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Lightweight structural cement composites with expanded polystyrene (EPS) for enhanced thermal insulation
Cement and Concrete Composites 102 (2019) 185–197
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Lightweight structural cement composites with expanded polystyrene (EPS) for enhanced thermal insulation
T
Anjaneya Dixita, Sze Dai Panga,∗, Sung-Hoon Kangb, Juhyuk Moonb,c,∗∗ a
Dept. of Civil and Environmental Engineering, National University of Singapore, Singapore Dept. of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea c Institute of Construction and Environmental Engineering, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea b
ARTICLE INFO
ABSTRACT
Keywords: Ultra-high performance concrete (UHPC) Expanded polystyrene (EPS) Micro-computed tomography (μCT) Thermal conductivity (TC) Percolation theory General media approximation Cost efficiency
The development of Expanded Polystyrene (EPS) concrete involves two major concerns: (a) poor strength resulting in the EPS concrete unsuitable for structural applications, and (b) segregation of the ultra-light weight of EPS during mixing (EPS is approximately 100 times lighter than concrete). Though EPS displays high insulation (thermal conductivity ≈ 0.04 W/m-K), these issues limit its usage in concrete. This study aims to develop a lightweight-EPS cement composite (LECC) having enhanced insulating capacity as well as satisfactory compressive strength for structural applications. To mitigate the deteriorating effect of EPS on strength, the LECC is developed using the base material of ultra-high performance concrete (UHPC). EPS beads of 3–5 mm diameter are mixed in UHPC in five proportions by volume of 0, 16, 25, 36, 45% and the resulting composites are tested for mechanical and thermal properties. Microstructural characterization is performed using micro-computed tomography (μCT). The choice of the UHPC ingredients proportion is found successful in achieving a balance between an optimum viscosity and satisfactory workability for uniform dispersion of EPS, confirmed by the flow values and μCT results. McLachlan's general effective media approximation, based on percolation theory, is used to homogenize the composite and estimate its thermal conductivity with satisfactory accuracy. The LECC thus developed displays a strength 45 MPa with a corresponding density of 1677 kg/m3 and thermal conductivity of 0.58 W/m-K.
1. Introduction The growing infrastructure demand globally has been accompanied by an obvious increment in the energy consumption, especially in residential and office buildings, where a major portion of the energy is consumed to operate the heat, ventilation and air-conditioning (HVAC) systems. A report by the International Energy Agency [1] suggests that the current energy usage on heating and/or cooling on account of thermal comfort along with water heating amounts to 60% of global energy consumption in buildings. With the demand for energy towards HVAC expected to triple by 2050, it is imperative to focus on pioneering techniques to either generate clean, eco-friendly energy or limit the energy needs in buildings. An effective way for the latter approach is to develop innovative construction materials with enhanced insulating properties to control the heat flow in and out of the buildings, thereby curtailing the need for electricity required to maintain thermal comfort. Recent years have seen a myriad of ways to modify the thermal
∗
conductivity (TC) of concrete. The fundamental idea is to introduce materials with very high insulation to bring down the TC of the resulting composite. This can be achieved using foams [2–4], light-weight aggregates (LWAs) such as expanded clay and expanded perlite [5–8] or expanded polystyrene (EPS) [9–19] and recently cenospheres, glass aggregates [6,9,20–26] and aerogels [27–29]. Table 1 shows a summary of various studies conducted in this field. A common observation in most of the researches is the drop in strength with an increase in the high insulation additives. Consequently, the insulating composite may not satisfy the strength criteria for structural applications, where the limit for minimum 28-days compressive strength is 17–20 MPa [30,31] in fib and ACI codes and 40 MPa in Singapore Building Code [32]. This limits their practical application to non-structural elements only. In case they do display satisfactory strength (cenospheres and glass microspheres), the cost of such ingredients is considerably more than conventional concrete ingredients. The balance between the trinity of cost, strength and insulating capacity is, thus, important in order to
Corresponding author. Corresponding author. Dept. of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea. E-mail addresses: [email protected] (S.D. Pang), [email protected] (J. Moon).
∗∗
https://doi.org/10.1016/j.cemconcomp.2019.04.023 Received 20 July 2018; Received in revised form 19 December 2018; Accepted 22 April 2019 Available online 25 April 2019 0958-9465/ © 2019 Elsevier Ltd. All rights reserved.
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Table 1 Contemporary works in the field of insulating concrete. Authors
Insulating/lightweight aggregate
Thermal Conductivity (W/m-K)
Density (kg/m3)
28-days Compressive strength (MPa)
Brooks et al. (2018)
Fly-ash Cenospheres (FAC) Glass Microspheres (GM) Expanded Polystyrene (EPS) FAC and GM Sintered Fly-ash (FA) Expanded Clay (EC) Glass Microspheres (GM) Glass Microspheres (GM) and Aerogel Crushed Glass (CG) Expanded Clay (EC) Fly-ash Cenospheres (FAC) and Aerogel Aerogel Fly-ash Cenopheres (FAC) Expanded Perlite (EP) Fly-ash (FA) and Autoclaving Recycled high-impact polystyrene (HIPS)
0.80–2.23 0.62–2.30 0.71–2.50 0.18 0.80–1.35 0.55–1.0 0.24–0.30 0.08–0.36 0.15–1.70 1.05–1.50 0.32–0.41 0.36–0.50 0.28–1.98 0.38–1.88 0.57–0.89 0.27–0.61
1396–2019 1344–2026 1300–2084 940 1650–2160 950–1270 800–950 600–1250 634.4–2076 1850–2000 1072–1201 1250–1625 966–2251 – 1457–1904 1560–1980
35.4–53.5 21.5–55.1 12.4–43.6 41.0 11.6–42.7 4.2–20.5 17.0–23.0 4.0–27.5 7.5–36.0 31.7–37.0 18.6–23.5 10.6–20.6 33.0–67.6 17.5–78.8 9.5–25.9 20.0–37.0
Huang et al. (2018) Garbalinska & Strazalkowski (2018) Chung et al. (2018) Zeng et al. (2018) Chung et al. (2017) Grabois et al. (2016) Hanif et al. (2016) Chung et al. (2016) Wu et al. (2015) Lu et al. (2015) Wongkeo et al. (2012) Wang and Meyer (2012)
develop a novel insulating composite for structural applications. Expanded polystyrene (EPS) is a very economical insulating material that is easily available globally and also extensively researched in concrete composites. The integration of EPS with concrete commenced in the 1970s. However, preliminary studies focused mainly on manufacturing wall claddings, partitions and other non-structural elements due to the low density and inferior strength of EPS concrete [19]. Various studies have been performed on the mechanical and thermal properties of EPS concrete [9–19]. Recently, the structural feasibility of EPS concrete has also been investigated, such as in the use in sandwich slabs [10–14]. However, to achieve EPS concrete with low TC values (say 1.0 W/m-K or less), the strength reduction in concrete makes it unsuitable for standalone structural applications. A possible technique to counter this is to increase the strength of the cement mix such as the use of ultra-high performance concrete (UHPC). The concept of UHPC was introduced in the 1980s. Also known as reactive powder concrete, it displays superior strength (more than 120 MPa) compared to conventional concrete, has high binder content (in excess of 800 kg per m3 of UHPC), very low water-cement ratio (generally below 0.25) and a highly dense microstructure due to the use of very fine ingredients [33]. The idea of utilizing UHPC in achieving high thermal insulation while retaining strength has been taken up recently, using aerogel as the insulating additive [29,34]. While the thermal conductivity of UHPC was reported as 2.3 W/m-K, UHPCaerogel composites with thermal conductivity as low as 0.4–0.55 W/mK were prepared with compressive strength of 19–20 MPa. Though UHPC helped in achieving structural grade insulating concrete, the economic implication associated with the current higher production cost of aerogel is a major downside. As an alternative, low-cost EPS can be an economically viable solution for insulating additive. Furthermore, replacing a portion of UHPC matrix with EPS will also reduce the amount of UHPC ingredients and thus help in bringing down the overall cost of the EPS composite. The study presented herein is an attempt to develop a structural grade lightweight-EPS cement composite (LECC) with low thermal conductivity (≈0.50 W/m-K) and displaying considerable compressive strength (more than 20 MPa) to qualify for standalone structural applications. EPS beads were added to UHPC mixtures (without steel fibres) in increasing percentages by volume of dry ingredients. The effect of EPS inclusion on the mechanical properties of LECC was studied by observing the changes in density, compressive strength and the elastic modulus. The microstructures of the LECC were analysed using microcomputed tomography (μCT) to better understand the pore characteristics and distribution. TC tests were performed to study the effects of EPS on the thermal properties of the LECCs. Finally, the experimental TC results were correlated to the analytical results obtained from
homogenization technique given by McLachlan [35] for effective TC of composite materials. 2. Experimental details 2.1. Materials The ingredients used to prepare the LECC in this study include ordinary Portland cement (OPC) conforming to ASTM type I, undensified silica fume (SF) (Grade 940-U Elkem Materials), silica sand (SS) (SAC Corporation, Korea), quartz powder (QP) (S-Sil 10 Microsilica, SAC Corporation, Korea), polycarboxylate based, high-range water reducing superplasticizer (SP) (Flowmix 3000U, Dongnam Co. Ltd., Korea), and light-weight filler in the form of EPS beads (Fig. 1). The EPS beads used in this study were 3–5 mm in diameter and had a density of 25 kg/m3. The particle size distributions of OPC and QP were obtained through laser diffraction particle size analyser, while SEM-based image processing technology was used for SF [36,37]. Fig. 2 shows the particle size distribution for the ingredients, including the distribution for SS as obtained from the manufacturer. 2.2. Mix design and specimen preparation The details of the mix proportion used in this study are mentioned in Table 2. Five different mixes (E0 to E4) were used with EPS content of 0%, 16%, 25%, 36% and 45% by volume of dry materials. Two preliminary trials were conducted to ascertain the appropriate mix for the study. The first trial contained constant OPC and SF and the other ingredients (SS and QP) were replaced with EPS. In the second trial, all the ingredients were replaced by EPS such that the ratio by weight of OPC: SF: SS: QP was constant at 1: 0.25: 1.10: 0.35. The mixes were tested for compressive strength and it was found that both the trials showed comparable strength with increasing EPS content (Fig. 3). The inferior strength-to-binder ratio of the first trial mix suggested that it
Fig. 1. Expanded Polystyrene beads used in the study. 186
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Fig. 2. Particle size distribution for cement, silica fume, quartz powder and silica sand used in the study.
