Modelling and Simulation in Engineering

Volume 2016, Article ID 8639545, 11 pages

http://dx.doi.org/10.1155/2016/8639545

## Fire Spalling Prevention via Polypropylene Fibres: A Meso- and Macroscale Approach

Department of Civil, Environmental and Architectural Engineering (DICEA), University of Padova, Via F. Marzolo 9, 35131 Padova, Italy

Received 26 December 2015; Accepted 19 July 2016

Academic Editor: Julius Kaplunov

Copyright © 2016 G. Mazzucco and G. Xotta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A deep understanding of concrete at the mesoscale level is essential for a better comprehension of several concrete phenomena, such as creep, damage, and spalling. The latter one specifically corresponds to the separation of pieces of concrete from the surface of a structural element when it is exposed to high and rapidly rising temperatures; for this phenomenon a mesoscopic approach is fundamental since aggregates performance and their thermal properties play a crucial role. To reduce the risk of spalling of a concrete material under fire condition, the inclusion of a low dosage of polypropylene fibres in the mix design of concrete is largely recognized. PP fibres in fact evaporate above certain temperatures, thus increasing the porosity and reducing the internal pressure in the material by an increase of the voids connectivity in the cement paste. In this work, the contribution of polypropylene fibres on concrete behaviour, if subjected to elevated thermal ranges, has been numerically investigated thanks to a coupled hygrothermomechanical finite element formulation. Numerical analyses at the macro- and mesoscale levels have been performed.

#### 1. Introduction

In the last three decades, catastrophic fire events in concrete tunnels (such as the Danish Great Belt one, the Channel Tunnel, Mont Blanc, and Tauern tunnels) led to the development of new fire protection systems to increase the safety of the people as well as the strength of concrete structures under high temperatures.

One of the principal problems in concrete under fire exposure is spalling, corresponding to the ablation of concrete segments until collapse of the structure, when exposed to high and rapidly rising temperatures. This phenomenon is influenced by many factors but can be explained by taking into account two main contributions: a thermal stress, generated by a thermal gradient between the heated surface and the internal concrete zone, and the pore pressure increments in concrete that occurs when the internal water evaporates [1].

In order to prevent spalling, when concrete structures are subjected to elevated temperatures, the role of polypropylene (PP) fibres into concrete mix design is largely recognized. These fibres are anisotropic monofilaments (diameter *μ*m and length mm) that are not able to increase the material stiffness, but under high temperatures the explosive spalling risk decreases if the volume content in the mix design is between 1 and 3 kg/m^{3} of concrete.

Studies have proved that PP fibres reduce pore pressure into the cement paste, so decreasing the risk of explosive spalling. In fact, the fibres are in a solid state at room temperature but when it increases the state changes; melting phase starts at about 165°C and over 325°C the fibres vaporize and the connected voids channels increase the permeability and diffusivity [1, 2] into concrete. PP evaporation process terminates when temperature is over 475°C.

In this work, the complex mechanism of polypropylene contribution on concrete behaviour under thermal conditions will be numerically investigated through a 3D thermohygromechanical finite element code [3, 4], appropriately updated to take into account the effect of the polypropylene fibres if they are added in the mix design [5]. Innovative concrete systems are investigated in [6, 7].

Numerical analyses at the macro- and mesoscale levels have been performed and validated considering experimental tests by literature. Recent theoretical and computational advances about composite structures also at nanoscale can be found in [8, 9].

To simulate spalling phenomenon, it is not possible to use a linear constitutive law of the material, as concrete has a brittle behaviour; numerically, the softening branch of the material can be described through several theories such as the fracture [10, 11] and damage [12, 13]. In this work, Mazars’ damage law [14] with nonlocal correction has been adopted.

A mesoscopic approach has a remarkable importance for understanding specific concrete phenomena, such as spalling. Indeed, this representation is able to determine the effects of internal hyperstaticity due to the different mechanical characteristics, triggering stress concentrations that can lead to damage.

#### 2. Concrete as a Multiphase Material

Although traditional engineering studies consider concrete as a homogeneous material, idealized as a continuum medium with average properties (macroscopic approach), concrete is a highly heterogeneous material and its composite behaviour is exceedingly complex.

On a macroscopic approach, most of the works proposed in literature assume phenomenological relationships based on macroscopic observations; even if this approach implies a series of simplifications, using continuum-type constitutive models, a satisfactory description of the basic features of the mechanical behaviour of concrete has been reached. Anyway, to obtain a deeper understanding of the macroscopic constitutive behaviour of concrete, it is necessary to adopt a lower scale of observation, that is, mesoscale.

A mesoscale approach will provide a more realistic description of concrete than the macroscale, influenced by the geometry and the properties of its multiple constituents. This could be expected, since the observed macroscopic behaviour is a direct consequence of the phenomena, which take place at the level of the material heterogeneities.

At this level, concrete becomes a mixture of cement paste with aggregates inclusions of various sizes. Aggregates generally occupy 60–80% of the volume of concrete and greatly influence its properties, mix proportion, and economy. Aggregates can be divided into two distinct categories: fine (often called sand) and coarse aggregates; the latter represents around 40–50% of concrete volume. However concrete is not just a two-phase composite; it has been found that the presence of grains in the cement paste causes a thin layer of matrix material surrounding each inclusion to be more porous than the bulk of the surrounding cement paste matrix. This layer is named interfacial transition zone (ITZ) and has relevant effects on the properties of concrete, being likely to act as the “weak link in the chain” when compared to the bulk cement paste and the aggregate particles [15, 16].

