Introduction

In general speaking (term), heavyweight self-compacting concrete (shorthand HWSCC) can be considered as heavyweight concrete meeting the rheological requirements of self-compacting concrete at fresh state or self-compacting concrete with bulk density higher than 2600 kg m−3. In the coming decades, one of the scientific research areas of engineering structures in which substantial understanding should be deepened is the special area of development and optimization of the concrete mix composition, which will meet both the simultaneous requirements of heavyweight concrete and self-compacting Concrete [1,2,3]. Hence, the development of heavyweight concrete satisfying all performance criteria of self-compacting concrete is a new challenge that requires a new-born concrete technology and optimization of material composition. Self-compacting concrete (SCC) is an advanced concrete with wide applications because of its high filling ability, passing ability, segregation resistance, and excellent workability [4,5,6,7,8]. One of the major benefits of SCC is the fact that it can be used in specific infrastructures with complicated design architecture where it is hard to use vibrators for concrete consolidation. Therefore, the development and fabrication of SCC are of fundamental importance to ensure that all gaps in the formwork of columns and beams are filled and densified [8]. SCC has been the subject of extensive and deep studies by several researchers over the last three decades in concrete science and technology. Careful attention has been paid to the optimization of material composition [9] because SCC is more sensitive than normal concrete to variations in the physical properties of its constituents and especially to changes in moisture content, grading curve, and aggregate shape [10, 11]. Aggregates for SCC are selected in terms of their grading, maximum size, and shape characteristics (including shape, angularity, and texture). The size and type of aggregates have an important effect on the workability of fresh concrete. Navarrete et al. [12] have established a relationship between the segregation of concrete and coarse aggregate density and size. Reducing the maximum aggregate size and density will be suitable for improving filling, passing ability, and segregation resistance. The polydispersity character of the particle size distribution may reduce viscosity, as Farris [13] has demonstrated that the lowest viscosity was obtained if the number of monosized fractions became infinitely important. SCCs are generally produced as lightweight and ordinary concretes [14]. Apart from Portland cement, supplementary cementitious materials like limestone [15, 16], fly ash [17,18,19], ground blast furnace slag [20, 21], metakaolin [22], or silica fume [17, 19] were successfully used to develop SCC.

A specific class of concrete using high-density aggregates, the so-called heavyweight concrete was developed and used mainly as biological shielding in operating nuclear power plants (NPPs), medical units, particle accelerator facilities, or repositories for radioactive nuclear wastes where the concrete is exposed to neutron or gamma-ray radiation [23,24,25,26,27]. Therefore, the development of heavyweight concrete, which can meet the function of a radiation shielding material and structural strength demands, with proven low activation and high mechanical properties, is highly required [1, 28,29,30]. In the case of the application of massive concrete structures in an irradiated environment, the chemical composition of individual constituents is even more decisive as it affects the shielding capacity with possible attenuation performance, volumetric stability, and other mechanical properties [2, 27]. Heavyweight concretes are scarcely explored due to the fact that other properties than compressive strength, namely the attenuation capacity vis-à-vis gamma and neutron radiations are more decisive in use of heavyweight concrete in massive construction [25, 26, 31]. Recently, high-compressive strength heavyweight concrete has been developed by using pure Portland cement and two types of aggregates: barite and magnetite [32, 33]. In this case, the hydration heat of cement binders and its rate played key roles in the durability of massive concrete structures due to the risk of thermal cracking. Indeed, massive constructions are under strict control of durability due to the temperature gradient that can cause cracks or surface shrinkage and fissure during the lifetime of the concrete. The exothermic hydration reaction of cement generates a fast temperature rise in the core of the concrete structure, originating a temperature difference with the concrete surface. As a consequence of non-uniform heat distribution and thermal conductivity, the temperature gradient will cause tensile stress [34]. When tensile stress is higher than tensile strength, then a thermal crack occurs on the surface of concrete or mortars. Ilker Beki Topcu [35] has pointed out the undesirable effect of the cracks due to shrinkage on the radioactive seepage in nuclear power plants. To avoid thermal crack due to hydration, supplementary cementitious materials (SCMs) such as granulated ground blast furnace slag (GGBFS), metakaolin, and limestone, would substitute the Portland cement in a binder to develop heavyweight concrete with low hydration heat [33]. Also, a careful examination of chemical composition, including radioactive elements by nuclear activation method (NAA) [36, 37] supplemented by optimization of hydration heat using a conduction calorimeter, has conducted authors to prepare heavyweight concrete without a thermal crack [38]. In addition to the mentioned applications as biological shielding, heavyweight concrete [5] is used as concrete shear walls for external and/or internal cross-ties with wire rope reinforcement.

