University of Colorado, Boulder

Behavior of Concrete Cylinder under Elevated Temperature

Focused on Surface Spalling

Keun Lee

1. Introduction

The performance of concrete cylinder is examined in order to illustrate the effect of high

temperature gradients and cover spalling. The specific problem is a concrete cylinder

subjected to a fire scenario in the interior. In actual structures the temperature

distribution and corresponding local values generally evolve at a fast pace, which means

that concrete behavior is affected by a number of structural parameters. However, in

laboratory tests it is hardly possible to recreate realistic fire scenarios, and it is also

meaningless, since material characterization has to be focused on the constitutive

behavior, which requires all possible structural effects to be removed. As a result,

laboratory testing generally relies on quasi steady thermal conditions, which lead to an

over-evaluation of bearing capacity of a given structural member, because such

phenomena as cover sapling and thermal gradients are ignored. The cover spalling of

the model is simulated using the failure analysis capabilities of Merlin that has been

developed since 1996 by Saouma.

2. Spalling of Concrete Structures

Spalling means the break off of layers or pieces of concrete from the surface of a

structural element. The spalling of normal concrete occurs due to rapid temperature

increase - typically 20˚C/min (Khoury, 2000). High strength concrete (HSC) has a

significantly higher potential for explosive spalling than normal strength concrete

(NSC) due to its low permeability. Explosive spalling of HSC may occur even at

relatively low heating rate - less than 5˚C/min (Phan, 2002). However, spalling occurs

only in narrow regions of the concrete specimen, which has been observed by many

researchers. There has been no explanation as to why spalling does not occur in all

specimens. Many researchers have been arguing about what is the main cause of

explosive spalling.

Spalling of concrete can be classified into four categories. They are aggregate spalling,

surface spalling, explosive spalling as violent breaking and corner spalling as non-

violent breaking. The main factor responsible for the first three types is the heating rate,

while the fourth type is influenced more by the maximum temperature. The following

table summarizes the natures and the main influential factors for concrete spalling. The

main factors are heating rate, permeability of concrete, moisture content, presence of

reinforcement and level of external applied load.

Table 2.1. Factors influencing spalling of concrete (Khoury, 2000)

In order to prevent the occurrence of concrete spalling, it is very important to

understand what happens in concrete that causes spalling, that is, to understand the

fundamental mechanisms that cause concrete spalling. There are several theories

explaining the spalling mechanisms, which may be classified in three categories: (a)

pore pressure spalling, (b) thermal stress spalling, and (c) combined pore pressure and

thermal stress spalling.

a. Pore pressure spalling

Fig. 2.1 shows the mechanism of pore pressure spalling. High temperature causes the

evaporation of free water near the concrete surface. The high vapor pressure in the

surface layer drives the water vapor to diffuse in two opposite directions: to the surface

and into the deeper part of the concrete specimen. With a sharp temperature increase at

the concrete surface (under rapid heating), the interior temperature of concrete remains

low. When the free water evaporates the vapor diffuses into the interior part of the

concrete (cooler part), where it condensates. The condensation of vapor increases the

moisture content of the concrete in that layer and thus reduces the permeability of the

concrete, which results in the formation of a barrier in the interior, the so-called

moisture clog (see Figs. 2.1(b) and 2.1(c)). The interior water vapor is blocked by the

clog, and the vapor pressure starts to build up rapidly. As soon as the pressure exceeds

the tensile strength, then spalling takes place. Fig. 2.2 shows the conceptual distribution

of temperature, pore pressure and moisture in a massive concrete section heated at the

unsealed surface on the right side.