Fig. 3. Comparison of 7-day compressive strength between first and second trial mixes.
contained a higher proportion of un-hydrated binder as compared to the second trial mix. Hence, same strength with lesser binder content would make the second trial mix a logical choice. The second approach with proportionate reduction in all the ingredients was, therefore, more effective and adopted for this study. The water-cement (w/c) ratio was kept at 0.22, and the SP/C ratio was kept constant at 0.03 since, using a higher SP content yielded a flowable mix resulting in segregation of EPS beads on the surface. As evident with the results of flow values in Table 2, the mixes had satisfactory flowability. Another observation was the steady decline in the flow values with increase in EPS content. This was a direct consequence of the reduction of fine ingredients, the overall water and the SP content per m3 of concrete. All of these constituents were governed by the cement content in the mix, which in turn varied inversely with the EPS content, hence the reduction. Regarding the fresh state characteristics of the mixes, UHPC displayed favourable behaviour to ensure uniform dispersion of EPS. The ingredients used in the formulation of UHPC were smaller than 1 mm, with about 60% of the dry ingredients being smaller than 100 μm. These micron-sized fine ingredients in UHPC coupled with the appropriate w/c ratio and SP dosage ensured that the resulting mixes had a paste-like consistency rather than a lean slurry. This helped in achieving sufficient viscosity to suspend the EPS beads throughout the matrix and thus prevent their segregation. The dry ingredients (OPC, SF, SS and QP) were mixed in a Hobart mixer for 2 min to obtain a well-blended mix. Water and the polycarboxylates based SP were then added and mixed till the mixture attained a flowy state. The EPS beads were added to the liquefied mixture and mixed for 10 min to attain uniformity. Nine cube specimens (50 mm side length) were prepared for each mix to measure the compressive strength and density. Three cylindrical specimens (100 mm diameter × 200 mm height) were prepared for testing the modulus of elasticity of hardened samples. Additional cylindrical specimens (50 mm diameter × 100 mm height), one for each mix, were cast to perform microstructural analysis using 3D micro-CT. For thermal
conductivity tests, 3 cuboids (50 × 50 × 15–20 mm) each for mix E0, E1 and E2 and two slabs (300 × 300 × 30 mm) each for mix E3 and E4 were prepared. All the samples were cured under ambient conditions of 30 °C and 64% relative humidity until the time of testing. For the LECC samples prepared for μ-CT analysis, rubber moulds were used for casting. On hardening, the moulds were cut open and the samples obtained were cured for 28 days. Thereafter, they were sealed in airtight plastic wrappings and were opened only at the time of testing. This ensured that the samples were prevented from atmospheric interactions and thus represented the pristine state of the microstructure of the concrete matrix when imaged. For the samples for TC tests, moisture content plays a significant role on the thermal properties of the sample [9,22]. Before testing for TC, the samples were oven dried at 105 °C for one week till a constant weight was achieved. The samples for mechanical tests were cured for 28 days and tested immediately after. 2.3. Experiment methodology 2.3.1. CT imaging and pore analysis To study the microstructural properties of the LECC, micro-CT imaging was performed using SkyScan 1173. The source voltage and current were fixed at 130 kV and 60 μA respectively. The exposure time for the X-ray beam was set at 500 ms and the rotational step of 0.3° was chosen. The image obtained had a resolution of 2240 × 2240 pixels while the image pixel size was 24.15 μm. A total of 2000 2D slices were obtained which were then stacked together to form a 3D rendering using Avizo 9.0®. The image analysis is discussed in details in the following sections. 2.3.2. Mechanical properties Cube specimens were used to determine the density of the LECC after 28-days of curing using water displacement method. Compressive
Table 2 Mix proportion of concrete mixes E0-E4 (per cum. concrete). MIX
EPS vol. (%)
OPC (kg)
EPS (kg)
SF (kg)
SS (kg)
QP (kg)
W/C
SP/C
Flow value (mm)
E0 E1 E2 E3 E4
0 16 25 36 45
900 720 693 648 585
0.00 3.52 5.81 8.45 11.45
225 180 173 162 146
990 792 762 713 644
315 252 243 227 205
0.22 0.22 0.22 0.22 0.22
0.03 0.03 0.03 0.03 0.03
249 228 222 212 165
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Fig. 5. Typical 2D raw CT slice for matrix (a) without EPS (mix E0) and (b) with EPS (mix E4).
3. Results and discussions 3.1. CT imaging and 3D characterization Fig. 5 shows the typical original slices obtained from the CT imaging. The slice in Fig. 5a shows the typical UHPC matrix without the EPS inclusion, while Fig. 5b represents a cross section with EPS, thus, having more pronounced pores in terms of size as well as distribution. The difference in densities of the matrix and the pores meant that the Xray captured the two entities in different colours. ‘Pores’, which here include both the air voids and the EPS beads, appear in black. The remaining bright or grey region in the slices, referred to as ‘matrix’, constitute the hydration products, unhydrated cement and other unreacted ingredients. The computational effort was minimized by fixing the region of analysis (ROA) to 1000 × 1000 pixels and a total of 1900 slices (24.15 × 24.15 × 45.885 mm3) in the central portion of the slices as shown in Fig. 6a. The raw images were cropped and converted from 24bit into 8-bit images using ImageJ. The contrast between pores and matrix was also slightly enhanced to bring out the pores against the matrix (Fig. 6b). For a more comprehensive analysis of pore distribution, a three dimensional reconstruction of the slices was performed later using Avizo®. The images obtained from ImageJ were imported to Avizo. The complete set (1900 slices for each mix) was imported as a single object and the software stacked the slices to form a 3D image. Additional processing was performed to smoothen the images, ensuring at the same time that the changes were minimal to preserve the pristineness of the image. First, a median filter with four iterations was applied. This helped in reducing noise and other unwanted artifacts by smoothening pore boundaries and merging or separating closely-spaced pores. This was followed by image segmentation to differentiate the pores from the matrix based on their grey-scale values. As mentioned before, the difference in grey-scale values was a result of the difference in densities of pores and matrix. Using the grey-scale histogram of the images, a limiting threshold value was established which would distinguish the
Fig. 4. Illustrative test set-ups for thermal conductivity using (a) Heat Flow Meter (HFM) and (b) Transient plane source (TPS) method [9].
strength of the cube specimens was determined using a 1000 kN Denison compressive testing machine according to ASTM C109 [38]. To determine the elastic modulus, ASTM C469 [39] was followed and the cylindrical specimens were tested using a 3000 kN Denison testing equipment under load controlled mode. The samples were loaded till 40% of their compressive strength and the strains were recorded using an unbonded extensometer. 2.3.3. Thermal conductivity tests Thermal conductivity for LECCs E3 and E4 were measured using slab specimens through a NETZSCH Heat Flow Meter (HFM 436/3/1) conforming to ASTM C 518 [40]. The equipment utilizes the heat flow technique, wherein a slab sample is placed between two plates that have heat flux transducers (Fig. 4a). Heat flux is released from the top plate and received at the bottom plate after passing through the specimen. The rate of heat flux is measured by the equipment and used to determine the TC values. The higher TC values for other mixes were measured using cuboid specimens through a HOTDISK Thermal Constants Analyser (TPS 2500S). The equipment employs the transient plane source technique conforming to ISO 22007–2:2015 [41]. A negligible heat capacity element is used for simultaneous heating and sensing purpose. The sensor (Kapton sensor in this study) is placed between two specimens of identical composition and is heated (Fig. 4b, [9]). The increase in temperature in the specimen is recorded and the data collected is used to determine the thermal properties. While testing, two input parameters can be adjusted to obtain the most appropriate set of readings, vis-à-vis the heating power of the element and the heating time. For this study, the power was varied between 0.12 and 0.2 W while the heating time varied from 20 to 40 s. The results presented in the later sections are the average of readings for each mix.
Fig. 6. Micro-CT slices (Mix E4): (a) Original slice, (b) Cropped slice showing region of analysis (1000 × 1000 pixels). 188
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Fig. 7. Image segmentation. Regions in blue indicate the selection (pores) in the image. (a) Segmentation without applying median filter (b) Segmentation with median filter. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 8. Volume rendering of the segmented images for mix E0 (air voids shown in ‘red’). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
pores from the matrix. Since, the attenuation energies of the air voids and EPS beads are similar owing to their comparable densities, they had approximately the same grey scale values and appeared black in the raw slice images. A threshold limiting range of 0–20 was applied to identify and isolate all the pores as shown in Fig. 7. The regions shown in ‘blue’ indicate the selection based on the threshold value, which in this case are the pores. A 3D volume rendering of the isolated pores showing their distribution in the ROA was performed, as shown in Fig. 8 for mix E0. The following sections describe the microstructural analyses performed thereafter.
Fig. 9. Histogram for pore count against pore volume: (a) Absolute pore count (b) Normalised pore count.
it can be seen that the distribution of the EPS beads across the depth of the sample is fairly uniform and not accumulated towards the top surface. The efficacy of the mix to avoid segregation was thus, established. The demarcation also helped in separating air voids from the EPS and hence, individual contributions to porosity by these two entities could be calculated. Table 3 shows the pore count for air voids, for EPS and the total pore count for the mixes studied. Though mixes E1 and E3 have substantially low count for total pores, the EPS count shows a consistent increase with an increase in the EPS content in the mix.