The development of heavyweight self-compacting concrete is a challenge in itself for the opposite characteristics of heavyweight concrete and self-compacting concrete. Heavyweight concrete contains high-density aggregates that cause low ability to flow and strong segregation due to gravity force. Self-compacting concrete is characterized by its ability to flow easily, resistance to segregation, and without the need for any external force of vibration. The formulation of mixture proportions for heavyweight self-compacting concrete will require more effort than for individual self-compacting or heavyweight concrete. The optimal proportions in this concrete depend not only on the composition of multicomponent cementitious binders, water-to-cement ratio, additives, and admixtures but mainly on the content and particle size distribution of high-density aggregates. Due to the lack of comprehensive works, the present study is one of the rare works aimed at develo** heavyweight concrete with characteristics of self-compacting concrete for specific applications.

Experimental

Materials a methods used

Heavyweight aggregates.

  1. 1.

    Barite from SABAR, s.r.o., Slovakia

  2. 2.

    Magnetite from LKAB Minerals, Sweden

Binder composite.

  1. 1.

    Portland cement CEM I 42.5 R EXTRA (CRH Slovensko a.s. Rohožník)

  2. 2.

    Metakaolin L05 Mefisto (České lupkové závody, a.s., Czech Republic)

  3. 3.

    Blast furnace slag (Kotouč Štramberk, spol. s r.o., Czech Republic)

  4. 4.

    Limestone (Calmit, spol. s.r.o., Slovakia)

The chemical and physical properties of all ingredients are reported in Table 3.

  1. 1.

    Steel micro-fibers with l = 6 mm, h = b = 0.017 mm

Three types of superplasticizers in an amount of 0.6 kg per 100 kg of cement were used.

  1. 1.

    Superplasticizer STACHEMENT 3000 (Stachema Bratislava a. s.). STACHEMENT 2000 is a superplasticizer based on polycarboxylates with a high plasticizing effect and a low decrease in the consistency of the concrete mixture. It is used in the production of self-compacting concrete in the Slovak Republic and is highly effective when used in a wide range of cements.

  2. 2.

    Superplasticizer STACHEMENT 910 (Stachema Bratislava a. s.). STACHEMENT 910 superplasticizer based on polycarboxylates with a high plasticizing and stabilizing effect. It is characterized by a very long workability time of the concrete mix and ensures the production of fine, easily workable concrete.

  3. 3.

    STABILAN KP-2 STABILAN KC03 (Stachema Bratislava a. s.). STABILAN KP-2 prevents aggregate segregation with a positive effect on the rheological properties of fresh concrete.

  4. 4.

    The cement and aggregates used were chemically analyzed through ED RFS Energy-dispersive X-Ray Fluorescence Spectrometer from SPECTO type SPECTRO XEPOS HE equipped with an X-ray lamp at State Geological Institute Dýoniz Štúr (Špišská Nová Ves).

  5. 5.

    The Phillips PW-1800 X-ray fluorescence (XRF) equipment was used to achieve the oxide composition analysis of CEM I 42.5 R at the control laboratory of the supplier at the cement plant Rohožník.

  6. 6.

    PC-Controlled Automatic Blain Apparatus Dyckerhoff system with one measuring cell was used to determine the specific surface.

  7. 7.

    The Automatic Density Analyzer gas pycnometer Quantachrome Pentapyc 5200e was used to measure the density of powder materials. The density value was used to calculate the amount of powder materials necessary for Blaine measurement.

  8. 8.

    The density of HWSCC was calculated from the weighted dried specimen after a period of curing according to the standard, divided by its volume.

Formulation (Mix design) mixture proportion

The procedure for preparing heavyweight self-compacting concrete is quite different from that of conventional heavyweight or self-compacting concrete. Foremost, aggregates (barite and magnetite) were separately crushed, sieved into different size fractions, and remixed to obtain aggregate mixtures with defined particle size distribution with the nominal maximum size of coarse aggregates 2 mm (Table 3).

