Development of strength and elastic modulus of concrete sealed in steel tube under sustained load at early age

Abstract

Concrete-Filled Steel Tubular Structures (CFSTSs) have become popular among the structural engineering community due to significantly higher load carrying capacity compared to conventional reinforced-concrete structures. Much research has been conducted on understanding the behavior of CFSTSs under various loading conditions and design theories have been established to predict the load carrying capacities of such structures. However, existing models do not consider the effects of sustained early loads on concrete strength and elastic modulus development of CFSTSs. With the need for rapid construction, CFSTSs may be subjected to loading at an early stage before concrete is fully cured. Such early loading may incur negative effects on strength and elastic modulus development of concrete within the confined environment. This paper propose theoretical models based on the compressive packing model (CPM) to simulate strength and elastic modulus development of early-age concrete under sustained stress. Development of concrete properties at early age is described using Hydration kinetics, and maximum paste thickness in the CPM model is modified using energy conservation to simulate sustained loads. Early concrete strength and the elastic modulus development rules were investigated experimentally for sustained loads. Predictions from the proposed models are compared with conventional models from CEB-FIP Model Code. Results showed that when loaded at a very early stage, a relatively high stress to strength ratio will result in causing damage in concrete. Such damage significantly affects the strength and elastic modulus development. Compared with concrete loaded at 28 days, concrete loaded at early stages showed significant reduction in concrete strength and elastic modulus.

Keywords

compressible packing model concrete early loading age elastic modulus strength development sustained load

Introduction

Concrete-Filled Steel Tubular (CFST) structural members have become popular among the construction engineers due to its many advantages over reinforced-concrete (RC) structural members. These advantages include high strength, increased ductility, as well as the ease of construction (Huang et al., 2016; Li et al., 2018). CFST structures (CFSTSs) have been widely used in bridge construction in China (Han, 2010; Xie et al., 2018). In CFSTSs, outer steel tube provides confinement to the concrete core. Therefore, the outer steel tube not only increases the concrete strength but also provides higher ductility as the main tensile reinforcement to the members. In addition, steel tube also acts as stay-in-place formwork for concrete casting, thus eliminating the need for additional formwork.

Due to increase demand for rapid construction, and considering the presence of the outer steel tube of CFSTSs, such structural members are often subjected to loading earlier than that in other types of structure. Due to support from outer steel tube, early-age concrete core is commonly regarded as being unstressed during construction of CFSTSs. However, in practice concrete can be subjected to loads at very early stage due to effects of shrinkage, temperature, gravity, or mold deformation. This is particularly relevant in the case of long-spanning relatively large cross section CFSTSs such as bridge arches, where early concrete stress can be significantly large relative to its strength. Early loading could induce damage in concrete, reducing its strength (Shen et al., 2016), which may influence overall structural performance both at early stage and post cure stage (Bergström and Byfors, 1980). Due to adopting in-situ test results, the current practice cannot consider possible damage of concrete due to early-age loading, thus may overestimate the strength and elastic modulus of concrete. Therefore, for CFSTSs, where early loading of concrete is possible to occur, structural concrete strength and elastic modulus estimations should consider effects from early loading.

Concrete mechanical properties are developed through time dependent chemical processes, thus strength and elastic modulus develops over a long period of time. Many efforts have been made to develop theoretical models to predict the concrete strength and elastic modulus development with time (e.g. Fédération Internationale du Béton (fib), 2012; Gencoglu et al., 2012; Taerwe and Caspeele, 2012; Wang and Luan, 2018; Yazdani et al., 2006), some on strength and elastic modulus development at early age (e.g. Beushausen et al., 2012; Jin et al., 2017; Kim et al., 2002a, 2002b), and some on the effects of preload on concrete-filled composite members (e.g. Li et al., 2019; Liew and Xiong, 2009, 2012; Papanikolaou et al., 2013; Patel et al., 2013, 2014), but only few considered early age and sustained loads. Some of the existing models are discussed in section 2 of this paper.

