (TC-5) was 

measured by TC-6. TC-3 and TC-4 were not used. 

Figure 24. Cable tray configuration for Intermediate Tests 13 and 14. 

In Tests 13 and 14, both Tray A and C were filled with random cables. The instrumented cable 

in the middle of the center row (TC-1) corresponded to an exposing temperature measured below 

the bundle (TC-3). TC-4 and TC-5 were not used. 
44

Intermediate Test 1

Location A, Random Fill, Bottom Row Center

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 1

Location A, Random Fill, Top Row Center

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 13

Location A, Random Fill, Center Row

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 13

Location C, Random Fill, Center Row

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 14

Location A, Random Fill, Center Row

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 14

Location C, Random Fill, Center Row

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 25. Summary of results for trays filled with random cable. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model. The 

measured temperature at Location A in Test 13 (middle left graph) is inconsistent with that 

at Location C (middle right graph). 
45

Air Drops 

There were 5 instances during the Intermediate Scale Tests when a single or small bundle of 

cables were configured as an “air drop;” that is, the cables were not supported by a tray or 

conduit. The results are shown in Figure 26. In three cases, an instrumented bundle of cables 

was “dropped” from Tray C down to Tray A. Both trays were directly in the fire plume. In the 

other two cases, the cables were suspended wall to wall at Location E. 

Intermediate Test 4

Location A-C, Air Drop

PVC/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 5

Location A-C, Air Drop

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 6

Location A-C, Air Drop

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 11

Location E, Air Drop

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 12

Location E, Air Drop

PE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

788 s

Figure 26. Summary of results for air drop cables in the Intermediate scale tests. Black 

indicates the exposing temperature; red the cable. Solid lines for experiment, dotted for 

model. 
46

Six Cable Bundles 

A common configuration for cables within the horizontal trays is shown below. Six cables were 

arranged in a small pyramid, two thermocouples were positioned above and below the bundle to 

measure hot gas temperatures, one thermocouple was positioned between two cables in the 

bundle, and one thermocouple was inserted under the jacket of one cable (labeled E in the 

figure). Note that the letters associated with the cables within the bundle are not associated with 

the letters used to designate the various trays and conduits within the test rig. 

The results of the Intermediate Scale Tests 

involving 6 cable bundles are shown on the 

following pages. The bundles were laid in 

trays at Locations A, C, F, and G. Locations 

A, C, and F were within the fire plume, 

while G was not. 

The THIEF model was tested using the 

measured gas temperature below the bundle 

(TC-3) as the specified exposing 

temperature. The predictions of the model 

were compared with the measured 

temperature within Cable E (TC-1). Where 

available, the graphs also display the 

measured electrical failure times of Cable E from the adjacent, electrically monitored bundle. 
47

Intermediate Test 3

Location A, 6 Cable Bundle

EPR/CPE, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

348 s

Intermediate Test 4

Location A, 6 Cable Bundle

XLPO/XLPO, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 5

Location A, 6 Cable Bundle

XLPO/XLPO, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

128 s

Intermediate Test 6

Location A, 6 Cable Bundle

XLPE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 7

Location A, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

354 s

Intermediate Test 8

Location A, 6 Bundle

PVC/PVC, 12/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

103 s

Intermediate Test 9

Location A, 6 Cable Bundle

PE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

128 s

Intermediate Test 10

Location A, 6 Cable Bundle

SR/Aramid Braid, 7/C

No Electrical Failure Until Sprinklers

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Sprinklers

Activated

Figure 27. Summary of results for 6 cable bundles, Location A. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model. 
48

Intermediate Test 11

Location A, 6 Cable Bundle

XLPE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 12

Location A, 6 Cable Bundle

XLPE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 2

Location C, 6 Cable Bundle

XLPE/CSPE 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

1025 s

Intermediate Test 2

Location C, 6 Cable Bundle

XLPE/CSPE 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

1253 s

Intermediate Test 3

Location C, 6 Cable Bundle

PE/PVC 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

576 s

Intermediate Test 4

Location C, 6 Cable Bundle

EPR/CPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 5

Location C, 6 Cable Bundle

Vita-Link, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

174 s

Intermediate Test 6

Location C, 6 Cable Bundle

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 28. Summary of results for 6 cable bundles, Locations A and C. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model. 
49

