Numerical Analysis for a Fire-related Spalling Failure Model of High-strength Concrete

*Kota Akashi1), Mitsuo Ozawa2), Kentaro Fujimoto3) and Sirjana Subedi Parajuli4)

1), 2), 3), 4) Department of Civil Engineering, Gunma University,

1-5-1. Kiryu, Gunma, Japan 2) ozawa@gunma-u.ac.jp

ABSTRACT

This paper reports on numerical analysis of explosive spalling of high-strength

concrete exposed to high-temperature conditions. In the study, ring restraint testing was performed in association with an axial symmetry model using the finite element method. The experiment was performed to support estimation of thermal stress from strain in a restraining steel ring in restrained concrete under the conditions of a RABT 30 rapid heating curve. Thermal stress calculation was based on the thin-walled cylinder model theory whereas the used spalling failure model was based on a tensile strain failure model. The results indicated that such modeling enables estimation of the point at which spalling initiates during heating and the consequent spalling depth. 1. INTRODUCTION

High-strength concrete (HSC) is widely used in building construction. Fire poses a serious risk to concrete buildings and structures because it often results in explosive spalling of HSC. There are two mechanisms by which concrete can be damaged by fire. The first is restrained thermal dilation resulting in biaxial compressive stress states parallel to the heated surface, which leads to tensile stress in the perpendicular direction (Fig. 1) (Ulm F. J. et al., 1999). The second is the build-up of concrete pore pressure due to vaporization of physically/chemically bound water resulting in tensile loading on the microstructure of the heated concrete (Fig. 2) (Anderberg Y., 1997). Polypropylene fibers are often added to HSC as an effective measure to prevent explosive spalling (Kalifa P. et al., 2000; Phan L. T., 2000). Tanibe et al. reported that a method involving the restraint of concrete with steel rings in heat testing can be used to clarify characteristics of thermal stress and explosive spalling behavior (Tanibe.T et al.,

1), 4)

Graduate student 2)

Associate professor

2014). The study reported here was performed to support estimation of thermal stress from the strain in a restraining steel ring and vapor pressure in restrained concrete under the conditions of a RABT 30 rapid heating curve. Thermal stress calculation was based on the cylindrical shell model theory (Timoshenko S. et al., 1959). Other papers (e.g.,Majorana.C.E. et al., 2010; Michel B. et al., 2015) have also reported on numerical simulation of concrete spalling during exposure to fire.

This paper reports on numerical analysis of explosive spalling of high-strength concrete exposed to high-temperature conditions. The analysis was based on ring restraint testing using an axial symmetry model with the finite element method. A spalling failure model based on a tensile strain failure model is also proposed.

2. MODEL FOR ESTIMATION OF THERMAL STRESS AND TENSILE STRAIN FAILURE

Figure 3 shows the method used to estimate thermal stress. First, specimens created using concrete with restrained steel rings were subjected to heat testing with the target measurements of internal concrete temperature, steel ring temperature, steel ring strain, vapor pressure inside the concrete, spalling time and spalling depth. Internal concrete deformation due to thermal expansion and vapor pressure caused by heating were restrained by the steel rings, and compressive stress was induced. Although such test setups have previously enabled qualitative evaluation, no simple procedure to routinely quantify the characteristics of materials under restrained expansion has been established. In this study, an instrumented ring setup was used to quantify the behavior of concrete under such expansion during heating. Thermal stress calculation was based on the thin-walled cylinder model theory (Timoshenko S. et al., 1959) as shown by Eqs. (1) and (2). Vapor pressure was measured at 5,10 25 and 40 mm from the heated surface.

vapthre σ (1)

R

tEεσ sθre (2)

Fig. 1 Thermal Stress Fig. 2 Vapor Pressure Fig. 3 Estimation of thermal stress

Figure 4 shows a tensile strain failure model of explosive spalling under thermal stress. Strain at a certain depth from the heated surface was calculated using Eqs. (3) and (4), and the index of the strain failure model was given by Eq. (5). Tensile strain failure occurred when the index of the strain failure model exceeded 1.0 (Iu > 1.0).