Against this background, this paper presents a study investigating the development of concrete strength and elastic modulus under early age sustained loads. Hydration kinetics is introduced on the basis of the compressible packing model (CPM) to simulate early concrete hydration, and maximum paste thickness (MPT) is modified to incorporate the effects of sustained loads. Two models are proposed to predict early concrete strength and elastic modulus development under sustained loads. Test specimens were prepared and loaded at different ages to obtain experimental data on strength and elastic modulus development of concrete under early age sustained loads. These experimental data were then used to obtain the empirical constants of the proposed theoretical models.

Strength and elastic modulus development models

Compressible packing model

Concrete is a mix of many constituents of different chemical composition and size. Particles of different sizes are randomly distributed making an inhomogeneous structure in mesoscale. These in-homogeneities presents significant challenges in establishing a theoretical model for concrete strength and elastic modulus development. De Larrard (1999) proposed a compressible packing model (CPM) to consider the influences of accumulation of aggregate compactness and close grained effects on concrete mixing (De Larrard, 1999), which can provide an approach to characterize the mixtures. De Larrard’s (1999) model for CPM was used as the basis for development of the strength models for concrete (De Larrard, 1999).

Strength development model

To simulate the relationship between strength and material composition, concrete is regarded as a two-phase material, including aggregates and cement paste, which is assumed homogeneous in a representative volume. De Larrard’s (1999) model assumed that coarser particles, which are acting as a support bed for surrounding soft medium composed of smaller particles, bear the maximum stress when a dry accumulation is subjected to an external load. In a random packing process, the coarse particles contact each other, as a result maximum stress occurs at the contact points. When cement paste is injected into the particle accumulation, where the paste volume exceeds that of the interstitial space in the dry accumulation, the particle accumulation expands evenly and becomes homogeneous gradually then a layer of cement paste under high stress is formed between any two coarse particles. The thickness of this cement layer is defined as maximum paste thickness (MPT), and its formation process is shown in Figure 1. MPT is related to concrete strength, expressed as (De Larrard, 1999):

MPT = d (\sqrt[3]{\frac{g^{*}}{g}} - 1)

(1)

Figure 1.

Maximum paste thickness formation.

where d is the maximum size of aggregate, g is the aggregate volume in unit volume of concrete after expansion, and g* is the volume of aggregate in a unit volume of particle accumulation before injecting cement paste (i.e. the packing density of the aggregate).

The simplified and universal Féret’s (1892) equation is commonly use to predict the concrete strength considering the influence of the cement paste and topological structure of aggregate (De Larrard, 1999):

f_{c} = f_{m} \cdot MP T^{- 0.13}

(2)

where f_c is the concrete strength (MPa), and $f_{m}$ is the cement paste strength at 28 days (MPa) given by:

f_{m} = K_{g} R_{c 28} (1 + ρ_{c} \frac{V_{W} + V_{a}}{c})^{- 2}

(3)

where K_g is a constant related to the aggregate, R_c28 is the ISO strength of the cement at 28 days (in MPa), ρ_c is the specific gravity of the cement (in kg/m³), c is the cement mass (in kg), and V_w and V_a are the volume (in m³) of water and air respectively.

Properties of the aggregates are assumed to be constant over time. With this assumption, concrete compressive strength at any age is given by (De Larrard, 1999):

f_{c} (t) = K_{g} R_{c 28} (d (t) + {(1 + ρ_{c} \frac{V_{W} + V_{a}}{c})}^{- 2}) MP T^{- 0.13}

(4)

where d(t) is a kinetics parameter at age t, which depends on the type of cement used.