Intermediate Test 7

Location C, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

355 s

Intermediate Test 8

Location C, 6 Cable Bundle

PE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

657 s

Intermediate Test 9

Location C, 6 Cable Bundle

PE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

313 s

Intermediate Test 10

Location C, 6 Cable Bundle

SR/Aramid Braid, 7/C

No Electrical Failure Until Sprinklers

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Sprinklers

Activated

Intermediate Test 11

Location C, 6 Cable Bundle

PVC/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 12

Location C, 6 Cable Bundle

PVC/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 13

Location F, 6 Cable Bundle

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 14

Location F, 6 Cable Bundle

XLPE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 29. Summary of results for 6 cable bundles, Locations C and F. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model. 
50

Intermediate Test 7

Location G, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

552 s

Intermediate Test 8

Location G, 6 Cable Bundle

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Intermediate Test 9

Location G, 6 Cable Bundle

PE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

776 s

Intermediate Test 10

Location G, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

731 s

Intermediate Test 11

Location G, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

464 s

Intermediate Test 12

Location G, 6 Cable Bundle

XLPE/PVC, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

534 s

Intermediate Test 13

Location G, 6 Cable Bundle

PE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 14

Location G, 6 Cable Bundle

XLPE/PVC, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 30. Summary of results for the 6 cable bundles, Location G. Black indicates the 

exposing temperature; red the cable. Solid lines for experiment, dotted for model. 
51

Twelve Cable Bundles 

In four instances during the Intermediate Scale Test Series, bundles of twelve cables were 

instrumented for thermal response, as shown below. Twelve cables were arranged in a small 

stack upon a ladder-backed tray, two thermocouples were positioned above and below the bundle 

to measure gas temperatures, one thermocouple was positioned between three cables in the 

bundle, and one thermocouple was inserted under the jacket of one cable (labeled A in the 

figure). Note that the letters associated with the cables within the bundle are not associated with 

the letters used to designate the various trays and conduits within the test rig. 

The results of the Intermediate Scale Tests 

involving 12 cable bundles are shown on the 

following page. The bundles were laid in 

trays at Locations A, B, and G. Location A 

was in the fire plume; Locations B and G 

were not. 

The THIEF model was tested using the 

measured gas temperature above the bundle 

(TC-2) as the specified exposing 

temperature. The predictions of the model 

were compared with the measured 

temperature within Cable A (TC-1). Where 

available, the graphs also display the 

measured electrical failure times of Cable A from the adjacent, electrically-monitored bundle. 
52

Intermediate Test 1

Location B, 12 Cable Bundle

XLPE/CSPE 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

1670 s

Intermediate Test 1

Location G, 12 Cable Bundle

XLPE/CSPE, 7/C

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

First Short

814 s

Intermediate Test 2

Location A, 12 Cable Bundle

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000 Intermediate Test 2

Location A, 12 Cable Bundle

XLPE/CSPE, 7/C

No Electrical Monitoring

Time (s)

0 600 1200 1800 2400 3000 3600

Temperature (°C)

0

200

400

600

800

1000

Figure 31. Summary of results for the 12 cable bundles. Black indicates the exposing 

temperature; red the cable. Solid lines for experiment, dotted for model. 
53

4.4 Summary of the Intermediate Scale Tests 

In all, 65 temperature predictions were compared to 65 measurements during the Intermediate 

Scale Test Series. The results are essentially 65 time histories of the predicted and measured 

inner cable temperatures. These graphs have been shown in the previous sections. To quantify 

the accuracy of the THIEF model, the same procedure that was developed for the Penlight results 

was followed. Instead of using the observed electrical failure times from the experiments, 

appropriate “threshold” values were used. The reason for this is that in the Intermediate Scale 

