A new test method to study the influence of pore pressure on fracture behaviour of concrete during heating
Introduction
Concrete tensile behaviour in reinforced concrete (R/C) members exposed to fire is made important by the tricky phenomenon of spalling, namely the – more or less – violent expulsion of chips and shards from the hot layers due to the interaction between (a) rising pressure in the pores due to water vaporization and (b) the stress induced by both thermal gradients and external loads. Explosive spalling is a still hot issue in structural design, since it may lead to a sizable reduction of the cross-sectional area and to the direct exposure of rebars to flames, dramatically speeding up the decrease in the load-bearing capacity of R/C members.
A number of studies have been conducted on this topic [1], [2] stressing the influence of both internal material factors (moisture content, porosity, tensile strength, fibre content) and external structural factors (heating rate, applied loads and constraints). These aspects control the relative roles of the two main mechanisms to which spalling can be ascribed [3], [4] (Fig. 1). First, the restrained thermal dilation of the exposed concrete leads to compressive stress parallel to the surface (Fig. 1b) and to radial tensile stress in curved elements and corners, which favour cracking and a local loss of material stability. Second, vapour pressure build-up in the pores due to water vaporization and moisture flow (Fig. 1c) substantially contributes to the explosive nature of spalling, with violent bursting of thin splinters in High-Performance Concrete (HPC).
Based on high speed camera recording, a clear relationship between gas pressure in the pores and velocity of spalled-off pieces has been shown by Zeiml et al. [5]. This evidence justifies the increasing attention to the thermo-hygral behaviour of concrete exposed to fire.
From the experimental point of view, several authors [5], [6], [7], [8] have directly measured local gas pressure in concrete specimens subjected to thermal transients. In most cases, this was done by embedding thin stainless steel pipes fitted with external pressure sensors. The setup normally includes a porous sensing head – to measure the mean pressure of larger volumes – and thermally stable silicon oil filling the pipe [9] – to improve the stiffness of the measuring chain. It has to be noted that the pressure measured in this way results from the equilibrium reached by the probe and the hot fluids (water, vapour, air) inside a limited volume of the cement matrix around the sensor head [10]. Nonetheless, consistent results have been obtained under different test conditions (concrete grade, moisture content, heating rate). Values as high as 5 MPa have been reported in the case of HPC [9], while lower values are reported for Normal-Strength Concrete – NSC [7] and polypropylene fibre concrete [6], [11].
A number of authors have investigated the influence of several parameters on both pore pressure and spalling depth [7], [8], [12]. Their studies cover a wide range of experimental results, from low to high values of pressure and from no spalling to large amounts of spalling. Though pore pressure is definitely a driving force in spalling, the authors concluded that no direct relationship was evident, in the cases considered, between severity of spalling and measured pore pressure values. Some specimens spalled with measured pore pressures lower than 0.5 MPa, while other specimens didn't spall even at pressures exceeding 3 MPa. Hence, Jansson and Boström [8] proposed a new spalling mechanism based on the concept of moisture clog: spalling is fostered by pore liquid pressure and by the lower strength of the hot, water-saturated concrete layer. Thermal dilation of liquid water inside the fully saturated pores may also initiate microcracking in the cement paste [13].
A second research line is focused on numerical models simulating the heat and mass transfer taking place in concrete when exposed to high temperatures. This involves the solution of a complex set of coupled differential equations and several approaches, based on different simplifying assumptions, have been proposed over the past thirty years [14]. Their consistency is often checked against the ability to fit temperature and pressure obtained in experimental tests. In these models, however, the mutual interaction between pore pressure and the mechanical response of the material is a critical problem, for which no experimental evidence is so far available in the literature.
As commonly done in multi-phase porous media, the total stress σtot sustained by the material is split into the effective stress σeff, borne by the solid skeleton, and the solid phase pressure ps exerted by pore fluids [15]:where I is the unit tensor (tensile stress and pressure are assumed to be positive).
The main point is to understand how solid phase pressure ps is related to the pressure in the pores, in order to define the hydrostatic tensile stress in the solid skeleton required to balance the pressure rising in the porous network. Solid phase pressure can be expressed as a combination of the gas and capillary pressures according to different expressions that have been proposed in the literature [16], as summarized in Table 1. In some models only the gas phase is considered, with different weight coefficients.