3.1.1. Pore analysis The image segmentation was followed by a thorough analysis of the 3D volume to obtain information about the characteristics of individual pores such as pore volume, surface area, anisotropy and inertia tensor values. To understand the relationship between the number of pores and the pore volume, a histogram for pore count was plotted as shown in Fig. 9a. As evident, majority of the pores lie in the volume range of 105–108 μm3, with mix E4 showing a notably higher peak in this range. Another way of studying the pore count is to normalize the data with the total pore count, so as to obtain a proportion wise distribution of number of pores against pore volume. This can be seen in Fig. 9b, where the normalised pore count histogram revealed that the proportion-wise trend among the mixes is much more similar. A close observation of the pore data for mix E0 revealed that except for a single pore with volume 1.38 × 1010 μm3, all the other pores were smaller than 1010 μm3. Therefore, the limiting size to demarcate the pores due to air voids was fixed at 1010 μm3. Any pore larger than this volume was attributed to EPS. Volume rendering based on this demarcation was done for mixes E1-E4 as shown in Fig. 10a-d. The air voids are represented in ‘red’ as before, while the EPS beads are shown in ‘white’. Through an elementary visual study of the rendered images,
3.1.2. Porosity comparison Based on the demarcation pore volume, the porosities due to air voids (pore volume below 1010 μm3) and due to EPS (pore volume above 1010 μm3) were calculated for the mixes. The distributions of cumulative porosities were then determined and shown in Fig. 11a, b. Porosities due to air voids were found similar across the mixes and lied in the range of 1.5%–2.0%, with mix E2 showing a slightly higher air void porosity. The behaviour for E2 can be explained by analysing in conjunction with the pore count data (Fig. 9a), where it can be seen that E2 has the highest number of air voids in the range of 106–108 μm3. The porosity data shows that the inclusion of EPS may have affected the 189
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Fig. 10. Volume rendering after separation of air voids and EPS beads for: (a) E0, (b) E1, (c) E2, (d) E3, (e) E4. Air voids are shown in red and EPS beads are shown in white. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
For a spherical pore, I11 ∼ I22 ∼ I33. The principal moments were calculated for all the pores using the software, and their ratios (I11/ I33, I22/ I33 ; I11 < I22 < I33 ) were separately plotted in a bivariate histogram for air voids as shown in Fig. 12(a–e) and for EPS in Fig. 13(a–d). It can be clearly observed that the histogram for air voids is more scattered than for EPS, as the latter are more uniformly shaped than the air voids. Also, since, EPS pores are predominantly spherical in shape, majority of the EPS data points lie in the region I11/ I33 > 0.4, I22/ I33 > 0.4 , with all the EPS histograms displaying a well pronounced cluster of points for I11/ I33 > 0.9, I22/ I33 > 0.9 . The histograms for air voids indicated that mixes E0 and E4 had dominant proportions of elongated voids since their graphs showed a large cluster near the origin. While the graphs of mix E1, E2 and E3 show that they had a fairly diverse range of void shapes since their data cluster were more spread out. For additional analysis, degree of anisotropy (DoA) in the EPS pores were also determined. The anisotropy of a pore is the measure of its sphericity. For a DoA of zero, the shape is considered as a perfect sphere. Fig. 14 shows the histogram for the DoA of EPS beads. To compensate for the variation in pore counts among the mixes, data normalised against the total pore count is shown. It can be seen from the figure that EPS are relatively isotropic in shape, which is in concurrence with the principal moments results. Major peaks for a DoA of 0.2 were observed for all the mixes with EPS. The proportion of EPS pores corresponding to this DoA varied from 30% (for mix E4) to 55% (mix E1). Minor peaks for mix E3 and E4 were also observed at a DoA of 0.9. These peaks may be attributed to the ‘slicing’ of EPS pores at the boundaries of ROA, which ultimately modified their principal moments. Since, a larger number of EPS pores fell on the boundary for E3 and E4, their secondary peaks are slightly higher than other mixes.
Table 3 Pore count: Air voids, EPS beads and total pores.
Pore count: Air voids Pore Count: EPS Total pore count
E0
E1
E2
E3
E4
28803 0 28803
18851 67 18918
36987 89 37076
16814 114 16928
43272 153 43425
pore count histogram, but the overall air void porosity remains largely unaffected. With regard to the EPS porosities, they follow an increasing trend with increasing EPS volume fraction, with the exception of mix E3 (Table 4). It should be noted here that the approach of demarcation volume (1010 μm3) was taken for uniformity in porosity calculation across various mixes. However, due to the cropping of slices to establish the ROA, some of the EPS beads that fell in the boundary of the cropped image were chopped and as a result had volume less than 1010 μm3. Hence, they were identified as air voids. This may have resulted in a conservative estimate of the EPS pores and an overestimation of the air voids porosity. The effect of this underestimation can be seen in the EPS porosity, where E2 and E3 show similar porosity. Comparing the porosity due to EPS beads obtained from μCT data to the volume content of EPS in the original design mix in Table 1, the values were found to be similar with the exception of mix E2 and E3. 3.1.3. Anisotropy and pore shape study The shape properties of the pores were also analysed. To study the shape characteristics, the inertia tensor method by Drach et al. [42] was used. The mass properties of a pore are written in a 3 × 3 matrix as given in Equation (1).
Ixx Ixy Ixz I = Iyx Iyy Iyz Izx Izy Izz
3.2. Density, compressive strength and elastic modulus (1)
The remarkable compressive strength of the UHPC is owing to its high cement content, and its highly dense concrete matrix. Due to the negligible strength and high compressibility of EPS, its inclusion led to the inevitable reduction in UHPC strength. The results from 7-days and
Where, Ixx, Iyy …, Izz are the moment of inertias about the coordinate axes x, y, and z. The eigenvalues of this matrix are equal to the principal moments (I11, I22 and I33) and are used to describe the pore geometry. 190
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observation may be attributed to the reduction of binder content (cement and silica fume) with increasing amount of EPS in the mixes. The error bars shown are for the maximum and minimum values compared to the mean of the three samples. The ultra-low density of EPS (∼25 kg/m3) also helped in achieving substantially lighter concrete. As evident from Table 5, the density reduced by 36% from 2301 kg/m3 for the reference mix E0 to 1463 kg/m3 for mix E4. Fig. 16 shows the variation of compressive strength with the density of concrete. The mixes used in this study were able to display significant strength even with high EPS content. Similar to the density and compressive strength, the elastic modulus of concrete also decreased with an increase in EPS content. The EPS beads provided little resistance to externally applied deformation and resulted in larger strains for the same applied loading. Repeatability in the results of the three cylinder specimens tested was satisfactorily established by the closely spaced data points as seen in Fig. 17. 3.3. Thermal conductivity Results from the thermal conductivity (TC) tests were encouraging. In general, the TC showed a decreasing trend with increasing EPS content as shown in Fig. 18. From E0 to E4, the TC value fell from 2.14 W/m-K, to 0.49 W/m-K, a substantial 77% drop in TC. The higher TC values for the E0, comparable to reported values for UHPC and normal concrete mixes (2.1–2.5 W/m-K) [3,9,20,29], may be attributed to the presence of silica sand which inherently has a higher conductivity. Additionally, the dense microstructure due to the presence of silica fume also contributed to better transfer of heat through the matrix. However, the inclusion of EPS negated this by introducing artificial voids and thus, improved the insulation of the mix. The goal of this study to develop an insulating concrete with standalone structural application was achieved most efficiently by mix E3 (based on the strength-to-TC ratio). The mix showed a strength of 44.7 MPa and TC of 0.58 W/m-K (Table 5). This translates to a proportionate reduction in strength (70%) and thermal conductivity (72%) when compared to the reference mix E0 (149 MPa and 2.14 W/m-K). The proposed LECCs have also been compared with existing studies [5,6,9,17,20,21,23,25,26,43–46] for a more judicious evaluation of their performance (Fig. 19). From an economical perspective, while majority of the studies involved conventional concrete or plain cement paste with costlier insulating additives, LECC was a product of a costly UHPC mix with very economical EPS. Though inclusion of EPS resulted in loss of salient features of UHPC, the resulting composite displayed comparable performance with other composites in terms of strength, TC and cost. This has been established by including the material costs of the other mixtures. The material costs have been calculated based on the prevailing market rates of the ingredients (refer Appendix). An efficiency index (EI) defined as compressive strength/(thermal conductivity*cost) has been used to provide a holistic view. This comparison has been limited to composites displaying TC values below 1.0 W/ m-K and satisfying the minimum strength criteria for structural purposes as per ACI 318–14 [31] (Fig. 20a) and HDB guidelines for Singapore [32] (Fig. 20b) which are in line with the aim of this study. Overall, it can be observed that the proposed LECC fares well in the comparison with recent works and displayed a well-balanced combination of cost, strength and thermal conductivity. It is noteworthy that in the responses of LECC in Figs. 16–18, there was a discernible change in property between E2 and E3 as observed by the sudden drop in modulus of elasticity and the reduction in thermal conductivity. To better understand this phenomenon, the theory of percolation threshold and general effective media (GEM) were referred to Refs. [35,47]. The following section explains the estimation of effective thermal conductivity of the LECC based on percolation theory.
Fig. 11. Cumulative porosity as a function of pore volume for (a) Air voids (b) EPS beads. (Values indicated in brackets for (b) are EPS porosity and total porosity respectively).
Table 4 Porosity comparison: Air voids, EPS beads and total pores.
Air voids induced porosity (%) EPS induced Porosity (%) Total porosity (%)
E0
E1
E2
E3
E4
1.76 0.00 1.76
1.71 10.84 12.54
2.76 18.36 21.11
1.62 18.44 20.06
1.84 43.22 45.05
28-days compressive strength showed a decreasing trend as the volume content of EPS increased (Fig. 15). Compared to mix E0, the reduction in 28-days compressive strength varied from 37% for mix E1 to 82% for mix E4. With the addition of EPS, the gain in strength in UHPC from 7 to 28 days was also found to be affected. For the reference mix E0, the increment in strength from 7 to 28 days was 24%, while for mix E4, there was no change in strength. The primary reason for this
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Fig. 12. Histogram for inertia tensors (I22/I33 vs I11/I33) for air voids: (a) E0, (b) E1, (c) E2, (d) E3, (e) E4.