Elastic modulus model

The triple sphere model of concrete elastic modulus, which is also based on CPM, is widely accepted by the research community to predict the concrete elastic modulus and can be expressed as (De Larrard, 1999):

E = [1 + 2 g \frac{E_{g}^{2} - E_{m}^{2}}{(g^{*} - g) E_{g}^{2} + 2 (2 - g^{*}) E_{g} E_{m} + (g^{*} + g) E_{m}^{2}}] E_{m}

(5)

where E_g, E_m, and E represent the elastic modulus of aggregate, cement matrix, and concrete composite material respectively. De Larrard and Belloc (1997) found experimentally that cement paste elastic modulus can be considered proportional to cement paste compressive strength at 28 days and given by:

E_{m} = φ f_{m}

(6)

where $φ$ is a constant that needs to be regressed.

Compressive strength development model

Kinetics parameter at age t, d(t) in equation (4) was found to vary linearly with log(t), but was only defined for t > 7 days (Baron et al., 1993), and sustained loads were not considered. Therefore, to account for early age sustained loads, equation (4) needs to be modified. Proposed modifications to equation (4) are presented next.

Hydration kinetics

Hydration kinetics have been used in the existing literature to characterize cement mechanical property development based on microscopic physical and chemical reaction mechanisms (Kirby and Biernacki, 2012; Valentini et al., 2014). Therefore, in order to model concrete strength development for t < 7 days, hydration kinetics function was introduced into the CPM.

Bentz (1997) proposed a simplified model of hydration kinetics on the basis of total, φ_T(t) and water filling, ϕ_W(t) porosity coefficients, which can be expressed as:

{\begin{matrix} ϕ_{W} (t) = \frac{ρ_{cem} (w / b) - (f_{\exp} + ρ_{cem} CS) α (t)}{1 + ρ_{cem} (w / b)} \\ ϕ_{T} (t) = \frac{ρ_{cem} (w / b) - f_{\exp} α (t)}{1 + ρ_{cem} (w / b)} \end{matrix}

(7)

where w/b is the water to binder ratio, α is the degree of hydration of the system, ρ_cem is the proportion of cementing material taken as 3.2, CS is the cement chemical shrinkage taken as 0.07 mL/g (Bentz, 2006), and f_exp is the coefficient of volumetric expansion for the cementing system taken as 1.15 (Bentz, 1997; Snyder and Bentz, 2004).

Hydration velocity mainly depends on $ϕ_{W} (t)$ and colloid un-hydration rate, γ(t) and can be expressed as;

d α / dt = k ϕ_{W} (t) γ (t)

(8)

where colloid un-hydration rate is given by:

γ (t) = \frac{1 - α (t)}{1 + ρ_{cem} (w / b)}

(9)

Substituting equations (7) and (9) into equation (8) gives:

α (t) = \frac{m {\exp [R (1 - m) t] - 1}}{\exp [R (1 - m) t] - m}

(10)

where $m = ρ_{cem} (w / b) / (f_{\exp} + ρ_{cem} CS)$ , $R = {k (f_{\exp} + ρ_{cem} CS) / [1 + ρ_{cem} (w / b)]}^{2}$ , and k is a proportional constant that changes with the cement chemical composition and curing temperature.

Since cement hydration can be influenced by fly ash content (Zhang and Sun, 2006), a factor K for fly ash was also introduced, thus modifying the equation (10) to be:

α (t) = K \cdot \frac{m {\exp [R (1 - m) t] - 1}}{\exp [R (1 - m) t] - m}

(11)

where K = 0.02x+1, and x = 1–5 corresponding to fly ash content of 10%, 20%, 30%, 40%, and 50% respectively.

Cement paste strength was modified using α(t) to consider t < 7 days, and considering α(t)∝f_m(t)/f_m(28), the cement paste compressive strength is expressed as:

f_{c} (t) = K_{g} R_{c 28} (α (t) \cdot {(1 + ρ_{c} \frac{V_{W} + V_{a}}{c})}^{- 2}) MP T^{- 0.13}

(12)

Modifying maximum paste thickness to consider sustained load effects

When concrete is under no external load, the volume evenly expands due to initial stress, σ₀ in the pressure system, and MPT is formed between neighboring aggregates. When we impose an external stress, σ’ MPT becomes MPT’, as shown in Figure 2, and work on coarse aggregate can be expressed as:

Δ W_{g} = - MPT' \cdot π \frac{d^{2}}{4} σ'

(13)

Figure 2.