According to Biot's theory, one option for compressible fluids inside a not-well cemented stiff skeleton, is to introduce bare gas pressure into the equilibrium equations [17]. Another – and opposite – option is to assume that gas pressure is exerted just inside the pores and should be then multiplied by the material porosity [4], according to Biot's model for well cemented sedimentary rocks. An intermediate value is obtained by considering the elastic solution for intensification of stress around a spherical cavity [18]. More sophisticated models also take capillary pressure into account, multiplied by the fraction of skeleton area in contact with liquid water [14], [16], [19]. Nonetheless, the role of capillary pressure does not seem critical, either in modelling fast heating and moisture transients [20], or in determining mechanical damage [21].
One general remark about the models cited is that they consider concrete as a porous solid in flow analysis of fluid phases, whereas the material is assumed to be a homogeneous continuum in mechanical analysis of the solid skeleton. However, exceeding “tensile strength” is the macroscopic result of unstable crack propagation through the same porous network where fluid pressure is exerted. Considering the influence of pressure on this internal instability would be a more consistent way of understanding the role played by water (liquid and vapour) in fostering the spalling phenomenon.
In order to substantiate this viewpoint, this study tackles the problem of designing a novel test setup aimed at performing a fracture test under different levels of sustained pore pressure. Contrary to most experimental techniques for material characterization at high temperature, requiring uniform steady-state temperature and not well known hygral conditions, here the test is carried out during a controlled transient. The objective is to clarify whether pore pressure may in itself – even without any significant contribution from thermal stress – be a sufficient driving force to exceed the mechanical strength and trigger explosive spalling in R/C members exposed to fire.
Section snippets
Test principle and setup
Concrete members in fire undergo high thermal gradients (due to low thermal diffusivity) and pressure build-ups (because of water vaporization in the pores). The latter is the main driving force of mass transfer, leading to both progressive drying close to the exposed surface and vapour migration toward the cold core of the structure, where water content may be increased due to vapour condensation. As a result, a quasi-saturated layer with reduced gas permeability can form, this fostering the
Mix design
Concrete type B40, thoroughly investigated by Mindeguia [10], was used, with the mix design reported in Table 2. B40 is a Normal-Strength Concrete (NSC), meaning that spalling in unstressed conditions is unlikely to occur. This choice is coherent with the purpose to prevent any unstable fracturing of the specimen during the preliminary heating stage. Two batches were cast: with and without 2 kg/m3 of monofilament polypropylene fibre (pp fibre, Table 3).
Casting and curing
Concrete was cast in 100 mm-sided cubic
Pore pressure trends at increasing temperature
The experimental results regarding the heating phase for the 22 specimens tested are shown in Fig. 8a and b in terms of temperature-time and pressure-time curves for the different heating rates. In Fig. 9 the pressure-temperature plots are compared with the saturation vapour pressure curve, PSV [25].
The results confirm the pore-pressure range observed by Mindeguia [10] for B40 concrete and can be summarized as follows:
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the qualitative development of pore pressure is similar for all the tests:
Numerical analysis
Experimental tests conducted under transient thermal conditions demonstrated the non-negligible influence of the heating rate, which governs the distribution of temperature in the samples and the consequent development of thermal stress. Thanks to the very limited extent of the specimens in directions orthogonal to the thermal gradient, the stress field parallel to the exposed face (biaxial compression at the surface followed by tension at some depth) is strongly reduced compared to real
Discussion of the experimental results
The results of the splitting tests performed at different heating rates and under different values of sustained pore pressure demonstrate that the apparent tensile strength of concrete fctapp is a function of: (a) actual material strength fctT (including the effect of chemo-physical transformations that occur up to temperature T), (b) pore pressure p developed in the pores (through the proportionality coefficient k) and (c) the detrimental effect Δfct(T,HR) of thermal stress due to heating:
Concluding remarks
In this work the influence of pore pressure on the fracture response of concrete at high temperature is investigated as a way of shedding light on one of the fundamental mechanisms behind the phenomenon of explosive spalling. To this purpose, a novel test setup has been devised which makes it possible to perform a conventional splitting cube test during a controlled thermo-hygral transient. A double-panel radiant heater preserves the symmetry relative to the fracture plane, while gas pressure
Acknowledgments
The authors wish to thank Mehmet Baran Ulak and Murat Hacioglu from Turkey and Davide Sciancalepore and Alessandro Simonini from Italy, who actively contributed to this study in partial fulfilment of their MS degree requirements at Politecnico di Milano.
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