The experimental procedures consisted of two phases. Firstly, mini V-funnel flow time, mini-slump flow diameter and time, and L-box height ratio were conducted on fresh concrete to optimize the formulation satisfying the rheological properties according to the guidelines for self-compacting concrete [39, 40]. Cement composite (65 mass% CEM I 42,5 R, 15 mass% BFS, 15 mass% limestone, and 5 mass% metakaolin) and aggregates according to optimized grading curves with a maximal size of 2 mm were homogenized together for 30 s, thereafter 70% of water was added and mixed for 1 min. The remaining 30% water containing combined superplasticizers was added and mixed for 1 min. The mixing procedure continued for 5 min, and after that, the whole mix was kept settling for 2 min before being remixed for just half a minute. The water-cement ratio was kept constant at 0.42. Then, mini V-funnel and S-cone were used for the measurement of flow time and diameter. The dimensions of the mini V-funnel and the mini Slump cone used to evaluate paste properties in the rational mixture design method are reported in (4). The preparation was repeated several times until the requirement reported by Okamura [7] was met.

The results are reported in Table 4. The values obtained are at the limits of rheological characteristics of self-compacting concrete reported in [41] due to the fact that high-density aggregates were used instead of normal ones. The binder-filler ratio lies between concrete and mortar composition, as Okamura and co-workers have proposed in the mix design method [6]. They have recommended mixing coarse and fine aggregate contents of 50% of solid coarse aggregate volume and 40% of mortar volume, respectively.

Preparation of sample

After the mix composition optimization, the second phase consisted of the preparation of fresh concrete considering the test procedure for mortars according to EN197-1 (2000) [42]. Three different mixtures prepared according to the composition reported in Table 4 were poured into 40 × 40x160 mm steel molds without any vibration and compaction and covered with plastic in order to avoid evaporation of surface water for 24 h at room temperature. Specimens were demolded 24 h after casting and separated into two groups. The first group was kept in wet conditions with 100% humidity at a temperature of (20 ± 2) °C to determine the bulk density and dynamic modulus before measuring tensile and compressive strength at different ages of 7, 28, and 90 days. The second one was cured under dry conditions in a climatic chamber with an average temperature of 22.6 °C and humidity of 21% from the first day to the 100th one. Curing conditions are equally important for determining the overall volume change in shrinkage concrete. Bulk density and dynamic modulus of elasticity were continuously monitored without destroying samples.

Text procedures

Isothermal calorimetric measurements of cement pastes were conducted on TAM AIR 8–Channel calorimeter as described elsewhere [43, 44].

The compressive and tensile strength of all specimens was measured according to the standard EN 196–1 (2000) [45] at the ages of 7, 28, and 90 days using a 3000 kN capacity concrete compression machine. The compressive strength was calculated as average value from the measurements of six specimens.

The dynamic modulus of elasticity (DME) was performed on 40 × 40x160 mm prism specimens using Ultrasonic Meter Matest. It was determined in two ways. The first option was the instantaneous measurement of samples cured under wet conditions before the destruction method of tensile and compressive determination (Fig. 7). The second procedure was the continual measurement of samples cured under dry conditions with an average temperature of 22.6 °C and humidity 21% from the first day to 100th one (Fig. 6).

The specimen was clamped at the middle section, and an electromagnetic exciter was placed against one end face of the specimen. A pick-up unit was placed against the other end face of the specimen. The exciter induced longitudinal vibrations, which were propagated within the specimen and received by the pick-up unit. The frequency was varied until a resonance frequency was obtained, i.e., the lowest frequency of the specimen. Knowing the resonance frequency, the dynamic modulus was calculated using the following equation:

$$ E_{{\text{d}}} = 4.n^{2} .L^{2} .\rho .10^{ - 15} $$
(1)

where Ed is the dynamic modulus of elasticity (GPa), n is the resonant frequency (Hz), L is the length of specimen (mm), and ρ is the density of specimen (kg m−3).