Test Series, some cables were monitored only for thermal response, some only for electrical 

response, and some were monitored for both using identical bundles. Consequently, it was not 

possible to draw conclusions about the THIEF model based on the measured failure times. A 

more appropriate test of the model is to compare its predictions of inner cable temperature 

directly with that which was measured for the time period between ignition of the fire and the 

point where the inner cable temperature measurements passed beyond a specified “threshold” 

value. From the Penlight series, the thermoset cables tested failed at temperatures between 

400 °C and 450 °C (752 °F and 842 °F); the thermoplastics failed between 200 °C and 300 °C 

(392 °F and 482 °F). The exact failure temperatures are not particularly important for this 

exercise, rather the time to reach some threshold temperature consistent with the particular type 

of cable under consideration. For the Intermediate Scale Tests involving thermoset cables, 

400 °C (752 °F) was chosen as the “threshold” temperature. For thermoplastics, 200 °C (392 °F) 

was chosen. 

The results are shown in Figure 32 and tabulated in Table 4. For the 65 point to point 

comparisons, the THIEF model under-predicted the times to reach the “threshold” temperature 

by 15 %, on average, and the standard deviation was 33 %. The model predictions in this case 

are noticeably less accurate than the Penlight predictions. This is by design. The THIEF model 

was designed to under-predict cable failure times because it assumes that a given cable is 

completely exposed to the elevated temperatures of the surrounding hot gases. In reality, a cable 

is almost always shielded in some way by other cables, the tray, the conduit, and so on. Often 

cables are buried deep within a loaded tray of other cables and do not respond nearly as quickly 

to hot gases as the THIEF model would predict. Indeed, the most under-predicted failure times 

for the Intermediate Scale Test Series are those of the 12 cable bundles. 

In predicting the outcomes of the Intermediate-Scale experiments, no attempt was made to 

modify or adjust the THIEF model to account for the relative position of the target cable within 

the bundle. Rather, the model was applied as it had been for the Penlight series, because that is 

the way the model is to be applied in practice. That is, it was assumed that the cable was not 

within a bundle, as there is no way to account for a bundle in the model. The reason for this 

assumption is that it is unlikely that a given cable randomly installed in a given tray will always 

be protected by its neighbors from hot gases of a fire. Thus, it is prudent to apply the THIEF 

model under the assumption that the cable will at some point along its length be directly exposed 

to the hot gases, and even if it is not, the prediction will err on the conservative side by 

predicting an early failure. Consider, for example, the points in Figure 32 labeled “6 Cable 

Bundle Inside Fire Plume.” These refer to the scenarios where bundles containing six cables 

were placed in a tray positioned at location A or C, directly above the fire and within the flaming 

region. The THIEF model under-predicted the time to reach threshold for these points to a 
54

greater extent than it did for the six cable bundles outside the fire plume because the model 

assumes that each cable within the bundle is directly exposed to the very hot gases of the fire 

plume with no accounting for the protection offered by surrounding cables. Outside the fire 

plume, the gases are less hot and gradually penetrate the bundle over longer time periods. In 

effect, outside the fire plume, there is less of a difference in temperature between the gases 

outside and inside the bundle. 

Measured Time to Threshold Temperature (s)

0 600 1200 1800 2400 3000

Predicted Time to Threshold Temperature (s)

0

600

1200

1800

2400

3000

Single Cable in Tray

Random Fill in Tray

6 Cable Bundle Outside Fire Plume

12 Cable Bundle in Tray

3 Cable Bundle in Conduit

Air Drop Cable(s)

6 Cable Bundle Inside Fire Plume 

μ−33%

μ=−15%

μ+33%

Figure 32. Summary of the Intermediate Scale Test predictions. The dashed lines indicate 

the average (-15 %) and standard deviation (33 %) of the data. Also note that the 

description “Inside Fire Plume” refers to locations A and C, which were within the flaming 

region of the fire. 
55

Table 4. Results of the Intermediate Scale THIEF Model Predictions. See Nowlen and 

Wyant (2007b) for details about each configuration. 