3.4. Estimation of thermal conductivity using percolation based homogenization
and is strongly affected by the morphological characteristics of the matrix and the aspect ratio and orientation of the inclusions [35,48–54]. Apart from conductivity problems, percolation theory has also been used to study the hydration and permeability in concrete [55–58]. The properties (mechanical, thermal etc.) of heterogeneous materials such as concrete are largely controlled by the microstructure: the positioning of voids, their size, inter-connectivity etc. The high degree of heterogeneity in concrete makes it difficult to predict the exact behaviour. However, these properties, can be estimated with appreciable accuracy using experimental results and employing appropriate homogenization techniques [59,60]. In particular, the effective thermal conductivity of insulating concrete has been estimated using homogenization by corroborating the experimental data with established analytical models [9,20,22]. The underlying assumption, similar to the percolation theory, is to consider the composite as a two-phase
Percolation theory is widely used to understand the physical properties of heterogeneous systems, especially conductivity problems. With regard to this study, the composite is considered as a porous medium with conducting-insulating phases. With increasing porosity, i.e., the insulating elements, there exist a critical volume fraction, referred as the percolation threshold, beyond which there would be a structural phase transition and the physical properties undergo substantial changes. This is based on the assumption that the inclusions would be sufficiently connected to form a percolating network throughout the composite [47], or that the inter-particle distance between the inclusions is sufficiently small to facilitate the flow of heat (or electrical current) through them [48]. The critical volume fraction, Φcr, corresponding to the percolation threshold varies for different composites
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Fig. 13. Histogram for inertia tensors for EPS beads: (a) E1, (b) E2, (c) E3, (d) E4.
McLachlan [35] gave the general effective media (GEM) model to homogenize the conductivity of binary composites based on percolation threshold and Bruggeman's symmetric theory for effective media approximation. The composite is assumed to consist of mixture of spherical grains of two components with infinite size range so that they completely fill the volume. The components possess finite conductivities, with one component (insulating i.e. EPS, λI) dispersed such that it remains coated with the host component (conducting i.e. UHPC, λC). The model has been used in various scenarios including permeability in concrete [56,57] and estimating thermal conductivity of porous media of common construction materials [49]. The general form of the equation is given by: 1/ t I 1/ t + I
(
A=
A
1/ t M ) 1/ t M
cr
1
cr
+
(1
)( C1/ t +A
1/ t C
1/ t M ) 1/ t M
=0
(2) (3)
where, Φ is the volume fraction of the dispersion (EPS), λM is the effective conductivity of the medium and t is the scaling exponent for curve fitting. Based on the previous literature involving spherical or similar-shaped inclusions, the value of Φcr was found to vary substantially: 0.18 [56], 0.4 [53], 0.496 [50] and 0.523 [48]. A possible explanation for this fluctuation may be the different assumptions made in the model while deriving the threshold values, vis-à-vis physical contact among inclusions or a minimum distance between them to initiate percolation. Blaszkiewz et al. [50], who also observed a remarkably higher Φcr as compared to the theoretical values, suggested that some of the filler inclusions may not be in physical contact with their neighbouring fillers due to partial surface wetting by the surrounding host. A similar pattern was observed in Ref. [54], wherein the
Fig. 14. Histogram of normalised pore count for degree of anisotropy for EPS beads.
material: the concrete matrix and the insulating additive, and the property is estimated based on the volume fraction of the individual phases. In the current study, the concrete phase was assumed to include the hydration products, unhydrated and unreacted ingredients, air voids and the superplasticizer while the other phase would include only the EPS beads. The sum of the volume fractions for the two phases would be unity.
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Fig. 15. 7-days and 28-days compressive strength for mixes E0-E4. Fig. 16. Variation of 28-days compressive strength with density.
Φcr value was kept at 0.798 and 0.685 for mineral soils and crushed rocks respectively. Even McLachlan [35] suggested the Φcr value to be 0.67 for 3D systems. The lower values suggested in the existing literature were primarily based on numerical simulations and/or analytical formulations. For a more judicious estimation, experimental data involving spherical (or similar shaped) inclusions were referred to Refs. [49,50,53]. It was found that a value in the range 0.30–0.40 would be appropriate. Therefore, Φcr = 0.37 was used in Equation (2). Additionally, the exponent for curve fitting, t, was fixed as 0.40, within the range of published values for 3D systems [54]. The effective TC thus obtained along with the experimentally obtained values are shown in Fig. 21 as a function of EPS content, Φ. Except for E4, all other experimental data points were estimated by the GEM model with satisfactory accuracy. It must be brought to attention that for curve fitting, the value of λI was taken as 0.10 W/m-K, higher than the true value for EPS (∼0.04 W/m-K). This ambiguity based on the TC of insulating inclusion was also observed in Ref. [54], where the authors had assumed much higher values for curve fitting (λair = 0.179 W/m-K). A possible explanation for this can be found in the argument given by Cote and Konrad [61], wherein they suggested that the existence of a ‘preferential path’ for heat flow along peat fibres in a sample with 96% porosity. This eventually lead to a higher experimental TC value, requiring them to assume the TC of air to be more than twice its true value for curve fitting. Another reason for this discrepancy is also the fact that the sample may not have been in ‘completely dry’ condition, and the presence of even slight moisture in the matrix could have augmented the conductivity. For the current study, this phenomenon did not affect the estimation of TC for Φ < 0.40, as observed in the additional GEM curve drawn for the true EPS conductivity. Overall, it was found that the GEM approximation based on percolation theory was satisfactory in estimating the thermal conductivity of LECCs.
Fig. 17. Variation of modulus of elasticity with EPS content.
4. Conclusion The fine ingredients in the UHPC mix proportion play a vital role in the uniform dispersion of EPS beads. With all the other ingredients smaller than 1 mm and 60% of which lie below 100 μm in size, the rheology of the fresh mix resembles a thick paste, viscous enough to
Table 5 Mechanical and thermal properties for mix E0-E4. Mix
Density (kg/m3)
Compressive strength (MPa)
Modulus of Elasticity (GPa)
Thermal Conductivity (W/m-K)
Strength-TC ratio (MPa.m.K/mW)
E0 E1 E2 E3 E4
2301 2045 1828 1677 1463
149.8 94.0 56.9 44.7 27.2
45.4 36.2 32.5 16.8 14.1
2.14 1.69 1.39 0.58 0.49
69.5 55.7 40.8 76.9 55.0
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Fig. 18. Variation of thermal conductivity with EPS content.
Fig. 20. Efficiency indices for contemporary works with thermal conductivity ≤ 1.0 W/m-K and satisfying minimum strength criteria as per: (a) ACI-318-14 (i.e.17 MPa), and (b) Singapore building code (i.e. 40 MPa). Fig. 19. Comparison of LECC with contemporary works on insulating concrete.
prevent EPS segregation. At the same time, a well-adjusted dosage of superplasticizer and water ensures the mix has sufficient flowability for ease of working and handling. These have been supported by the μCT results and flow values respectively. The air void porosity of the composites remains largely unaffected by the change in EPS volume as observed from the pore data analysis. Furthermore, the ultra-high strength of UHPC is an effective tool to counter the degrading effect of EPS on the concrete strength. Even with 45% EPS volume, the compressive strength measured in mix E4 is 27 MPa, making it suitable for structural application. Whereas based on the strength-thermal conductivity (TC) ratio, mix E3 with compressive strength of 44.7 MPa, density of 1677 kg/m3 and thermal conductivity of 0.58 W/m-K is the most optimal combination of strength and insulation among the mixtures studied. McLachlan's approximation and percolation theory predict the TC of the LECCs with good accuracy, suggesting that beyond the percolation threshold (Φcr = 0.37), change in EPS volume may not have a proportionate change in insulation capacity of the composite. Comparison with contemporary works reveals that while considering strength, insulation and cost, the proposed LECC is a novel composite with comparable properties to the fore-runners in the field of insulating concretes.
Fig. 21. Comparison between percolation based GEM and experimental data. 195
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Acknowledgements
by Singapore Ministry of Education Academic Research Fund Tier 1 Grant (Grant no. R-302-000-183-114).
This research was supported in the National University of Singapore APPENDIX-Material costs and Efficiency Index (EI) calculations Material costs Material Ordinary Portland cement Natural/River sand Silica fume Silica sand Quartz powder Limestone powder Fly-ash Fly-ash cenosphere (FAC) QK-300 type FAC [20] Glass microsphere (GM) Crushed glass (CG) Aerogel Expanded perlite (EP) Expanded clay (EC) High-impact polystyrene (HIPS) Expanded polystyrene (EPS) Magnesium oxide cement Author
TC (W/mK)
CS (MPa)
Cost (US $/m3)
EI
Author
LECC
44.7 27.2 45.8 37.9 35.4 35.1 35.2 50.9 48.5 21.0 23.0 22.0 19.0 32.0 29.0 20.0 20.5
275 235 275 275 275 370 370 370 370 534 525 525 520 200 320 680 130
280 234 196 170 161 148 144 172 187 151 146 150 122 302 216 109 157
Zeng et al. (2018)
Garba. & Strazal.