Mercury intrusion porosimeter Quantachrome Poremaster 60GT (Quantachrome UK Limited) was used for the determination of the pore structure parameters of the composites after 28 days. About 2 g of samples without coarse aggregates used for the tests were soaked in acetone and dried in a vacuum atmosphere at (105 ± 2) °C for 24 h before testing. The maximum applied pressure of mercury was 414 MPa, equivalent to a Washburn pore radius of 1.8 nm according to Eq. (2):

$$ r = - \frac{{2\gamma {\text{cos}}\theta }}{P} $$
(2)

where r is the pore radius, γ the surface tension of mercury (N m−1), θ the contact angle between mercury and the solid materials, and P is the applied pressure[46,47,48].

Scanning Electron Microscope Zeiss, ZEISS EVO LS 10 was used in this study to examine the microstructure of hardened pastes. Prepared cross sections were finished with ion beam milling to get the best possible surface for high-resolution observation.

In addition to the performance tests of mechanical and physical properties, 30 samples (10 from each HWSCC) were prepared in a cylindrical mold with a width of 2 cm and a diameter of 30 cm to evaluate ballistic resistance. The results will be published later.

Results and discussion

Characteristics of used materials

In this research work, three mixtures of heavyweight self-compacting concrete were prepared. Filler materials (barite, magnetite), binders (CEM I 42.5 R), SCM (granulated blast furnace slag, metakaolin, limestone), and additives (water, superplasticizers) were used. The oxide composition of aggregates is reported in Table 1. Likewise, the oxide composition of CEM I 42.5 R, granulated blast furnace slag, metakaolin, and limestone is depicted in Table 1.

Table 1 The oxide composition of high-density aggregates and cementitious materials determined by XRF
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The density of aggregates and the specific surface are reported in Table 2.

Table 2 Physical characteristics of used materials
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Optimized grading curves particle size distribution grading curve

Heavy-density aggregates of barite and magnetite were crushed and sieved to set a grading curve with the composition depicted in Table 3 for the preparation of HWSCC1, HWSCC2, and HWSCC3. The binder used is labeled CEMHWCC. Regarding the grain size composition of fillers, the optimized mix composition is composed of an aggregate of sand size and powder to achieve the self-compactibility of heavyweight self-compacting concrete. It is evident that coarse aggregates of magnetite or barite larger than 2 mm can affect the passing ability of the concrete mix and also can enhance the flow spread. On the contrary, the use of a smaller maximum size of coarse aggregates may increase the passing ability (Fig. 1).

Table 3 Particle size composition of the optimized grading curve
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Fig. 1
figure 1

Cumulative hydration and heat flow of different binders

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The grading curve of high-density aggregate for preparing heavyweight concrete (HWSCC) was set by mixing barite and magnetite in a barite/magnetite ratio of 65/35 in each fraction. The given ratio provides concrete with a bulk density higher than 2600 kg g−3.

Optimization of binder composition through the heat of hydration

Optimization of cementitious composite based on the hydration of heat was performed by TAM AIR 8-Channel isothermal calorimeter consisting of eight-channel couples (sample and reference) to compare heat flow and cumulative heat of CEM I 42.5 R and binder composite. Heat flow and overall cumulative heat of the binder used in the preparation of HWSCC are represented by their curves in Fig. 2. For the comparison, heat flow and overall cumulative heat of CEM I 42.5 R and HWC (75 mass% CEM I 42.5 R) are also represented by their curves at Fig. 2. HWC was used to prepare a high strength heavyweight concrete [32].

Fig. 2
figure 2

Determination of flowability of HWSCCs

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The hydration of CEM I 42.5 R and HWC during 72 h has generated high heat (320 J g−1, 285 J g−1, respectively), which has caused the surface shrinkage. In this case, the hydration heat of cement played a crucial role in creating these cracks due to the thermal gradient between the core and surface of the concrete. Indeed, the massive structure of heavyweight concrete should be under strict control of durability at an earlier curing period due to the temperature gradient, which leads to cracks or surface shrinkage [32, 33]. Therefore, hydration heat becomes a key factor in optimizing binder composite for designing new kinds of heavyweight concrete for massive structures [38].

Part of the cement has been reduced to 65 mass% to avoid surface cracks due to the temperature gradient. Heat hydration of the CEMHWSCC composite (65 mass% CEM I 42.5 R, 15 mass% BFS, 15 mass% limestone, and 5 mass% metakaolin) is relatively low (237 J g−1) and corresponds to the type of massive heavyweight concrete.