Test 

Location 

Figure 

17 

Cable 

Configuration 

Cable 

Composition 

(Insulation/Jacket)

Threshold 

Temperature

(°C) 

Measured 

Time to 

Threshold 

(s) 

Predicted

Time to 

Threshold 

(s) 

1 A Random Fill XLPE/CSPE 400 390 140 

1 A Random Fill XLPE/CSPE 400 380 720 

1 B 12 Bundle XLPE/CSPE 400 2710 2117 

1 D 3+1 Conduit XLPE/CSPE 400 2070 1824 

1 E 3+1 Conduit XLPE/CSPE 400 2490 2200 

1 G 12 Bundle XLPE/CSPE 400 2406 1355 

2 A 12 Bundle XLPE/CSPE 400 1644 336 

2 A 12 Bundle XLPE/CSPE 400 984 306 

2 C 6 Bundle XLPE/CSPE 400 792 402 

2 C 6 Bundle XLPE/CSPE 400 689 390 

2 E Single PVC/PVC 200 540 540 

2 G Single PVC/PVC 200 600 564 

3 A 6 Bundle EPR/CPE 400 252 126 

3 C 6 Bundle PE/PVC 200 185 72 

3 E Single PVC/PVC 200 474 528 

3 G Single PVC/PVC 200 384 504 

4 A 6 Bundle XLPO/XLPO 400 252 138 

4 C 6 Bundle EPR/CPE 400 185 126 

4 A-C Air Drop PVC/PVC 200 162 180 

4 E Single XLPE/CSPE 400 -- -- 

4 G Single XLPE/CSPE 400 -- -- 

5 A 6 Bundle XLPO/XLPO 400 180 126 

5 C 6 Bundle Vitalink 400 527 192 

5 A-C Air Drop XLPE/CSPE 400 414 228 

5 E Single EPR/CPE 400 1350 1700 

5 G Single EPR/CPE 400 1500 1500 

6 A 6 Bundle XLPE/PVC 400 138 228 

6 C 6 Bundle PE/PVC 200 144 72 

6 A-C Air Drop PE/PVC 200 138 210 

6 E 3 Conduit PE/PVC 200 1098 1098 

6 G 3 Conduit PE/PVC 200 1260 1260 

7 A 6 Bundle XLPE/PVC 400 180 162 

7 C 6 Bundle XLPE/PVC 400 311 192 

7 E 3+1 Conduit PVC/PVC 200 1356 1272 

7 G 6 Bundle XLPE/PVC 400 1100 900 

8 A 6 Bundle PVC/PVC 200 102 90 

8 C 6 Bundle PE/PVC 200 378 228 
56

Test 

Location 

Figure 

17 

Cable 

Configuration 

Cable 

Composition 

(Insulation/Jacket)

Threshold 

Temperature

(°C) 

Measured 

Time to 

Threshold 

(s) 

Predicted

Time to 

Threshold 

(s) 

