 Vietnamese steel-slag as an aggregate (called steel-slag concrete): Lam et al. [22][23][24] suggested to apply the steel-slag aggregate for roller-compacted concrete pavement, while Nguyen et al. [25,26] and Tran et al. [27] studied steel-slag aggregate for making concrete used in structural members. Although these references provided some information on steel-slag concrete, further investigation is still required as follows: (a) The compressive strength is always the key parameter of normal concrete and/or high-performance concrete. This is due to their strengths under compression being much greater than those under tension, even for strain-hardening fiber-reinforced concrete with its high tensile strength more than 10 MPa [28][29][30]. On the other hand, the compression strength of concrete has been well known to depend upon time during cement hydration, and clear information on compressive strength of steel-slag concrete will help better utilization of this concrete type, e.g., how significant is 28-day compressive strength in comparison with one-year compressive strength? In general, time is the main influencing factor affecting the construction progress. (b) The scale effect of traditional concrete has been investigated for decades: the mechanical properties of traditional concrete were highly size and shape-dependent due to its brittle nature [31][32][33][34]. In compression, there have been two main different testing standards for compressive specimens using cubic shape or cylindrical shape. The cylindrical shape, with a size of 150 mm in diameter and 300 mm in height, has been applied mostly in Canada, United States, and Australia, whereas the cubic shape with dimensions of 150 mm or 100 mm have been applied mostly in Europe and Vietnam [35]. The Vietnamese standard TCVN 8218:2009 [35] provides conversion factors for the compressive strength of traditional concrete with various specimen sizes and shapes. Nonetheless, the size and shape-dependent compressive strength of steel-slag concrete is still questionable, and it should be investigated and compared with that of traditional concrete using existing models/theories. The clear understanding of the size and shape effect on the strength of steel-slag concrete would help civil engineers properly design structural members using steel-slag concrete. (c) For traditional concrete, Poisson's ratio was reported to be from 0.15 to 0.2 for normal-weight (ACI 318 [36]). Is the value of Poisson's ratio for steel-slag concrete similar to traditional concrete?
The above questions have motivated this investigation, with specific objectives listed as follows: (1) to discover the age-dependent compressive strength of the steel-slag concretes, (2) to investigate the modulus of elasticity and Poisson's ratio of steel-slag concrete, (3) to explore size and shape-dependent compressive strength of the steel-slag concrete, and, (4) to investigate the effect of water amount added in mixture on compressive properties of steel-slag concrete. Except objective 1, the other objectives were studied with experimental tests at the 28-day age.

Materials and Specimen Preparation
In the previous studies [25,26], the authors investigated the compositions of steel-slag concretes in a wide range of partial materials to achieve the best workability and mechanical strengths, and these properties were then compared with those of traditional concretes using natural aggregate. Based on the initial studies, this research would focus on the steel-slag concrete with compressive strength ranging from 30 to 45 MPa. The compositions of three types of steel-slag concretes were presented in Table 1 and their names were as follows: XT01, XT02, XT03 containing cement/water (C/W) ratios of 1.76, 2.00, 2.21, respectively (i.e., W/C ratios of 0.57, 0.50, 0.45, respectively). In all types, steel-slag material was designed as the coarse aggregate while the fine aggregate was river sand. Figure 1 presents the layout of the testing program in this study. It was noticed that there were two types of steel-slag from an electric arc furnace: black slag (electric arc furnace slag, EAFS) and white slag (ladle furnace slag, LFS) which were generated by remelting unalloyed and alloyed steel waste, respectively [37]. The steel-slag aggregate used in this study was black slag, as shown in Figure 2a. Figure 2b presents the photos of the prepared specimens. The size distribution of fine aggregate particles and coarse aggregate particles were displayed in Table 2. Table 3 supplies the physical properties of the steel-slag material used while Table 4 provides the chemical composition of steel-slag material. For the task of objective 1, the compressive specimens were tested using cube specimens of 100 mm. In the task of objective 2, the cylinder specimens with dimensions of 100 × 300 mm (diameter × height) were tested regarding ASTM C469 [38]. For objective 3, six types of sizes and shapes of the specimens would be prepared as follows: cube 70.7 mm, cube 100 mm, cube 150 mm, cylinder 70 mm, cylinder 100 mm and cylinder 150 mm in diameter; the cylinder height was designed to be double of the diameter. The 100 mm cube specimens were also used for objective 4. The cement type was used in this study was PCB40 INSEE, produced from Vietnam.      A laboratory mixer with a volume of 150 liters was used to mix materials. All casted specimens were placed for 24 h in a laboratory with a temperature of 28 ± 5 • C prior to demolding, and after that, they were cured in water with temperature of 25 ± 5 • C. It was noticed that the temperature in laboratory and in the water tank mentioned above were very common in southern Vietnam, thus it was very suitable to practically apply the steel-slag concrete referring to the test results. The curing time depended upon the study objective. Next, the cured specimens were moved out of the water Materials 2020, 13, 1928 5 of 19 tank and dried at room temperature. For each series, at least three specimens were examined and then averaged for investigating the material properties.