Rheological characteristics

A series of experimental preparations were necessary to obtain proper mix designs for heavyweight self-compacting concrete to meet the consistency behaviors defined by EFNARC [8]. Table 4 reports different mixtures with different consistency values.

Table 4 Determination of rheological characteristics
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Table 5 reports the results of optimized material composition. The values obtained are at the limits of the rheological characteristics of self-compacting concrete because high-density aggregates were used instead of normal ones. Moreover, EFNARC [38] is for normal concrete with a density under 2600 kg m−3. The binder-filler ratio lies between mortars and concrete composition.

Table 5 Optimized material composition
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The concrete composition (Table 6) has been set considering the results of hydration heat, nuclear activation analysis as reported by Dragomirová [39], and rheological measurement depicted in Table 5.

Table 6 Optimized material composition of the concrete samples (mass %)
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Determination of bulk density

To classify self-compacting concrete as heavyweight concrete, it is necessary to determine the bulk density of concrete. Two bulk density measurement procedures were adopted. The first one is the instantaneous determination of the bulk density of samples cured under wet conditions before the destructive method of tensile and compressive strength measurement at 7, 28, and 90 days. The second one consisted of continuously monitoring the bulk density of the same samples over time till 90 days cured under dry conditions (average laboratory temperature: 22.6 °C, average humidity: 21%). The bulk density of each HWSCC cured under wet conditions at different ages is stable, but it depends on the type of fillers (barite, magnetite, or barite + magnetite). With regard to the content of aggregate in concrete and the density of fillers, one can note that all specimens can be considered as heavyweight concrete with a bulk density higher than 2600 kg m−3. Referring to the rheological characteristics depicted in Table 5 and considering Fig. 3, it is clear that these specimens are heavyweight concretes meeting the characteristics of self-compacting concrete.

Fig. 3
figure 3

Bulk density of different heavyweight self-compacting concretes

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The dry bulk density development from the early age to 100 days of continual monitoring text is shown in Fig. 4. It can be seen that HWSCC2 kept its higher density during all curing times than HWSCC1 and HWSCC3. The bulk density of each sample increases very slightly from the beginning. These values are lower than those obtained at the corresponding time of instantaneous measurement of samples cured under wet conditions. It is clear that the desiccation of samples and hydration degree under wet conditions have influenced bulk density. However, the evolution of bulk density corresponds to the development of shrinkage cured under the same conditions after 10 days.

Fig. 4
figure 4

Development of drying bulk density

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Development of shrinkage

The drying shrinkage development of the three HWSCCs determined by continual measurement is plotted in Fig. 5. It is worth noting that the shrinkage tendencies of all the samples have a similar course with negligible differences within the first 10 days but with quick development. The same findings were reported by Lyu [49], who observed the shrinkage occurring mainly in the early stage till the 10th day. After this period, samples underwent shrinkage with different intensities in relationship with the bulk density of aggregates, showing that the higher the filler density, the higher the dry shrinkage value. It is known that magnetite significantly affects the magnitude of concrete shrinkage because the flux of moisture in the pore structure of concrete is mainly related to the restraining effect of the amount and type of aggregates.

Fig. 5
figure 5

Drying shrinkage development of samples

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Along with the determination of shrinkage characteristics and bulk density, the dynamic modulus of elasticity (DME) of samples was determined in a continuous regime under dry conditions. The results are reported in Fig. 6. Drying dynamic modulus of elasticity (DDME) is related to shrinkage within the first 15 days. It increases with increasing shrinkage. After this period, shrinkage, as well as dynamic modulus of elasticity, remains constant. Hence, a relationship between dry dynamic modulus of elasticity and dry bulk density development can be established, but a consistent correlation with dry shrinkage is difficult to find.

Fig. 6
figure 6

Development of drying dynamic modulus of elasticity

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Mechanical properties

The DME, compressive, and tensile strength measured at determined curing times of 7, 28, and 90 days are depicted in Figs. 7–9. While the DME is nearly constant for each specimen over the curing time (Fig. 7), compressive and tensile strength increase with increasing time but at different rates. Surprisingly, specimens made from magnetite with high bulk density have the highest compressive strength. The hardness of high-density aggregates plays a decisive role in improving the mechanical properties. Indeed, aggregates' crack and fissure propagation determines the stress resistance. Iffat [50] has established that denser concrete generally provides higher strength and fewer amounts of voids and porosity. The content of filler and water in concrete is the main factor influencing the mechanical properties. HWSCC2 has the highest aggregate content and the lowest water content.