8 E 3+1 Conduit XLPE/CSPE 400 2328 2190 

8 G 6 Bundle PE/PVC 200 1722 1566 

9 A 6 Bundle PE/PVC 200 72 72 

9 C 6 Bundle PE/PVC 200 84 84 

9 E 3+1 Conduit XLPE/CSPE 400 2094 1956 

9 G 6 Bundle PE/PVC 200 924 768 

10 A 6 Bundle SR/Aramid 400 156 126 

10 C 6 Bundle SR/Aramid 400 210 156 

10 E 3+1 Conduit PE/PVC 200 1206 1080 

10 G 6 Bundle XLPE/PVC 400 678 690 

11 A 6 Bundle XLPE/PVC 400 312 120 

11 C 6 Bundle PVC/PVC 200 72 72 

11 E 3+1 Air Drop PE/PVC 200 552 696 

11 G 6 Bundle XLPE/PVC 400 1020 804 

12 A 6 Bundle XLPE/PVC 400 228 132 

12 C 6 Bundle PVC/PVC 200 84 84 

12 E 3+1 Air Drop PE/PVC 200 612 732 

12 G 6 Bundle XLPE/PVC 400 936 810 

13 A Random Fill XLPE/CSPE 400 1278 198 

13 C Random Fill XLPE/CSPE 400 840 642 

13 E 3+1 Conduit XLPE/CSPE 400 1660 1590 

13 F 6 Bundle PE/PVC 200 690 640 

13 G 6 Bundle PE/PVC 200 1300 1160 

14 A Random Fill XLPE/CSPE 400 90 108 

14 C Random Fill XLPE/CSPE 400 180 162 

14 E 3+1 Conduit PE/PVC 200 1130 970 

14 F 6 Bundle XLPE/PVC 400 546 360 

14 G 6 Bundle XLPE/PVC 400 1362 1690 
57

5. LESSONS LEARNED FROM CAROLFIRE 

Both the Penlight and Intermediate scale experiments and simulations discussed in the previous 

sections raise several issues that affect the practical implementation of the THIEF algorithm into 

a fire model. 

5.1 Characterizing the thermal environment 

The boundary condition for the THIEF model is the net heat flux to the cable surface. If the 

cable or cables are within a hot, smoky gas layer, then the heat flux can be calculated in terms of 

the surrounding gas temperature, Tg : 

( ) ( ) q = Tg − Ts + h Tg − Ts ′′ 4 4 & εσ (5.1) 

The gas temperature is computed by the fire model, and is usually a function of time. The 

convective heat transfer coefficient, h, is usually assumed to be constant, except in 

computational fluid dynamics models, where it can be calculated based on local flow conditions. 

 The cable surface temperature, Ts , is computed within the THIEF algorithm. 

If the cable or cables are directly exposed to the fire, Eq. (5.1) does not apply, as then the heat 

flux is not simply a function of the surrounding gas temperature. Different types of fire models 

treat this situation differently, but regardless, the net heat flux to the cable is: 

4

q qinc σTs &′′ = ε & − ε (5.2) 

where the subscript “inc” refers to the incident heat flux. A point source radiation model, for 

example, calculates the incident heat flux, from which the net heat flux can be obtained by 

subtracting off the re-radiated component. 

5.2 Specifying a “failure temperature” 

The THIEF model only predicts the interior temperature of a cable. It is assumed by the user 

that the cable fails at some experimentally determined temperature. For most of the cables tested 

in the CAROLFIRE program, electrical failure correlated fairly well to interior temperature, with 

thermoplastic cables failing at temperatures between 200 °C and 250 °C (392 °F and 482 °F); 

and thermosets failing between 400 °C and 450 °C (752 °F to 842 °F) (Nowlen and Wyant 

2007b). However, there were several cables tested that did not fail at these temperatures. In 

fact, several cables ignited and burned, but did not fail electrically until water was applied. 

5.3 Defining the cable within the fire model 

THIEF is only a target model, like the activation model of a sprinkler or smoke detector. It 

requires that the fire model in which it is embedded as a subroutine provide it only with a heat 

flux as input and it only outputs a “failure time” – it does not affect the overall thermal 
58

environment unless it is explicitly included in the fire model as an object that drains energy from 

the surrounding gases, like a wall or larger obstruction. Most simple fire models do not explicitly 

include targets as objects that can affect the overall thermal environment. In fact, the THIEF 

calculation could be performed separately as part of the post-processing phase. 

5.4 Modeling cable burning 

It was noted by Nowlen and Wyant (2007b) during the CAROLFIRE experiments that cable 

ignition often occurred just after electrical failure. It was speculated that the short circuit acts 

like a pilot to ignite flammable vapors that off-gas as the cables heat up. The THIEF model can 

predict the temperature rise within the cable to a level of accuracy that has been demonstrated in 

the previous two sections. However, the model cannot predict ignition and burning. This is not 

to say that the fire model within which THIEF is implemented cannot predict ignition and 

burning; but this depends on the type of model. For example, empirical correlations, like those 