0.58 0.49 0.85 0.81 0.80 0.64 0.66 0.80 0.70 0.26 0.30 0.28 0.30 0.53 0.42 0.27 1.00
Huang et al. (2018)
0.18
41.0
740
308
Brooks et al. (FAC) Brooks et al. (GM)
Chung et al. (2018)
Wang and Meyer (2012)
(US$/m3) 189 52 440 663 663 265 88 700 1120 1380 506 500 40 165 1560 38 725
(US$/ton) 60 20 200 250 250 100 40 1000 1600 3000 200 5000 400 300 1500 1500 230
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Lightweight structural cement composites with expanded polystyrene (EPS) for enhanced thermal insulation
T
Anjaneya Dixita, Sze Dai Panga,∗, Sung-Hoon Kangb, Juhyuk Moonb,c,∗∗ a
Dept. of Civil and Environmental Engineering, National University of Singapore, Singapore Dept. of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea c Institute of Construction and Environmental Engineering, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea b
ARTICLE INFO
ABSTRACT
Keywords: Ultra-high performance concrete (UHPC) Expanded polystyrene (EPS) Micro-computed tomography (μCT) Thermal conductivity (TC) Percolation theory General media approximation Cost efficiency
The development of Expanded Polystyrene (EPS) concrete involves two major concerns: (a) poor strength resulting in the EPS concrete unsuitable for structural applications, and (b) segregation of the ultra-light weight of EPS during mixing (EPS is approximately 100 times lighter than concrete). Though EPS displays high insulation (thermal conductivity ≈ 0.04 W/m-K), these issues limit its usage in concrete. This study aims to develop a lightweight-EPS cement composite (LECC) having enhanced insulating capacity as well as satisfactory compressive strength for structural applications. To mitigate the deteriorating effect of EPS on strength, the LECC is developed using the base material of ultra-high performance concrete (UHPC). EPS beads of 3–5 mm diameter are mixed in UHPC in five proportions by volume of 0, 16, 25, 36, 45% and the resulting composites are tested for mechanical and thermal properties. Microstructural characterization is performed using micro-computed tomography (μCT). The choice of the UHPC ingredients proportion is found successful in achieving a balance between an optimum viscosity and satisfactory workability for uniform dispersion of EPS, confirmed by the flow values and μCT results. McLachlan's general effective media approximation, based on percolation theory, is used to homogenize the composite and estimate its thermal conductivity with satisfactory accuracy. The LECC thus developed displays a strength 45 MPa with a corresponding density of 1677 kg/m3 and thermal conductivity of 0.58 W/m-K.
1. Introduction The growing infrastructure demand globally has been accompanied by an obvious increment in the energy consumption, especially in residential and office buildings, where a major portion of the energy is consumed to operate the heat, ventilation and air-conditioning (HVAC) systems. A report by the International Energy Agency [1] suggests that the current energy usage on heating and/or cooling on account of thermal comfort along with water heating amounts to 60% of global energy consumption in buildings. With the demand for energy towards HVAC expected to triple by 2050, it is imperative to focus on pioneering techniques to either generate clean, eco-friendly energy or limit the energy needs in buildings. An effective way for the latter approach is to develop innovative construction materials with enhanced insulating properties to control the heat flow in and out of the buildings, thereby curtailing the need for electricity required to maintain thermal comfort. Recent years have seen a myriad of ways to modify the thermal
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conductivity (TC) of concrete. The fundamental idea is to introduce materials with very high insulation to bring down the TC of the resulting composite. This can be achieved using foams [2–4], light-weight aggregates (LWAs) such as expanded clay and expanded perlite [5–8] or expanded polystyrene (EPS) [9–19] and recently cenospheres, glass aggregates [6,9,20–26] and aerogels [27–29]. Table 1 shows a summary of various studies conducted in this field. A common observation in most of the researches is the drop in strength with an increase in the high insulation additives. Consequently, the insulating composite may not satisfy the strength criteria for structural applications, where the limit for minimum 28-days compressive strength is 17–20 MPa [30,31] in fib and ACI codes and 40 MPa in Singapore Building Code [32]. This limits their practical application to non-structural elements only. In case they do display satisfactory strength (cenospheres and glass microspheres), the cost of such ingredients is considerably more than conventional concrete ingredients. The balance between the trinity of cost, strength and insulating capacity is, thus, important in order to
Corresponding author. Corresponding author. Dept. of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea. E-mail addresses: [email protected] (S.D. Pang), [email protected] (J. Moon).
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https://doi.org/10.1016/j.cemconcomp.2019.04.023 Received 20 July 2018; Received in revised form 19 December 2018; Accepted 22 April 2019 Available online 25 April 2019 0958-9465/ © 2019 Elsevier Ltd. All rights reserved.
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Table 1 Contemporary works in the field of insulating concrete. Authors
Insulating/lightweight aggregate
Thermal Conductivity (W/m-K)
Density (kg/m3)
28-days Compressive strength (MPa)
Brooks et al. (2018)
Fly-ash Cenospheres (FAC) Glass Microspheres (GM) Expanded Polystyrene (EPS) FAC and GM Sintered Fly-ash (FA) Expanded Clay (EC) Glass Microspheres (GM) Glass Microspheres (GM) and Aerogel Crushed Glass (CG) Expanded Clay (EC) Fly-ash Cenospheres (FAC) and Aerogel Aerogel Fly-ash Cenopheres (FAC) Expanded Perlite (EP) Fly-ash (FA) and Autoclaving Recycled high-impact polystyrene (HIPS)
0.80–2.23 0.62–2.30 0.71–2.50 0.18 0.80–1.35 0.55–1.0 0.24–0.30 0.08–0.36 0.15–1.70 1.05–1.50 0.32–0.41 0.36–0.50 0.28–1.98 0.38–1.88 0.57–0.89 0.27–0.61
1396–2019 1344–2026 1300–2084 940 1650–2160 950–1270 800–950 600–1250 634.4–2076 1850–2000 1072–1201 1250–1625 966–2251 – 1457–1904 1560–1980
35.4–53.5 21.5–55.1 12.4–43.6 41.0 11.6–42.7 4.2–20.5 17.0–23.0 4.0–27.5 7.5–36.0 31.7–37.0 18.6–23.5 10.6–20.6 33.0–67.6 17.5–78.8 9.5–25.9 20.0–37.0
Huang et al. (2018) Garbalinska & Strazalkowski (2018) Chung et al. (2018) Zeng et al. (2018) Chung et al. (2017) Grabois et al. (2016) Hanif et al. (2016) Chung et al. (2016) Wu et al. (2015) Lu et al. (2015) Wongkeo et al. (2012) Wang and Meyer (2012)
develop a novel insulating composite for structural applications. Expanded polystyrene (EPS) is a very economical insulating material that is easily available globally and also extensively researched in concrete composites. The integration of EPS with concrete commenced in the 1970s. However, preliminary studies focused mainly on manufacturing wall claddings, partitions and other non-structural elements due to the low density and inferior strength of EPS concrete [19]. Various studies have been performed on the mechanical and thermal properties of EPS concrete [9–19]. Recently, the structural feasibility of EPS concrete has also been investigated, such as in the use in sandwich slabs [10–14]. However, to achieve EPS concrete with low TC values (say 1.0 W/m-K or less), the strength reduction in concrete makes it unsuitable for standalone structural applications. A possible technique to counter this is to increase the strength of the cement mix such as the use of ultra-high performance concrete (UHPC). The concept of UHPC was introduced in the 1980s. Also known as reactive powder concrete, it displays superior strength (more than 120 MPa) compared to conventional concrete, has high binder content (in excess of 800 kg per m3 of UHPC), very low water-cement ratio (generally below 0.25) and a highly dense microstructure due to the use of very fine ingredients [33]. The idea of utilizing UHPC in achieving high thermal insulation while retaining strength has been taken up recently, using aerogel as the insulating additive [29,34]. While the thermal conductivity of UHPC was reported as 2.3 W/m-K, UHPCaerogel composites with thermal conductivity as low as 0.4–0.55 W/mK were prepared with compressive strength of 19–20 MPa. Though UHPC helped in achieving structural grade insulating concrete, the economic implication associated with the current higher production cost of aerogel is a major downside. As an alternative, low-cost EPS can be an economically viable solution for insulating additive. Furthermore, replacing a portion of UHPC matrix with EPS will also reduce the amount of UHPC ingredients and thus help in bringing down the overall cost of the EPS composite. The study presented herein is an attempt to develop a structural grade lightweight-EPS cement composite (LECC) with low thermal conductivity (≈0.50 W/m-K) and displaying considerable compressive strength (more than 20 MPa) to qualify for standalone structural applications. EPS beads were added to UHPC mixtures (without steel fibres) in increasing percentages by volume of dry ingredients. The effect of EPS inclusion on the mechanical properties of LECC was studied by observing the changes in density, compressive strength and the elastic modulus. The microstructures of the LECC were analysed using microcomputed tomography (μCT) to better understand the pore characteristics and distribution. TC tests were performed to study the effects of EPS on the thermal properties of the LECCs. Finally, the experimental TC results were correlated to the analytical results obtained from
homogenization technique given by McLachlan [35] for effective TC of composite materials. 2. Experimental details 2.1. Materials The ingredients used to prepare the LECC in this study include ordinary Portland cement (OPC) conforming to ASTM type I, undensified silica fume (SF) (Grade 940-U Elkem Materials), silica sand (SS) (SAC Corporation, Korea), quartz powder (QP) (S-Sil 10 Microsilica, SAC Corporation, Korea), polycarboxylate based, high-range water reducing superplasticizer (SP) (Flowmix 3000U, Dongnam Co. Ltd., Korea), and light-weight filler in the form of EPS beads (Fig. 1). The EPS beads used in this study were 3–5 mm in diameter and had a density of 25 kg/m3. The particle size distributions of OPC and QP were obtained through laser diffraction particle size analyser, while SEM-based image processing technology was used for SF [36,37]. Fig. 2 shows the particle size distribution for the ingredients, including the distribution for SS as obtained from the manufacturer. 2.2. Mix design and specimen preparation The details of the mix proportion used in this study are mentioned in Table 2. Five different mixes (E0 to E4) were used with EPS content of 0%, 16%, 25%, 36% and 45% by volume of dry materials. Two preliminary trials were conducted to ascertain the appropriate mix for the study. The first trial contained constant OPC and SF and the other ingredients (SS and QP) were replaced with EPS. In the second trial, all the ingredients were replaced by EPS such that the ratio by weight of OPC: SF: SS: QP was constant at 1: 0.25: 1.10: 0.35. The mixes were tested for compressive strength and it was found that both the trials showed comparable strength with increasing EPS content (Fig. 3). The inferior strength-to-binder ratio of the first trial mix suggested that it
Fig. 1. Expanded Polystyrene beads used in the study. 186
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Fig. 2. Particle size distribution for cement, silica fume, quartz powder and silica sand used in the study.