,, cyxyxre Eεσ (3)

2 , cyxz νεε (4)

ftzuI (5)

where, σre : restrained stress σth : thermal stress σ vap : vapor pressure t : steel ring thickness εθ

: steel ring circumferential- direction strain

Es : steel ring elastic modulus

R : steel ring radius νc : apparent Poisson's ratio of concrete

Ec : elastic modulus of concrete εz : strain at a certain depth from the heated

surface

σx､y : stress in the x or y direction εx,y :: strain in the x or y direction

εt-f : ultimate strain upon tensile failure

Iu : index of the strain failure model Iu > 1 Tensile strain upon failure

Fig. 4 Tensile strain failure model of explosive spalling

3. FIRE TESTING OF RING-RESTRAINED SPECIMENS 3.1 Experimental outline

High-strength concrete with a compressive strength of 90 MPa and a water content ratio of 4.5% was used in the study, and fire testing was performed over a period of two months. Figure 5 shows the configuration and dimensions of the two experimental specimens with a pair of steel rings each (diameter: 300 mm; thickness: 8 mm; length: 50 mm; Ec (elastic modulus): 210 GPa; Fy (yield strength): 295 MPa). Four strain gauges and four thermo-couples were attached 5, 10, 25 and 40 mm from the heated surface and the outer surface of the steel rings. Stainless steel pipes (inner diameter: 2 mm; length: 200 mm) were placed in the concrete 5, 10, 25 and 40 mm from and parallel to the heated surface. Four type-K thermocouples were placed in the central zone of the specimens 5, 10, 25 and 40 mm from the heated surface. The heating tests were based on a RABT 30 heating curve (Fig. 6). Strain gauges and thermocouples were attached 5, 10, 25 and 40 mm from the heated surface and the outer surface of the steel ring.

3.2 Experimental results

Figure 7 shows internal temperatures of the specimen at 5, 10, 25 and 40 mm from the heated surface. Explosive spalling was seen between four and twelve minutes of heating time. The values measured at points 5 and 10 mm from the heated surface were 350 and 150°C, respectively, at five minutes, and the depth of spalling was up to 10 mm from the heated surface at this time.

Figure 8 shows the results of restrained thermal stress calculation based on ring strain at 5, 10, 25 and 40 mm from the heated surface. After 10 minutes of heating, thermal stress levels reached 9 MPa at 5 mm.

Figure 9 shows a time history of vapor pressure at points 5, 10, 25 and 40 mm from the heated surface at ten minutes. The value began to increase at 100°C and reached

Fig. 5 Fire testing of steel ring specimen Fig. 6 RABT 30 heating curve

0.4 MPa at a point 5 mm from the heated surface at 2.7 minutes, then reached 6 MPa at a point 10 mm from the heated surface at 6 minutes. When explosive spalling occurred, vapor pressure had built to 4.5 and 6 MPa at points 5 and 10 mm from the heated surface, respectively.

Figure 10 shows depths of spalling after the heating test. The maximum value was about 60 mm, and the depth at the center part was greater than that at the outer part. The specimens were severely damaged.

Figure 11 shows the relationship between spalling depth and time during the heating test. Spalling began approximately 3 minutes after heating began and ended at 12 minutes at a depth of 50 mm.