Figure 2.1 Mechanism of pore pressure spalling (Schneider and Horvath, 2002)

Figure 2.2 Gradients of temperature, pore pressure and moisture in a massive concrete

section heated at the unsealed left-hand surface (Khoury,2000)

In this process, the sharp temperature reduction (high temperature gradient) from the

surface plays an important role, and the high gradient occurs only under very rapid

heating of massive concrete components. This is why fast heating is a necessary

condition for the spalling. Another necessary condition is low permeability of concrete

and the size of the concrete structure, otherwise the vapor would readily escape to the

surface and there would be no pressure build-up. On the other hand, high temperature

causes the dehydration of chemically bonded water in the cement paste, which

contributes to the high pore pressure and spalling. This is why spalling takes place in the

HPC concretes with low moisture content. This also explains that high initial water

content in concrete is not a necessary condition for spalling.

b. Thermal stress spalling

This mechanism is the result of thermo-mechanical coupling, in which the temperature

gradient upon rapid heating causes severe thermal stress gradients in the concrete

component. In the high temperature zone (on the surface) concrete expands more than in

the low temperature zone (the interior part). As a self-equilibrating thermal stress state

develops, a thin layer near the surface is in compression while the interior part is in

tension. Because of the high temperature gradient, the compressive stress in the thin

surface layer can be very high, which causes buckling and delamination of the outer

layer, observed in the form of spalling. Therefore, the main factor of thermal stress

spalling is the excessive thermal stress generated by rapid heating of massive concrete

components and structures.

c. Combined pore pressure and thermal stress spalling

In most cases, a combination of the two mechanisms takes place. Fig 2.3 shows forces

acting in heated concrete. Explosive spalling generally occurs under the combined effect

of pore pressure, and compression in the exposed surface region induced by thermal

stress and external loading and internal cracking. Consequently the pore pressure needs

to be considered together with both the thermal and the load-induced stresses before the

occurrence of explosive spalling. Fig. 2.4 show the experimental setup for testing

concrete spalling and the fractured concrete specimens at NIST.

Figure 2.3 Forces acting in heated concrete (Zhukov, 1975)

Figure 2.4 Test set up, Pore pressure specimen, and Specimen failure (Phan, 2002)

Figure. 2.5 show the experimental results for testing of high strength concrete spalling

in the specific range temperature without mechanical loading and remnants of exploded

cylinder is shown in Figure.2.4 (NIST)

Figure 2.5 Core temperature and time ranges of observed explosive spalling

Figure 2.6 Remnants of an exploded cylinder and rendering of the fracture formation

3. Surface Spalling under Thermal Stress for unstressd state –

Overview

The numerical simulation is performed for surface spalling under high temperature

without mechanical loading. So, the overall review of surface spalling is considered

here. Tendency for surface spalling is increased by followings :

- High moisture content

- Dense concrete (HPC)

- Compressive stress from external load and prestress

- Rapid temperature rise

- Considerable unsymmetrical temperature distribution

- Cross-section with thin sections

- High reinforcement concentration

Heating of concrete is characterized by a steep thermal gradient when exposed to fire

due to the low conductivity and high heat capacity. This renders thermal stresses which

generally are two- or three- dimensional. Consequently tensile stresses arise which can

reach the tensile strength. These tensile stresses can sometimes alone or in superposition

of pore pressure in one direction cause spalling. When the thermal compressive stresses

in the hot outer layer are developed and meet each other in a coner tensile stresses

appear. If this tensile stress reach the tensile strength the triangular coner piece can spall

off as indicated in the Figure 3.1. The same problem occurs for a heated convex surface

where radial tensile stresses develops

(a) (b)

Figure 3.1 Thermal stress at a a) corner and b) convex surface

4. Transient Heat Analysis

First, the transient heat analysis is performed for temperature gradient effect in order to

apply to mechanical analysis sequentially. The thermal properties are in Figure. 4.1 and

Figure. 4.2 for the conductivity and heat capacity which are temperature-dependent..

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0 100 200 300 400 500 600 700 800 900

Temperature [C]

Con

duct

ivity

[Kca

l/(m

h C

)]

Figure 4.1 Concrete conductivity

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 100 200 300 400 500 600 700 800 900

Temperature [C]

Hea

t cap

acity

[Kca

l/(K

g C

)]

Figure 4.2 Concrete heat capacity

The rate of heating is 40ºC/min and temperature on surface increases from 20 to 620ºC.