Fig. 3. Comparison of 7-day compressive strength between first and second trial mixes.
contained a higher proportion of un-hydrated binder as compared to the second trial mix. Hence, same strength with lesser binder content would make the second trial mix a logical choice. The second approach with proportionate reduction in all the ingredients was, therefore, more effective and adopted for this study. The water-cement (w/c) ratio was kept at 0.22, and the SP/C ratio was kept constant at 0.03 since, using a higher SP content yielded a flowable mix resulting in segregation of EPS beads on the surface. As evident with the results of flow values in Table 2, the mixes had satisfactory flowability. Another observation was the steady decline in the flow values with increase in EPS content. This was a direct consequence of the reduction of fine ingredients, the overall water and the SP content per m3 of concrete. All of these constituents were governed by the cement content in the mix, which in turn varied inversely with the EPS content, hence the reduction. Regarding the fresh state characteristics of the mixes, UHPC displayed favourable behaviour to ensure uniform dispersion of EPS. The ingredients used in the formulation of UHPC were smaller than 1 mm, with about 60% of the dry ingredients being smaller than 100 μm. These micron-sized fine ingredients in UHPC coupled with the appropriate w/c ratio and SP dosage ensured that the resulting mixes had a paste-like consistency rather than a lean slurry. This helped in achieving sufficient viscosity to suspend the EPS beads throughout the matrix and thus prevent their segregation. The dry ingredients (OPC, SF, SS and QP) were mixed in a Hobart mixer for 2 min to obtain a well-blended mix. Water and the polycarboxylates based SP were then added and mixed till the mixture attained a flowy state. The EPS beads were added to the liquefied mixture and mixed for 10 min to attain uniformity. Nine cube specimens (50 mm side length) were prepared for each mix to measure the compressive strength and density. Three cylindrical specimens (100 mm diameter × 200 mm height) were prepared for testing the modulus of elasticity of hardened samples. Additional cylindrical specimens (50 mm diameter × 100 mm height), one for each mix, were cast to perform microstructural analysis using 3D micro-CT. For thermal
conductivity tests, 3 cuboids (50 × 50 × 15–20 mm) each for mix E0, E1 and E2 and two slabs (300 × 300 × 30 mm) each for mix E3 and E4 were prepared. All the samples were cured under ambient conditions of 30 °C and 64% relative humidity until the time of testing. For the LECC samples prepared for μ-CT analysis, rubber moulds were used for casting. On hardening, the moulds were cut open and the samples obtained were cured for 28 days. Thereafter, they were sealed in airtight plastic wrappings and were opened only at the time of testing. This ensured that the samples were prevented from atmospheric interactions and thus represented the pristine state of the microstructure of the concrete matrix when imaged. For the samples for TC tests, moisture content plays a significant role on the thermal properties of the sample [9,22]. Before testing for TC, the samples were oven dried at 105 °C for one week till a constant weight was achieved. The samples for mechanical tests were cured for 28 days and tested immediately after. 2.3. Experiment methodology 2.3.1. CT imaging and pore analysis To study the microstructural properties of the LECC, micro-CT imaging was performed using SkyScan 1173. The source voltage and current were fixed at 130 kV and 60 μA respectively. The exposure time for the X-ray beam was set at 500 ms and the rotational step of 0.3° was chosen. The image obtained had a resolution of 2240 × 2240 pixels while the image pixel size was 24.15 μm. A total of 2000 2D slices were obtained which were then stacked together to form a 3D rendering using Avizo 9.0®. The image analysis is discussed in details in the following sections. 2.3.2. Mechanical properties Cube specimens were used to determine the density of the LECC after 28-days of curing using water displacement method. Compressive
Table 2 Mix proportion of concrete mixes E0-E4 (per cum. concrete). MIX
EPS vol. (%)
OPC (kg)
EPS (kg)
SF (kg)
SS (kg)
QP (kg)
W/C
SP/C
Flow value (mm)
E0 E1 E2 E3 E4
0 16 25 36 45
900 720 693 648 585
0.00 3.52 5.81 8.45 11.45
225 180 173 162 146
990 792 762 713 644
315 252 243 227 205
0.22 0.22 0.22 0.22 0.22
0.03 0.03 0.03 0.03 0.03
249 228 222 212 165
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Fig. 5. Typical 2D raw CT slice for matrix (a) without EPS (mix E0) and (b) with EPS (mix E4).
3. Results and discussions 3.1. CT imaging and 3D characterization Fig. 5 shows the typical original slices obtained from the CT imaging. The slice in Fig. 5a shows the typical UHPC matrix without the EPS inclusion, while Fig. 5b represents a cross section with EPS, thus, having more pronounced pores in terms of size as well as distribution. The difference in densities of the matrix and the pores meant that the Xray captured the two entities in different colours. ‘Pores’, which here include both the air voids and the EPS beads, appear in black. The remaining bright or grey region in the slices, referred to as ‘matrix’, constitute the hydration products, unhydrated cement and other unreacted ingredients. The computational effort was minimized by fixing the region of analysis (ROA) to 1000 × 1000 pixels and a total of 1900 slices (24.15 × 24.15 × 45.885 mm3) in the central portion of the slices as shown in Fig. 6a. The raw images were cropped and converted from 24bit into 8-bit images using ImageJ. The contrast between pores and matrix was also slightly enhanced to bring out the pores against the matrix (Fig. 6b). For a more comprehensive analysis of pore distribution, a three dimensional reconstruction of the slices was performed later using Avizo®. The images obtained from ImageJ were imported to Avizo. The complete set (1900 slices for each mix) was imported as a single object and the software stacked the slices to form a 3D image. Additional processing was performed to smoothen the images, ensuring at the same time that the changes were minimal to preserve the pristineness of the image. First, a median filter with four iterations was applied. This helped in reducing noise and other unwanted artifacts by smoothening pore boundaries and merging or separating closely-spaced pores. This was followed by image segmentation to differentiate the pores from the matrix based on their grey-scale values. As mentioned before, the difference in grey-scale values was a result of the difference in densities of pores and matrix. Using the grey-scale histogram of the images, a limiting threshold value was established which would distinguish the
Fig. 4. Illustrative test set-ups for thermal conductivity using (a) Heat Flow Meter (HFM) and (b) Transient plane source (TPS) method [9].
strength of the cube specimens was determined using a 1000 kN Denison compressive testing machine according to ASTM C109 [38]. To determine the elastic modulus, ASTM C469 [39] was followed and the cylindrical specimens were tested using a 3000 kN Denison testing equipment under load controlled mode. The samples were loaded till 40% of their compressive strength and the strains were recorded using an unbonded extensometer. 2.3.3. Thermal conductivity tests Thermal conductivity for LECCs E3 and E4 were measured using slab specimens through a NETZSCH Heat Flow Meter (HFM 436/3/1) conforming to ASTM C 518 [40]. The equipment utilizes the heat flow technique, wherein a slab sample is placed between two plates that have heat flux transducers (Fig. 4a). Heat flux is released from the top plate and received at the bottom plate after passing through the specimen. The rate of heat flux is measured by the equipment and used to determine the TC values. The higher TC values for other mixes were measured using cuboid specimens through a HOTDISK Thermal Constants Analyser (TPS 2500S). The equipment employs the transient plane source technique conforming to ISO 22007–2:2015 [41]. A negligible heat capacity element is used for simultaneous heating and sensing purpose. The sensor (Kapton sensor in this study) is placed between two specimens of identical composition and is heated (Fig. 4b, [9]). The increase in temperature in the specimen is recorded and the data collected is used to determine the thermal properties. While testing, two input parameters can be adjusted to obtain the most appropriate set of readings, vis-à-vis the heating power of the element and the heating time. For this study, the power was varied between 0.12 and 0.2 W while the heating time varied from 20 to 40 s. The results presented in the later sections are the average of readings for each mix.
Fig. 6. Micro-CT slices (Mix E4): (a) Original slice, (b) Cropped slice showing region of analysis (1000 × 1000 pixels). 188
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Fig. 7. Image segmentation. Regions in blue indicate the selection (pores) in the image. (a) Segmentation without applying median filter (b) Segmentation with median filter. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 8. Volume rendering of the segmented images for mix E0 (air voids shown in ‘red’). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
pores from the matrix. Since, the attenuation energies of the air voids and EPS beads are similar owing to their comparable densities, they had approximately the same grey scale values and appeared black in the raw slice images. A threshold limiting range of 0–20 was applied to identify and isolate all the pores as shown in Fig. 7. The regions shown in ‘blue’ indicate the selection based on the threshold value, which in this case are the pores. A 3D volume rendering of the isolated pores showing their distribution in the ROA was performed, as shown in Fig. 8 for mix E0. The following sections describe the microstructural analyses performed thereafter.
Fig. 9. Histogram for pore count against pore volume: (a) Absolute pore count (b) Normalised pore count.
it can be seen that the distribution of the EPS beads across the depth of the sample is fairly uniform and not accumulated towards the top surface. The efficacy of the mix to avoid segregation was thus, established. The demarcation also helped in separating air voids from the EPS and hence, individual contributions to porosity by these two entities could be calculated. Table 3 shows the pore count for air voids, for EPS and the total pore count for the mixes studied. Though mixes E1 and E3 have substantially low count for total pores, the EPS count shows a consistent increase with an increase in the EPS content in the mix.