0 5 10 150

200

400

600

800

1000

1200

Tem

per

ature

(℃)

Heating time　(min)

：5mm：10mm：25mm：40mm

0 5 10 150

2

4

6

8

10

Heating time　(min)

Rest

rain

ed s

tres

s　(M

Pa)

：5mm：10mm：25mm：40mm

0 5 10 150

2

4

6

8

Heating time　(min)

Vap

ou

r p

ress

ure

(M

Pa) ：5mm

：10mm：25mm：40mm

Fig. 9 Vapor pressure and heating time Fig. 10 Spalling after heating test

Fig. 7 Temperature and heating time Fig. 8 Thermal stress and heating time

4. NUMERICAL SIMULATION OF FIRE-RELATED SPALLING 4.1 Outline of FEM analysis

Figure 12 shows fire spalling analysis of the specimen containing a restraining ring of radius 150 mm, height 100 mm and thickness 8 mm. An axial symmetry model was used in conjunction with the finite element method. ASTEA-MACS analysis code was used for thermal and stress analysis, and the bottom of the steel ring was insulated. The bottom and open part of the specimen was heated, with a RABT 30 heating curve adopted for the bottom (Fig. 6). The heat transfer coefficient of the bottom part of the concrete was 30 W/m2°C, and the corresponding figures for the steel ring and the upper part of the concrete were 10 and 12 W/m2°C, respectively. Figures 13 to 14 show how the thermal conductivity of concrete and steel depend on temperature, Figure 15 shows specific heat and related temperature, and Figures 16 to 20 show the residual compressive strength, elastic modulus and tensile strength and temperature of the concrete and steel ring, respectively.

4.2 Spalling model criteria

The index of the strain failure model Iu as shown in Equation (5) was used in this study. It is assumed that tensile strain failure and concrete spalling occur when Iu exceeds the value of 1.0. The apparent Poisson’s ratio is 0.2, and the ultimate strain upon tensile failure is 500 μ.

0 5 10 150

10

20

30

40

50

Heating time (min)

Sp

alli

ng

dep

th

(mm

)

Fig. 11 Spalling depth and heating time

Fig. 12 Axial symmetry model Fig. 13 Thermal conductivity (concrete)

0 500 10000

1

2

Th

erm

al

co

nd

ucti

vit

y (

W/m℃

)

Temperature (℃)

0 200 400 600 800 10001

1.2

1.4

1.6

1.8

2[10

5]

Temperature (℃)Ela

stic

Mo

du

lus

of

Ste

el

(MP

a)

0 200 400 600 800 10000

100

200

300

Temperature (℃)

Com

pre

ssiv

e st

rength

(M

Pa)

Concrete

Steel

Fig. 14 Thermal conductivity (steel) Fig. 15 Specific heat (concrete and steel)

Fig. 16 Residual elastic modulus of steel Fig. 17 Residual elastic modulus of concrete

Fig. 18 Residual compressive strength (concrete and steel )

Fig. 19 Residual tensile strength of concrete

0 500 10000

10

20

30

40

50

60

Th

erm

al

co

nd

ucti

vit

y (

W/m℃

)

Temperature (℃) 0 500 10000

1

2

Spec

ific

hea

t (k

J/kg℃

)

Temperature　(℃)

:Concrete:Steel

0 200 400 600 800 10000

10000

20000

30000

40000

50000

Temperature (℃)

Ela

stic

Mo

du

lus

of

Ste

el

(MP

a)

0 200 400 600 800 10000

1

2

3

4

5

6

Temperature (℃)

Tensi

le s

trength

(M

Pa)

Concrete

0

50

10

0

高さ

(mm

)

0 142 径(mm)

4.3 Results and discussion

Figure 21 shows temperatures during heating as determined from analysis. The values at 10 and 25 mm are similar to the measured temperatures. The measurement values at 10 mm exhibit a significant change at 5 minutes, when spalling was observed. The temperature determined from analysis at 25 mm was similar to the measured value. Figure 22 shows a comparison of experimental and analytical spalling depths. It can be seen that the maximum estimated value was around 50 mm at 12 minutes. These outcomes clearly indicate that the proposed model can be used to analyze spalling depth up to 12 minutes from the start of heating. In this study, the application of 500 μ as the ultimate strain upon tensile failure produced favorable results in spalling depth calculation up to 12 min.