Test Setup and Procedure
A MATEST machine with 150-ton capacity, as shown in Figure 3a, was used for the experimental tests. The machine was used by applying displacement-controlled loading under speed of 1.0 mm/min for all specimens. It was noticed that the cylinder compressive specimens should have their surfaces smoothed carefully before testing. All tests were conducted at room temperature of 28 ± 5 • C and relative humidity of 70-80%. The compressive strength (named f c ) was given by Equation (1), as the ratio of maximum applied load (P max ) to the section area of the specimen section (A). Figure 3b presents the 150 mm-diameter cylinder with a frame attached according to ASTM C469, for measuring both axial and lateral displacement during testing.
Materials 2020, 4, x FOR PEER REVIEW 6 of 22 presents the 150 mm-diameter cylinder with a frame attached according to ASTM C469, for measuring both axial and lateral displacement during testing.  Table 5 and Figure 4 show the compressive strengths ( ) of the steel-slag concretes with dependence upon testing age (t). As shown in Figure 4, the compressive strengths, regardless of steelslag concrete types, developed quickly at the early testing age, and more and more slowly at later   Table 5 and Figure 4 show the compressive strengths ( f c ) of the steel-slag concretes with dependence upon testing age (t). As shown in Figure 4, the compressive strengths, regardless of steel-slag concrete types, developed quickly at the early testing age, and more and more slowly at later testing age. This observation was completely consistent with normal concrete [36]. At any testing age, the order of steel-slag concrete in terms of compressive strength was not changed as follows: XT03 > XT02 > XT01, i.e., the compressive strength increased with increasing of the C/W. The compressive strength at 7 days and 28 days were about 55-66% and 69-73% of the compressive strength at 365 days, respectively.    Figure 5 shows the photos describing a typical cracking behavior of the steel-slag concretes: the failure crack propagated across the steel-slag particles (coarse aggregate), and this may be attributed to the lower strength of coarse aggregate (e.g., steel-slag) in comparison with the mixture strength. In order to predict the f c at any value of t, the relationship between f c and t should be mathematically modeled. Based on the shapes of testing performances on Figure 4, a hyperbolic curve was suggested to fit the testing curves using Equation (2). The suggested equation was completely satisfied with the boundary condition: as the testing age was zero, the compressive strength of steel-slag concrete would be zero, and, as the testing age reached infinity, the compressive strength would reach a constant value.

Dependence of Compressive Strength on Testing Age of Steel-Slag Concretes
Here a and b are the constants characterizing material properties. To obtain the values of a and b, Equation (2) was changed into Equation (3).
Equation (3) was in linear relationship with a common expression of Using the least square method with linear regression, the value of a and b can be obtained. Equation (4) and Figure 4a provide the results of linear regression analyses while Equation (5) and Figure 4b provide the analyzed relationships between compressive strength and testing age of three steel-slag concretes.  Note: These data use the cubic specimen