3.1.1. Pore analysis The image segmentation was followed by a thorough analysis of the 3D volume to obtain information about the characteristics of individual pores such as pore volume, surface area, anisotropy and inertia tensor values. To understand the relationship between the number of pores and the pore volume, a histogram for pore count was plotted as shown in Fig. 9a. As evident, majority of the pores lie in the volume range of 105–108 μm3, with mix E4 showing a notably higher peak in this range. Another way of studying the pore count is to normalize the data with the total pore count, so as to obtain a proportion wise distribution of number of pores against pore volume. This can be seen in Fig. 9b, where the normalised pore count histogram revealed that the proportion-wise trend among the mixes is much more similar. A close observation of the pore data for mix E0 revealed that except for a single pore with volume 1.38 × 1010 μm3, all the other pores were smaller than 1010 μm3. Therefore, the limiting size to demarcate the pores due to air voids was fixed at 1010 μm3. Any pore larger than this volume was attributed to EPS. Volume rendering based on this demarcation was done for mixes E1-E4 as shown in Fig. 10a-d. The air voids are represented in ‘red’ as before, while the EPS beads are shown in ‘white’. Through an elementary visual study of the rendered images,
3.1.2. Porosity comparison Based on the demarcation pore volume, the porosities due to air voids (pore volume below 1010 μm3) and due to EPS (pore volume above 1010 μm3) were calculated for the mixes. The distributions of cumulative porosities were then determined and shown in Fig. 11a, b. Porosities due to air voids were found similar across the mixes and lied in the range of 1.5%–2.0%, with mix E2 showing a slightly higher air void porosity. The behaviour for E2 can be explained by analysing in conjunction with the pore count data (Fig. 9a), where it can be seen that E2 has the highest number of air voids in the range of 106–108 μm3. The porosity data shows that the inclusion of EPS may have affected the 189
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Fig. 10. Volume rendering after separation of air voids and EPS beads for: (a) E0, (b) E1, (c) E2, (d) E3, (e) E4. Air voids are shown in red and EPS beads are shown in white. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
For a spherical pore, I11 ∼ I22 ∼ I33. The principal moments were calculated for all the pores using the software, and their ratios (I11/ I33, I22/ I33 ; I11 < I22 < I33 ) were separately plotted in a bivariate histogram for air voids as shown in Fig. 12(a–e) and for EPS in Fig. 13(a–d). It can be clearly observed that the histogram for air voids is more scattered than for EPS, as the latter are more uniformly shaped than the air voids. Also, since, EPS pores are predominantly spherical in shape, majority of the EPS data points lie in the region I11/ I33 > 0.4, I22/ I33 > 0.4 , with all the EPS histograms displaying a well pronounced cluster of points for I11/ I33 > 0.9, I22/ I33 > 0.9 . The histograms for air voids indicated that mixes E0 and E4 had dominant proportions of elongated voids since their graphs showed a large cluster near the origin. While the graphs of mix E1, E2 and E3 show that they had a fairly diverse range of void shapes since their data cluster were more spread out. For additional analysis, degree of anisotropy (DoA) in the EPS pores were also determined. The anisotropy of a pore is the measure of its sphericity. For a DoA of zero, the shape is considered as a perfect sphere. Fig. 14 shows the histogram for the DoA of EPS beads. To compensate for the variation in pore counts among the mixes, data normalised against the total pore count is shown. It can be seen from the figure that EPS are relatively isotropic in shape, which is in concurrence with the principal moments results. Major peaks for a DoA of 0.2 were observed for all the mixes with EPS. The proportion of EPS pores corresponding to this DoA varied from 30% (for mix E4) to 55% (mix E1). Minor peaks for mix E3 and E4 were also observed at a DoA of 0.9. These peaks may be attributed to the ‘slicing’ of EPS pores at the boundaries of ROA, which ultimately modified their principal moments. Since, a larger number of EPS pores fell on the boundary for E3 and E4, their secondary peaks are slightly higher than other mixes.
Table 3 Pore count: Air voids, EPS beads and total pores.
Pore count: Air voids Pore Count: EPS Total pore count
E0
E1
E2
E3
E4
28803 0 28803
18851 67 18918
36987 89 37076
16814 114 16928
43272 153 43425
pore count histogram, but the overall air void porosity remains largely unaffected. With regard to the EPS porosities, they follow an increasing trend with increasing EPS volume fraction, with the exception of mix E3 (Table 4). It should be noted here that the approach of demarcation volume (1010 μm3) was taken for uniformity in porosity calculation across various mixes. However, due to the cropping of slices to establish the ROA, some of the EPS beads that fell in the boundary of the cropped image were chopped and as a result had volume less than 1010 μm3. Hence, they were identified as air voids. This may have resulted in a conservative estimate of the EPS pores and an overestimation of the air voids porosity. The effect of this underestimation can be seen in the EPS porosity, where E2 and E3 show similar porosity. Comparing the porosity due to EPS beads obtained from μCT data to the volume content of EPS in the original design mix in Table 1, the values were found to be similar with the exception of mix E2 and E3. 3.1.3. Anisotropy and pore shape study The shape properties of the pores were also analysed. To study the shape characteristics, the inertia tensor method by Drach et al. [42] was used. The mass properties of a pore are written in a 3 × 3 matrix as given in Equation (1).
Ixx Ixy Ixz I = Iyx Iyy Iyz Izx Izy Izz
3.2. Density, compressive strength and elastic modulus (1)
The remarkable compressive strength of the UHPC is owing to its high cement content, and its highly dense concrete matrix. Due to the negligible strength and high compressibility of EPS, its inclusion led to the inevitable reduction in UHPC strength. The results from 7-days and
Where, Ixx, Iyy …, Izz are the moment of inertias about the coordinate axes x, y, and z. The eigenvalues of this matrix are equal to the principal moments (I11, I22 and I33) and are used to describe the pore geometry. 190
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observation may be attributed to the reduction of binder content (cement and silica fume) with increasing amount of EPS in the mixes. The error bars shown are for the maximum and minimum values compared to the mean of the three samples. The ultra-low density of EPS (∼25 kg/m3) also helped in achieving substantially lighter concrete. As evident from Table 5, the density reduced by 36% from 2301 kg/m3 for the reference mix E0 to 1463 kg/m3 for mix E4. Fig. 16 shows the variation of compressive strength with the density of concrete. The mixes used in this study were able to display significant strength even with high EPS content. Similar to the density and compressive strength, the elastic modulus of concrete also decreased with an increase in EPS content. The EPS beads provided little resistance to externally applied deformation and resulted in larger strains for the same applied loading. Repeatability in the results of the three cylinder specimens tested was satisfactorily established by the closely spaced data points as seen in Fig. 17. 3.3. Thermal conductivity Results from the thermal conductivity (TC) tests were encouraging. In general, the TC showed a decreasing trend with increasing EPS content as shown in Fig. 18. From E0 to E4, the TC value fell from 2.14 W/m-K, to 0.49 W/m-K, a substantial 77% drop in TC. The higher TC values for the E0, comparable to reported values for UHPC and normal concrete mixes (2.1–2.5 W/m-K) [3,9,20,29], may be attributed to the presence of silica sand which inherently has a higher conductivity. Additionally, the dense microstructure due to the presence of silica fume also contributed to better transfer of heat through the matrix. However, the inclusion of EPS negated this by introducing artificial voids and thus, improved the insulation of the mix. The goal of this study to develop an insulating concrete with standalone structural application was achieved most efficiently by mix E3 (based on the strength-to-TC ratio). The mix showed a strength of 44.7 MPa and TC of 0.58 W/m-K (Table 5). This translates to a proportionate reduction in strength (70%) and thermal conductivity (72%) when compared to the reference mix E0 (149 MPa and 2.14 W/m-K). The proposed LECCs have also been compared with existing studies [5,6,9,17,20,21,23,25,26,43–46] for a more judicious evaluation of their performance (Fig. 19). From an economical perspective, while majority of the studies involved conventional concrete or plain cement paste with costlier insulating additives, LECC was a product of a costly UHPC mix with very economical EPS. Though inclusion of EPS resulted in loss of salient features of UHPC, the resulting composite displayed comparable performance with other composites in terms of strength, TC and cost. This has been established by including the material costs of the other mixtures. The material costs have been calculated based on the prevailing market rates of the ingredients (refer Appendix). An efficiency index (EI) defined as compressive strength/(thermal conductivity*cost) has been used to provide a holistic view. This comparison has been limited to composites displaying TC values below 1.0 W/ m-K and satisfying the minimum strength criteria for structural purposes as per ACI 318–14 [31] (Fig. 20a) and HDB guidelines for Singapore [32] (Fig. 20b) which are in line with the aim of this study. Overall, it can be observed that the proposed LECC fares well in the comparison with recent works and displayed a well-balanced combination of cost, strength and thermal conductivity. It is noteworthy that in the responses of LECC in Figs. 16–18, there was a discernible change in property between E2 and E3 as observed by the sudden drop in modulus of elasticity and the reduction in thermal conductivity. To better understand this phenomenon, the theory of percolation threshold and general effective media (GEM) were referred to Refs. [35,47]. The following section explains the estimation of effective thermal conductivity of the LECC based on percolation theory.
Fig. 11. Cumulative porosity as a function of pore volume for (a) Air voids (b) EPS beads. (Values indicated in brackets for (b) are EPS porosity and total porosity respectively).
Table 4 Porosity comparison: Air voids, EPS beads and total pores.
Air voids induced porosity (%) EPS induced Porosity (%) Total porosity (%)
E0
E1
E2
E3
E4
1.76 0.00 1.76
1.71 10.84 12.54
2.76 18.36 21.11
1.62 18.44 20.06
1.84 43.22 45.05
28-days compressive strength showed a decreasing trend as the volume content of EPS increased (Fig. 15). Compared to mix E0, the reduction in 28-days compressive strength varied from 37% for mix E1 to 82% for mix E4. With the addition of EPS, the gain in strength in UHPC from 7 to 28 days was also found to be affected. For the reference mix E0, the increment in strength from 7 to 28 days was 24%, while for mix E4, there was no change in strength. The primary reason for this
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Fig. 12. Histogram for inertia tensors (I22/I33 vs I11/I33) for air voids: (a) E0, (b) E1, (c) E2, (d) E3, (e) E4.