described in NUREG-1805 (Iqbal and Salley 2004), use experimentally obtained ignition 

temperatures and burning rates to estimate the heat release and spread rates of various types of 

cables. More detailed fire models can predict, to some degree, ignition and burning, but these 

models require far more thermo-physical property data than does THIEF, and this still remains a 

critical hurdle in developing this functionality in the models. 
59

6 CONCLUSION 

A thermally-induced electrical failure (THIEF) model for cables has been shown to work 

effectively in realistic fire environments. The THIEF model is essentially nothing more than the 

numerical solution of the one-dimensional heat conduction equation within a homogenous 

cylinder with fixed, temperature-independent properties. The model was used to predict the 

inner cable temperature of 100 instrumented cables from the CAROLFIRE Penlight (35 single 

cable experiments; 66 point to point comparisons) and Intermediate Scale Test Series (14 

experiments; 65 point to point comparisons). Because the Penlight experiments tested single 

cables that were heated uniformly on all sides, the one-dimensional THIEF model accurately 

predicted the times for the temperature inside the cable jacket to reach “threshold” values that 

are typically observed when the cable fails electrically. For 66 measurements, the model underpredicted the time to reach threshold temperature by 3 %, on average. In the Intermediate Scale 

experiments, where the cable configurations were more typical of actual installations, the model 

under-predicted the times to reach threshold temperature by 15 %, on average. This latter result 

is realistically conservative – the THIEF model does not account for the shielding effects of 

cable bundles, and thus over-predicts cable temperatures and under-predicts “failure” times. 

The cables included in the study ranged from 7 mm (0.25 in) to 19 mm (0.75 in) in diameter, a 

common size for control cables, plus some instrument and low power cables. The copper 

content by volume ranged from 0.07 to 0.36 and the content by mass ranged from 0.31 to 0.89. 

The volume and mass fractions are not direct model inputs, but rather the average density of the 

cable as a whole. Nevertheless, the range in cable properties demonstrates that the THIEF model 

is applicable to a wide variety of cables with no need for additional information beyond the cable 

diameter, mass per length, and an empirical “failure” temperature. In addition, there was no 

indication from the model results that indicated a bias related to the number of conductors, 

plastic composition, or copper content. 

While there are various ways to refine the THIEF model – multiple layers of materials, two or 

three spatial dimensions, temperature dependent thermal properties, polymeric decomposition, 

and so on – it is unlikely that any of these enhancements would dramatically improve its overall 

accuracy, especially in light of the uncertainty associated with the fire simulation of the entire 

compartment. According to a recent NRC/EPRI verification and validation (V&V) study of five 

different fire models (NUREG-1824/EPRI 1011999), the error in the predicted net convective 

and radiative heat transfer to various “targets” is on the order of 20 % or higher, depending on 

the type of model. Given an uncertainty of 20 % in the exposing heat flux for the simple cable 

failure calculation, it is unclear how additional complexity would generate better results than 

those presented in this report. 
61

7 REFERENCES 

1. Andersson, P. and P. Van Hees (2005) “Performance of Cables Subjected to Elevated 

Temperatures,” Fire Safety Science – Proceedings of the Eighth International 

Symposium, International Association for Fire Safety Science. 

2. Chourio, G. (2007). Probabilistic Models to Estimate Fire-Induced Cable Damage in 

Nuclear Power Plants, Ph.D. Thesis, University of Maryland, College Park. 

3. Hamins, A, A. Maranghides, R. Johnsson, M. Donnelly, J. Yang, G. Mulholland and R.L. 

Anleitner (2006). Report of Experimental Results for the International Fire Model 

Benchmarking and Validation Exercise #3, NIST Special Publication 1013-1, National 

Institute of Standards and Technology, Gaithersburg, Maryland (Also published by the 

US Nuclear Regulatory Commission as 

NUREG/CR-6905). 

4. Incropera, F.P. and D.P. DeWitt (1990). Fundamentals of Mass and Heat Transfer, 

(3rd ed.), John Wiley & Sons, New York. 