The only heating phase is considered at the current analysis. Figure. 4.3 shows

temperature history on surface.

20

120

220

320

420

520

620

0 0.05 0.1 0.15 0.2 0.25

Time [unit]

Tem

pera

ture

[C]

Figure 4.3 Temperature vs. time on the surface

The distribution of temperature and profile are in Figure. 4.4 and Figure. 4.5

Figure 4.4 Temperature distribution (Abaqus)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Diameter [in]

Tcu

r / T

sur

Figure 4.5 Normalized temperature profile

Temperature gradient is the steepest for region from surface to 0.5 in and reduce

gradually to the center.

5. Preliminary Analysis – Thermo Elastic Analysis

The thermo elastic analysis is performed to investigate how temperature gradient affects

to mechanical analysis. Boundary conditions are prescribed to allow the model expand

freely. The number of nodes is 1952 and of elements is 3214.

Figure 5.1 Model and boundary condition

The analysis results under uniform temperature and temperature gradient are compared

in Figure. 5.2 , Figure.5.3 and 5.4. All stress components are free under uniform

temperature increment, but under temperature gradient from heat transient analysis, very

large stress components are observed because of linear elastic material properties and

temperature-dependent material properties. Linear elastic modulus is degraded due to

increment of temperature, but thermal expansion coefficients increase to 5 times larger

than initial values.

Table 5.1 Material property

o[ c]T ( ) [psi]cf T

( ) [psi]tf T

( ) [ksi]E T

( )Tα ( )Tν

20 4000 400 3605 8.57E-6 0.2

100 3959 346 3051 9.68E-6 0.2

200 3793 292 2424 1.15E-5 0.2

300 3498 237 1869 1.43E-5 0.2

400 3076 183 1386 1.88E-5 0.2

500 2525 129 975 2.73E-5 0.2

600 1847 75 636 5.0E-5 0.2

Figure 5.2 σxx under uniform temperature distribution (Abaqus)

Figure 5.3 τxy under transient temperature distribution (Abaqus)

Figure 5.4 VonMises stress under under transient temperature distribution (Abaqus)

6. NPFM Analysis

As observed the stiff temperature gradient is from the surface to 0.5 in, so two different

material properties for two regions, which is from surface to 0.5 in inside and other part,

are prescribed and updated at certain temperatures (Table 6.1). 3-node triangular

element is used for solid element and the linear elastic behavior is assumed.

6.1. Material Properties

Table 6.1 Averaged Material properties at region 1 and region 2

E (T)

[ksi]

α(T)

e-6

T

[C]

3317 9.6744 100

3017 11.732 183

2686 13.483 275

1542 16.949 366

1130 23.077 460

R2

789 35.714 552

Interface element is inserted between two regions and nonlinear plastic fracture analysis

is performed to investigate surface crack and spalling. The material properties for

interface element which are independent of temperature are in Table. 6.2.

E (T)

[ksi]

α(T)

e-6

T

[C]

3391 8.95522 50

2842 10.2040 132

2574 11.0090 175

2115 12.8760 254

1687 15.6250 336

R1

1319 19.6720 415

Table 6.2 Material property of interface element

Kns

[kips/in]

Knn

[kips/in]

ft’

[ksi]

c

[ksi]

θ

[o]

Ψ

[o]

GI

[kips/in]

GII

[kips/in]

dmax

[in]

145.1 145.1 0.58 1.451 38.6 32 5.71e-4 5.71e-3 0.3937

6.2. Interface Crack

The decrease in tensile strength is not abrupt but is rather gradual. This is caused by the

presence of the fracture process zone, along which the energy of the system is gradually

dissipated, which can be represented following model.

Figure 6.1 Failure function of the interface

c : Cohesion φf : Friction angel [ Degree] σt : Tensile strengthe along the interface

τ1,τ2 : Two tangential components of the interface traction vector. σ : Normal traction component.