3.4. Estimation of thermal conductivity using percolation based homogenization
and is strongly affected by the morphological characteristics of the matrix and the aspect ratio and orientation of the inclusions [35,48–54]. Apart from conductivity problems, percolation theory has also been used to study the hydration and permeability in concrete [55–58]. The properties (mechanical, thermal etc.) of heterogeneous materials such as concrete are largely controlled by the microstructure: the positioning of voids, their size, inter-connectivity etc. The high degree of heterogeneity in concrete makes it difficult to predict the exact behaviour. However, these properties, can be estimated with appreciable accuracy using experimental results and employing appropriate homogenization techniques [59,60]. In particular, the effective thermal conductivity of insulating concrete has been estimated using homogenization by corroborating the experimental data with established analytical models [9,20,22]. The underlying assumption, similar to the percolation theory, is to consider the composite as a two-phase
Percolation theory is widely used to understand the physical properties of heterogeneous systems, especially conductivity problems. With regard to this study, the composite is considered as a porous medium with conducting-insulating phases. With increasing porosity, i.e., the insulating elements, there exist a critical volume fraction, referred as the percolation threshold, beyond which there would be a structural phase transition and the physical properties undergo substantial changes. This is based on the assumption that the inclusions would be sufficiently connected to form a percolating network throughout the composite [47], or that the inter-particle distance between the inclusions is sufficiently small to facilitate the flow of heat (or electrical current) through them [48]. The critical volume fraction, Φcr, corresponding to the percolation threshold varies for different composites
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Fig. 13. Histogram for inertia tensors for EPS beads: (a) E1, (b) E2, (c) E3, (d) E4.
McLachlan [35] gave the general effective media (GEM) model to homogenize the conductivity of binary composites based on percolation threshold and Bruggeman's symmetric theory for effective media approximation. The composite is assumed to consist of mixture of spherical grains of two components with infinite size range so that they completely fill the volume. The components possess finite conductivities, with one component (insulating i.e. EPS, λI) dispersed such that it remains coated with the host component (conducting i.e. UHPC, λC). The model has been used in various scenarios including permeability in concrete [56,57] and estimating thermal conductivity of porous media of common construction materials [49]. The general form of the equation is given by: 1/ t I 1/ t + I
(
A=
A
1/ t M ) 1/ t M
cr
1
cr
+
(1
)( C1/ t +A
1/ t C
1/ t M ) 1/ t M
=0
(2) (3)
where, Φ is the volume fraction of the dispersion (EPS), λM is the effective conductivity of the medium and t is the scaling exponent for curve fitting. Based on the previous literature involving spherical or similar-shaped inclusions, the value of Φcr was found to vary substantially: 0.18 [56], 0.4 [53], 0.496 [50] and 0.523 [48]. A possible explanation for this fluctuation may be the different assumptions made in the model while deriving the threshold values, vis-à-vis physical contact among inclusions or a minimum distance between them to initiate percolation. Blaszkiewz et al. [50], who also observed a remarkably higher Φcr as compared to the theoretical values, suggested that some of the filler inclusions may not be in physical contact with their neighbouring fillers due to partial surface wetting by the surrounding host. A similar pattern was observed in Ref. [54], wherein the
Fig. 14. Histogram of normalised pore count for degree of anisotropy for EPS beads.
material: the concrete matrix and the insulating additive, and the property is estimated based on the volume fraction of the individual phases. In the current study, the concrete phase was assumed to include the hydration products, unhydrated and unreacted ingredients, air voids and the superplasticizer while the other phase would include only the EPS beads. The sum of the volume fractions for the two phases would be unity.
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Fig. 15. 7-days and 28-days compressive strength for mixes E0-E4. Fig. 16. Variation of 28-days compressive strength with density.
Φcr value was kept at 0.798 and 0.685 for mineral soils and crushed rocks respectively. Even McLachlan [35] suggested the Φcr value to be 0.67 for 3D systems. The lower values suggested in the existing literature were primarily based on numerical simulations and/or analytical formulations. For a more judicious estimation, experimental data involving spherical (or similar shaped) inclusions were referred to Refs. [49,50,53]. It was found that a value in the range 0.30–0.40 would be appropriate. Therefore, Φcr = 0.37 was used in Equation (2). Additionally, the exponent for curve fitting, t, was fixed as 0.40, within the range of published values for 3D systems [54]. The effective TC thus obtained along with the experimentally obtained values are shown in Fig. 21 as a function of EPS content, Φ. Except for E4, all other experimental data points were estimated by the GEM model with satisfactory accuracy. It must be brought to attention that for curve fitting, the value of λI was taken as 0.10 W/m-K, higher than the true value for EPS (∼0.04 W/m-K). This ambiguity based on the TC of insulating inclusion was also observed in Ref. [54], where the authors had assumed much higher values for curve fitting (λair = 0.179 W/m-K). A possible explanation for this can be found in the argument given by Cote and Konrad [61], wherein they suggested that the existence of a ‘preferential path’ for heat flow along peat fibres in a sample with 96% porosity. This eventually lead to a higher experimental TC value, requiring them to assume the TC of air to be more than twice its true value for curve fitting. Another reason for this discrepancy is also the fact that the sample may not have been in ‘completely dry’ condition, and the presence of even slight moisture in the matrix could have augmented the conductivity. For the current study, this phenomenon did not affect the estimation of TC for Φ < 0.40, as observed in the additional GEM curve drawn for the true EPS conductivity. Overall, it was found that the GEM approximation based on percolation theory was satisfactory in estimating the thermal conductivity of LECCs.
Fig. 17. Variation of modulus of elasticity with EPS content.
4. Conclusion The fine ingredients in the UHPC mix proportion play a vital role in the uniform dispersion of EPS beads. With all the other ingredients smaller than 1 mm and 60% of which lie below 100 μm in size, the rheology of the fresh mix resembles a thick paste, viscous enough to
Table 5 Mechanical and thermal properties for mix E0-E4. Mix
Density (kg/m3)
Compressive strength (MPa)
Modulus of Elasticity (GPa)
Thermal Conductivity (W/m-K)
Strength-TC ratio (MPa.m.K/mW)
E0 E1 E2 E3 E4
2301 2045 1828 1677 1463
149.8 94.0 56.9 44.7 27.2
45.4 36.2 32.5 16.8 14.1
2.14 1.69 1.39 0.58 0.49
69.5 55.7 40.8 76.9 55.0
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Fig. 18. Variation of thermal conductivity with EPS content.
Fig. 20. Efficiency indices for contemporary works with thermal conductivity ≤ 1.0 W/m-K and satisfying minimum strength criteria as per: (a) ACI-318-14 (i.e.17 MPa), and (b) Singapore building code (i.e. 40 MPa). Fig. 19. Comparison of LECC with contemporary works on insulating concrete.
prevent EPS segregation. At the same time, a well-adjusted dosage of superplasticizer and water ensures the mix has sufficient flowability for ease of working and handling. These have been supported by the μCT results and flow values respectively. The air void porosity of the composites remains largely unaffected by the change in EPS volume as observed from the pore data analysis. Furthermore, the ultra-high strength of UHPC is an effective tool to counter the degrading effect of EPS on the concrete strength. Even with 45% EPS volume, the compressive strength measured in mix E4 is 27 MPa, making it suitable for structural application. Whereas based on the strength-thermal conductivity (TC) ratio, mix E3 with compressive strength of 44.7 MPa, density of 1677 kg/m3 and thermal conductivity of 0.58 W/m-K is the most optimal combination of strength and insulation among the mixtures studied. McLachlan's approximation and percolation theory predict the TC of the LECCs with good accuracy, suggesting that beyond the percolation threshold (Φcr = 0.37), change in EPS volume may not have a proportionate change in insulation capacity of the composite. Comparison with contemporary works reveals that while considering strength, insulation and cost, the proposed LECC is a novel composite with comparable properties to the fore-runners in the field of insulating concretes.
Fig. 21. Comparison between percolation based GEM and experimental data. 195
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Acknowledgements
by Singapore Ministry of Education Academic Research Fund Tier 1 Grant (Grant no. R-302-000-183-114).
This research was supported in the National University of Singapore APPENDIX-Material costs and Efficiency Index (EI) calculations Material costs Material Ordinary Portland cement Natural/River sand Silica fume Silica sand Quartz powder Limestone powder Fly-ash Fly-ash cenosphere (FAC) QK-300 type FAC [20] Glass microsphere (GM) Crushed glass (CG) Aerogel Expanded perlite (EP) Expanded clay (EC) High-impact polystyrene (HIPS) Expanded polystyrene (EPS) Magnesium oxide cement Author
TC (W/mK)
CS (MPa)
Cost (US $/m3)
EI
Author
LECC
44.7 27.2 45.8 37.9 35.4 35.1 35.2 50.9 48.5 21.0 23.0 22.0 19.0 32.0 29.0 20.0 20.5
275 235 275 275 275 370 370 370 370 534 525 525 520 200 320 680 130
280 234 196 170 161 148 144 172 187 151 146 150 122 302 216 109 157
Zeng et al. (2018)
Garba. & Strazal.
0.58 0.49 0.85 0.81 0.80 0.64 0.66 0.80 0.70 0.26 0.30 0.28 0.30 0.53 0.42 0.27 1.00
Huang et al. (2018)
0.18
41.0
740
308
Brooks et al. (FAC) Brooks et al. (GM)
Chung et al. (2018)
Wang and Meyer (2012)
(US$/m3) 189 52 440 663 663 265 88 700 1120 1380 506 500 40 165 1560 38 725
(US$/ton) 60 20 200 250 250 100 40 1000 1600 3000 200 5000 400 300 1500 1500 230
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