Fig. 7
figure 7

Dynamic modulus of elasticity determined under wet conditions

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Fig. 8
figure 8

Compressive strength of HWSCC determined at different ages

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Fig. 9
figure 9

Tensile strength of HWSCC determined at different ages

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Three-point bending fracture test

The specimens used in the three-point bending fracture test to determine tensile strength have dimensions of 40 mm × 40 mm × 160 mm; an incision with a width of 2 mm and a depth of 10 mm was reserved in the middle of the bottom surface. Tensile strength depends on the type of specimens and, hence, on the density of fillers. The evolution of tensile strength is not excessive with time, with negligible variations within the standard statistic deviations.

At the macroscopic level, concrete comprises mortar, aggregates, and an interfacial transition zone (ITZ). The interfacial transition zone (ITZ) plays a key role in the compactness of concrete, affecting the compressive strength and overall porosity. Indeed, the interfacial transition zone [51] exists around aggregates (fillers) in concrete and always represents the weakest part, allowing crack propagation and aggressive element ingress, hence the strength-limiting phase in concrete.

The scanning electronic microscope images representing the cement paste matrix and the ITZ in concrete are shown in Fig. 10.

Fig. 10
figure 10

Microstructure of samples cured under wet conditions after 28 day strength measurement

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The sample was analyzed after mechanical tests. It is clear that the crack at ITZ is more pronounced in samples containing barite or mixed high-density aggregates than in samples with magnetite alone. The adhesion of cement matrix on aggregate is of great importance. Though aggregates are considered as inert filler in concrete, surface contact and adhesion force influence crack propagation and, hence, mechanical properties. When a mixture of barite and magnetite is used, the propagation of cracks with the same intensity as in the sample with barite alone is observed. It is probable that the crack initiated at ITZ of barite triggers a propagation that, once it reaches the surface of magnetite, continues its path with the same intensity. The improved mechanical properties of HWSCC containing magnetite are due to the higher packing of cement paste on the aggregate surface, leading to the reduced size and porosity of the interfacial transition zone (Fig. 10b). Furthermore, the reduced water-to-binder ratio and amount of magnetite in HWSCC2 are also responsible for the improvement of mechanical properties.

Pore structure analysis

After testing 28 day tensile and compressive strength, a matrix of hardened heavyweight self-compacting concrete was carefully extracted and analyzed by MIP to establish a correlation between mechanical properties and pore structure. The results of pore structure characteristics such as interparticle porosity (spaces between particles), intraparticle porosity (within particles), median pore radius, bulk density, and total surface area are reported in Table 7. These parameters, therefore, provide relevant information regarding the performance of heavyweight self-compacting Concrete. While HWSCC1 and HWSCC3 have similar pore characteristics, thus justifying similar mechanical properties, HWSCC2 containing magnetite as a filler presents different values. It is clear that a correlation between mechanical properties and intraparticle porosity affecting total porosity can be established. The bulk density determined by MIP corresponds to that experimentally measured.

Table 7 Pore characteristics of HWC samples
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The total surface area is the sum of the surface area of all pores and voids filled to pressure P.

Total porosity is the sum of interparticle porosity and intraparticle porosity.

These pore parameters result from the following equations [47]:

$$ {\text{Interparticle}} \,{\text{porosity}} \left( \% \right) = 100\frac{{V_{{\text{v}}} }}{{V_{{\text{b}}} }} $$
(3)
$$ {\text{Intraparticle}} \,{\text{porosity}} \left( \% \right) = 100\frac{{V_{{\text{t}}} - V_{{\text{v}}} }}{{V_{{\text{b}}} }} $$
(4)
$$ {\text{Mercury}}\, {\text{intrusion}} \left( {{\text{total}}} \right) {\text{porosity}} \left( \% \right) = 100\frac{{V_{{\text{t}}} }}{{V_{{\text{b}}} }} $$
(5)

where Vb is the bulk volume of the sample, Vv is the volume of mercury intruded up to the interparticle filling limit, and Vt is the total volume of mercury intruded up to the maximum pressure.