5. Iqbal, N. and M. Salley (2004). Fire Dynamics Tools, NUREG-1805, U.S. Nuclear 

Regulatory Commission, Washington, DC. 

6. McGrattan, K.B, S. Hostikka, J.E. Floyd, H.R. Baum and R.G. Rehm (2007). Fire 

Dynamics Simulator (Version 5) Technical Reference Guide, NIST Special Publication 

1018-5, National Institute of Standards and Technology, Gaithersburg, Maryland. 

7. Nowlen, S.P. and Wyant, F.J. (2007a). CAROLFIRE Test Report Volume 1: General Test 

Descriptions and the Analysis of Circuit Response Data, NUREG/CR-6931/V1, US 

Nuclear Regulatory Commission, Washington, DC.

8. Nowlen, S.P. and Wyant, F.J. (2007b). CAROLFIRE Test Report Volume 2: Cable Fire 

Response Data for Fire Model Improvement, NUREG/CR-6931/V2, US Nuclear 

Regulatory Commission, Washington, DC.

9. U.S. NRC (1975). “Cable Fire at Browns Ferry Nuclear Power Station,” NRC Bulletin 

BL-75-04, U.S. Nuclear Regulatory Commission, Washington, DC, March. 

10. U.S. NRC and EPRI (2007). Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, NUREG-1824, U.S. Nuclear Regulatory 

Commission, Rockville, Maryland. 

11. Weast, R.C. (ed.). (1982) CRC Handbook of Chemistry and Physics, CRC Press, Inc., 

Boca Raton, Florida.
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 

(9-2004) 

NRCMD3.7

BIBLIOGRAPHIC DATA SHEET 

 (See instructions on the reverse) 

1. REPORT NUMBER 

(Assigned by NRC, Add Vol., Supp., Rev., 

 and Addendum Numbers, if anv.) 

NUREG/CR-6931, Vol. 3 

3. DATE REPORT PUBLISHED 

April 2008 

 

2. TITLE AND SUBTITLE 

Cable Response to Live Fire (CAROLFIRE), Volume 3: Thermally-Induced Electrical 

Failure (THIEF) Model

4. FIN OR GRANT NUMBER 

N6414

6. TYPE OF REPORT 

Technical

5. AUTHOR(S) 

Kevin McGrattan

7. PERIOD COVERED (Inclusive Dates) 

 

8. PERFORMING ORGANIZATION – NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address: if contractor, provide 

name and mailing address.) 

National Institute of Standards and Technology 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8663

9. SPONSORING ORGANIZATION – NAME AND ADDRESS (If NRC, type “Same as above”, if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, and 

mailing address.) 

Division of Risk Analysis 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

10. SUPPLEMENTARY NOTES

J. Dreisbach, NRC Project Manager

11. ABSTRACT (200 words or less) 

This report describes a thermally-induced electrical failure (THIEF) model’s ability to predict the behavior of power, 

instrument, and control cables during a fire. The model is intended to be incorporated as a subroutine for 

deterministic fire models, and it is of comparable accuracy and simplicity to the activation algorithms for various 

other fire protection devices (e.g., sprinklers, heat and smoke detectors). THIEF model predictions are compared to 

experimental measurements of instrumented cables in a variety of configurations, and the results indicate that the 

model is an appropriate analysis tool for nuclear power plant applications. This work was performed as part of the 

CAROLFIRE (Cable Response to Live Fire) program sponsored by the U.S. Nuclear Regulatory Commission. The 

experiments for CAROLFIRE were conducted at Sandia National Laboratories, Albuquerque, New Mexico. Details 

of the CAROLFIRE experimental program are contained in Volumes 1 and 2 of this three-volume series. 

13. AVAILABILITY STATEMENT 

unlimited 

14. SECURITY CLASSIFICATION 

(This page) 

unclassified 

(This report) 

unclassified

15. NUMBER OF PAGES 

 

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.) 

Fire Modeling 

Risk-Informed

16. PRICE 

 

NRC FORM 335 (9-2004)