For the numerical simulations at the mesolevel mesoscopic continuum models have been adopted; each single composite constituent itself has been approached as a multiphase material, fully described and characterized via a coupled thermohygromechanical model.

Coarse aggregates have been simplified assuming spherical shapes, in order to eliminate possible stress concentrations generated by the angularities; they are distributed randomly in the concrete sample and have an elastic behaviour (they do not creep and do not damage).

The mortar matrix, comprehensive of the cement paste and of the fine aggregates, and the ITZ, whose thickness is strictly related to the diameter of each aggregate, are homogeneous materials; they can be subjected to creep and damage.

Finally PP fibres, having a size on the order of micrometer, are not explicitly represented in the mesoscale approach; their presence and effect have been taken into consideration updating the concrete formulation as explained in the subsequent section.

#### 3. Theoretical Background

Concrete is considered as a multiphase system where the voids of the skeleton are partly filled with liquid and partly with a gas phase. The liquid phase consists of bound water and capillary water, while the gas phase, that is, moist air, is a mixture of dry air and water vapor and it is assumed to behave as an ideal gas.

When higher than standard temperatures are taken into account, several phenomena are considered within the code, dealing with concrete as a porous medium: heat conduction, vapor diffusion, and liquid water flow in the voids.

As regards the mechanical field, the model couples shrink, creep, and damage within the constitutive law of the material. For details, please refer to [17, 18].

In order to take into account the effect of PP fibres, concrete porosity formulation has been enriched and the microcracking that appears after PP fibres vaporization around the void channels has been considered [5].

##### 3.1. PP Fibres Effect on Concrete Porosity

Total porosity at different temperatures and different dosages of fibres can be expressed as [5]where the capillary porosity and the micro- and macroporosities and terms depend only on the mix design, while the rest of the equation is related to the PP fibres effect at different temperatures. Specifically, the porosity terms dependent on fibres mean the following: is related to aggregates ITZ connected by fibres; is due to ITZ formation around fibres; is related to voids variation due to PP fibres relaxation; takes into account micro air bubbles connection and consequent porosity increment; considers void channels formation, at high temperatures, after fibres evaporation; and finally is the porosity increment to the microthermal cracks.

Appling this porosity formulation to the hygrothermomechanical FE code, the hydraulic diffusivity will vary accordingly.

Following Bazant’s formulation [19], is so expressed: where is the diffusivity part, dependent on the physics characteristics related to the ratio.

The PP fibres employed in the concrete material at elevated temperatures, increasing the porosity and the connections between the material voids and not affecting the chemical reactions in the matrix, can be taken into account modifying only the term : where and are constitutive parameters.

##### 3.2. Microcracking Related to PP Fibres

An aspect that has to be considered, when determining the concrete diffusivity containing PP fibres, is the microcracking that appears around the void channels once the fibres evaporate [20]. The cracks, being a mechanical response of the cement paste due to a local stiffness variation, cause a void increment, so reducing the internal concrete pressure after the peak and causing a variation in hydraulic diffusivity.

For the determination of the microthermal cracks, a formulation that considers a damage variable dependent only on temperature has been developed [21]:where and are the minimum and maximum temperatures when microcracks occur and is the initial thermal expansion. The term is the linear variation of the thermal expansion during heating and is the thermal variation when microcrack takes place:where is the tangent modulus of the damaged curve *.*

The hygrometric diffusivity has been modified to take into account the microcrack contribution as follows:where can be found experimentally.

##### 3.3. Visco-Elasto-Damaged Formulation

The skeleton of the concrete material has been represented as a viscoelastic material coupled with Mazars’ damage formulation [3].

Following a FE formulation the stress-strain relation can be so expressed:where is the analysis time, is the relaxation time, , are the stress and strain tensors, respectively, is the scalar damage parameter,** B** is the derivative shape function operator, and is the relaxation function, dual to the compliance or creep function, in accordance with the Maxwell-Chain model:where represents the th elastic modulus of the Maxwell unit and* y* is the reduction time parameter.

The damage variable* d* is evaluated following Mazars’ formulation [14], where the load function is assumed as follows:where* k* is an internal variable and is the equivalent strain:The damage law is an exponential function, subdivided in a compression and in a traction part:where , (with ), and are the material parameters; are the coupled coefficients.

#### 4. Numerical Models

##### 4.1. 3D Numerical Analyses at the Macro- and Mesolevel without PP Fibres Inclusions

Before investigating the effect of polypropylene fibres, the behaviour of a base cell of concrete, without addition of PP fibres, modelled at the macro- and mesolevel and subjected only to a heating rate has been presented in this subsection.

A representation of the concrete at the mesolevel will allow us to determine the effects of internal hyperstaticities due to the different characteristics of the individual phases, which are due to concentrations of stresses and strains during the heating process of the material and that can lead to a mechanical damage. Such concentrations are not visible by using macroscopic models.

Details of the cell adopted in the analyses are visible in Figure 1; symmetry conditions have been assumed to simplify the numerical model.