Figure 6.2 Bi-linear softening law for fracture energy

The critical opening and sliding corresponding to zero cohesion and tensile strength are

denoted by wσ and wc. It should be noted that GFIIa is not the pure mode II fracture

energy, but rather is the energy dissipated during a shear test with high confining

normal stress. The residual shear strength is obtained from the failure function by

setting both c and σt equal to 0, which corresponds to the final shape of the failure

function. uieff is the norm of the inelastic displacement vector ui .

7. Analysis Results

7.1. Stress Distribution

Stress contour in x-direction are shown in Figure.7.1~7.4 at different temperatures of

120ºC, 320ºC, 520ºC and 620ºC. Compressive stresses increase form 0.86[ksi] to

2.91[ksi] on a surface at ∇T=100~600ºC, and tensile stresses in the center region

increase 0.4[ksi]~1.35[ksi] at the same temperature screen. The reason having different

stresses is the variation of temperature distribution. Also maximum stress at the highest

temperature is much lower than the result of the thermo elastic analysis because of that

cracks along interface between two different regions that have different material

properties.

Figure 7.1 σxx contour at ∇T=100ºC (Merlin)

Figure 7.2 σxx contour at ∇T=300ºC (Merlin)

Figure 7.3 σxx contour at ∇T=500ºC (Merlin)

Figure 7.4 σxx contour at ∇T=600ºC (Merlin)

The cracks are to be occurred not only on the surface but also center region, but in the

current analysis elastic solid elements are employed for continuum region. Based on

two major assumption of that the material properties continuum element are constant

and interface elements are placed between two different regions that are evaluated with

the approximate estimation by the extent of temperature gradient, the model-based

simulation using Merlin are performed, of which results may not realistic.

Figure 7.5 VonMises Stress at ∇T=600ºC at different scale (Merlin)

Though two assumption, the current analysis where the model is allowed to expand

freely led to surface spalling as shown in Fig 2.6 and Fig.7.5 for thermal loading only

which are qualitative rather than quantitative in nature.

7.2. Stress History

σxx history at different locations are investigated in Figure 7.6 ~ 7.8. As expected

compressive stress on a surface increase but increment of stress is not severe because

stress is extracted along x-direction.(Figure 7.6).

Figure 7.6 σxx vs. Temperature at a point on the surface along x-axis (Merlin)

Stress at the point of inside interface element in x-axis is in tension(Figure 7.7) and σyy

on the surface in x-axis is compressive stress, 0~2.91[ksi] at different temperatures. This

increasing stress confinement will result in triaxial stress state under mechanical loading,

and might lead to explosive spalling which needs to be explored in the future. Figure 7.8

shows σxx at the center is in tension which increases as temperature increase.

Figure 7.7 σxx vs. Temperature at a point on inside interface along x-axis (Merlin)

Figure 7.8 σxx vs. Temperature at the center (Merlin)

7.3. ft’ vs. COD and Fracture Energy

Fracture energy at a certain crack is considered. Mode II fracture energies along the

cracks are almost zero because the deformation is increased in radial direction. In Figure

7.9 Mode I fracture energy at a certain crack is evaluated, value of which is almost the

same one as input of Fracture energy.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

COD [in]

Ten

sile

Str

engt

h [k

si]

Figure 7.9 ft’ vs. COD and Mode I Fracture energy

GF

8. Concluding Remarks

The model-based simulation of cylinder using Merlin led to surface spalling for thermal

loading which are qualitative rather than quantitative in nature because of two

assumptions:

► Two major assumption

- Material properties of continuum elements are constant

- Crack location is placed based on the rate of temperature gradients

► Future Study

Many factors should be considered to evaluate crack propagation due to surface spalling

and explosive spalling. In future study, following factors are to be considered:

- Moisture in concrete porous media

- Mechanical loading

- Random crack location

- Temperature-dependence material properties at interface element

- Cooling phase for considering residual stress

- Different scale study (Meso Scale)

Reference

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Boulder

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