It can be remarked that intraparticle porosity (within particles) decreases with increasing bulk density of fillers. It may be dependent on the aggregate content in concrete. Indeed, magnetite has the highest bulk density and highest content. Median pore radius and total surface area express a good relationship with mechanical properties and bulk density of aggregate.

Another relevant demonstration of the pore structure difference is illustrated by particle size distribution shown in Fig. 11, where four regions on PSD curves can be clearly observed: 0–50 nm, 50–1000 nm, 1000–3000 nm, and 3000–60,000 nm. The difference in pore structure between different HWSCCs lies mainly in the 50–1000 nm regions corresponding to capillary pores, where HWSCC2 is distinguished by its absence. These capillary pores correspond to intraparticle porosity [48]. Other characteristics of PSD are almost similar. The presence of pores with a size between 50 and 1000 nm could express the size of ITZ around aggregates, as shown by SEM.

Fig. 11
figure 11

Particle size distribution of hardened heavyweight self-compacting concrete samples

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The figure illustrates the course and total intruded volume in concrete during the application of pressure from the minimum pressure to the highest one.

The cumulative pore volume depicted in Fig. 12 expresses the summation of mercury volume intruded into the pores and interparticle voids versus the applied pressure. It is clear that samples containing magnetite aggregate have the lowest volume intruded, characterizing thus the lowest porosity. If Fig. 12 shows the total summation of mercury intruded, Fig. 13 characterizes the change in the volume of mercury intruded per unit of interval pore radius. Dv(r) is calculated as follows [46]:

$$ D_{{\text{v}}} \left( r \right) = \frac{P}{r}\frac{{{\text{d}}V}}{{{\text{d}}P}} $$
(6)
$$ r = \frac{{2\gamma {\text{cos}}\theta }}{P} $$
(7)
$$ D_{{\text{v}}} \left( r \right) = \frac{{{\text{d}}V}}{{{\text{d}}P}}\left| {\frac{{P^{2} }}{{2\gamma {\text{cos}}\theta }}} \right| $$
(8)
Fig. 12
figure 12

Cumulative volume intruded

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Fig. 13
figure 13

Volume change as a function of the equivalent radius of applied pressure

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At high pressures (equivalent to low radius), the Dv(r) data are extremely sensitive to any slight fluctuation in the dV/dP term due to the multiplication by the P2 term in the above equation. It can be seen in Fig. 13 that volume change is the lowest for the sample containing magnetite. The results correlate very well with data depicted in Table 7 with regards to intraparticle porosity.

The mechanical properties (compressive and tensile, DME) are related to the porosity of concrete, which in turn is dependent on the water-cement ratio, degree of hydration, and aggregate characteristics [52]. In the case of investigated samples, binder, conditions of hydration, and water-to-binder ratio were the same, making us postulate that the hydration degree could be similar. The main factor affecting mechanical properties is the type of fillers. Indeed, aggregate size, shape, and surface roughness affect the quality of the ITZ, packing density, and bond between cement paste and aggregate.

Conclusions

The development of heavyweight self-compacting concrete has met the conformity requirements of two different classes of concrete: self-compacting concrete with rheological parameters according to The European Guidelines for Self-Compacting Concrete and heavyweight concrete with a bulk density exceeding 2600 kg m−3. To achieve these goals

  1. 1.

    The composition of the binder was optimized based on hydration using a conduction calorimeter to avoid thermal stress.

  2. 2.

    Particle size distribution (grading curve) of fillers was carefully optimized with a maximum size not exceeding 2 mm.

  3. 3.

    Aggregate content in heavyweight self-compacting concrete is lower than in ordinary heavyweight concrete or self-compacting concrete.

  4. 4.

    The consistency parameters as determined by V-funnel, S-Cone diameter, and S-Cone time are at the limit of those reported in different literatures due to the fact that heavyweight self-compacting concrete is special concrete.

  5. 5.

    Magnetite aggregate provides higher mechanical properties, tighter adhesion at the interfacial transition zone, and denser pore structure than barite or a mix of barite and magnetite.

  6. 6.

    Curing conditions have influenced bulk density, shrinkage, and dynamic modulus of elasticity.