Figure 23 shows temperature development contour representation and spalling depth at 3, 8 and 12 min. No spalling had occurred after 3 min. of heating, but was observed at 8 and 12 min. with depths of 25 and 50 mm, respectively.

These outcomes clearly demonstrate the effectiveness of the proposed model, especially for spalling depth estimation up to 12 min.

0 5 10 150

10

20

30

40

50

60

Heating time (min.)

Sp

alli

ng d

epth

(m

m) ：Ana.

：Meas.

Fig. 20 Residual tensile strength of steel Fig. 21 Internal temperature (Meas. vs. Ana.)

Fig. 22 Spalling depth and time (Meas. Vs. Ana.)

Fig. 23 a) Temperature contour and spalling after 3 min of heating

0 200 400 600 800 10000

100

200

300

Temperature (℃)

Tensi

le s

trength

(M

Pa)

Steel

0 2 4 6 8 100

100

200

300

400

500

Heating time (min.)

Inte

rnal

tem

per

atu

re (℃

)

Ana.：10mm：25mm

Meas.：10mm：25mm

5. CONCLUSIONS

In this study, numerical analysis of explosive spalling in high-strength concrete exposed to high-temperature conditions was performed in ring restraint testing using an axial symmetry model with the finite element method. The following conclusions were drawn: 1) Analysis temperatures were similar to measured temperatures. 2) The maximum estimated spalling depth was around 50 mm at 12 minutes. The

results indicate that the proposed model can be used to analyze spalling depth up to 12 minutes from the start of heating.

3) Adoption of a value of 500 µ for the ultimate strain upon tensile failure produced favorable results for spalling depth calculation up to 12 min.

4) The experimental outcomes clearly show the viability of the proposed model, especially for spalling depth estimation up to 12 min. In future work, a spalling model allowing consideration of vapor pressure and heat

from concrete-related vaporization will be developed. Acknowledgement

This study was financially supported by the East Nippon Expressway Company Limited (NEXCO East) and by a Grant-in Aid for Scientific Research C (General) from the Japan Society for the Promotion of Science (No. 25420459; head: Dr. M. Ozawa). The authors would like to express their gratitude to these organizations for their financial support. REFERENCES Ulm F. J. et al. (1999), “The Chunnel Fire. II Analysis of concrete damage,” Journal of

Engineering Mechanics. 125, 283-289 Anderberg Y.(1997), “Spalling phenomena in HPC and OC,” Proceedings of the

0

50

10

0

高さ

(mm

)

0 142 径(mm)

25 mm 50mm

Fig. 23 b) Temperature contour and spalling depth after 8 min. of heating

Fig. 23 c) Temperature contour and spalling depth after 12 min. of heating

International Workshop on Fire Performance of High-Strength Concrete, Phan, L. T., Carino, N. J., Duthinh, D., Garboczi, E. (eds.), Gaithersburg, MD: NIST, 69-73

Kalifa P. et al. (2000), “Spalling and pore pressure in HPC at high temperatures,” Cement and Concrete Research, 30,1915-1927

Phan L. T.(2000), “Pore pressure and explosive spalling in concrete,” Materials and Structures, 41, 1623-1632

Tanibe.T. et al.(2014), “Steel Ring-based Restraint of HSC Explosive Spalling in High-temperature Environments,” Journal of Structural Fire Engineering, Volume 5, Number 3, 239-250

Timoshenko S. et al.(1959), “Theory of Plates and Shells,” second edition, McGraw-Hill Book Company

C. E. Majorana et al.(2010), “An approach for modelling concrete spalling in finite strains,” Mathematics and Computers in Simulation 80,1694–1712

Michel B. et al. (2015), “Hygro-thermo-mechanical analysis of spalling in concrete walls at high temperatures as a moving boundary problem,” International Journal of Heat Mass transfer 85,110-134