Comparison between two MPT formation progress under external load.

where d is the effective diameter of a coarse aggregate particle, which can be approximated by the average aggregate diameter.

Therefore, work on the cement paste is given by:

Δ W_{c} = \frac{1}{2} k_{m} {(MPT' - MPT)}^{2}

(14)

where $k_{m}$ is the cement mortar stiffness given by:

k_{m} \propto \frac{E_{m} \cdot π d^{2}}{4 \cdot MPT}

The relationship between internal and external work is:

Δ W = (V_{g} \cdot Δ W_{g} + V_{c} \cdot Δ W_{c}) / V

(15)

where V is the specimen volume; and V_c and V_g are the total cement paste and aggregate volumes, respectively.

If volume is constant (i.e. the cement is incompressible), then total work = 0, and equation (15) becomes:

V_{g} \cdot Δ W_{g} + V_{c} \cdot Δ W_{c} = 0

(16)

Substituting equations (6), (13), and (14) into equation (16) gives:

MPT' = δ \cdot MPT

(17)

where a/c is the volume ratio of the aggregate and cement, and

δ = [1 + \frac{(a / c) σ'}{φ f_{m}}] + \sqrt{{[1 + \frac{(a / c) σ'}{φ f_{m}}]}^{2} - 1}

The cement paste strength development model considering early and sustained load can be expressed as:

f_{c} (t) = K_{g} R_{c 28} α (t) \cdot (1 + ρ_{c} \frac{V_{W} + V_{a}}{c})^{- 2} (δ \cdot MPT)^{- 0.13}

(18)

From equation (6), cement paste elastic modulus can be expressed as

E_{m} = φ f_{m} = φ \cdot α (t) \cdot (1 + ρ \frac{V_{w} + V_{a}}{c})^{- 2}

(19)

and the elastic modulus development model can be established from equation (5) by substituting equation (19) for $E_{m}$ .

Experimental setup and procedure

This section presents the details of an experimental program aimed at investigating the influence of different sustained loading on strength and elastic modulus of concrete. According to the mechanical characteristics of concrete-filled steel tube, the existence of outer steel tube restrains the concrete core and improves the strength of composite members. The confined effect between steel tube and concrete will become significant as the concrete core reaches or approaches the strain peak value, which means the confined effect of steel tube on concrete core is relatively small before the concrete core reaches its peak strength (Mander and Priestley, 1988). Therefore, bolted steel molds were adopted and groups of cylindrical concrete specimens were casted and subjected to the sustained load within steel tube at different ages. Compressive strength and elastic modulus of the demolded concrete core were tested until the scheduled unload time. The experimental details are as follows.

Material and mixture

The concrete was prepared with ordinary Portland cement (ρ_c = 3100 kg/m³), coarse aggregates (5–25 mm), and sand (0.08–2.0 mm). Concrete mix proportions are given in Table 1, while the cement chemical components is shown in Table 2.

Table 1.

Concrete mixture proportions (kg/m³).

Cement	Fly ash	Fine aggregate	Coarse aggregate	Water	Admixture
378	42	809	1029	162.5	5.76

Table 2.

Cement chemical components.

Component	CaO	SiO₂	Al₂O₃	Fe₂O₃	MgO	Na₂O	K₂O	MnO	TiO₂	P₂O₅	SO₃	L.O.L
Proportion (%)	63.66	22.42	6.11	4.34	0.92	0.22	0.55	0.14	0.23	0.05	0.26	0.51

Specimen preparation

A total of 48 cylindrical concrete specimens with 113 mm diameter and 226 mm height were prepared in 16 groups according to ICS (2009). To ensure concrete core could be taken out of the steel confinement for strength and elastic modulus testing, each steel tube was manufactured as two pieces and assembled to a tube (Figure 3) before casting concrete. The concrete casting was carried out according to GB/T 50082 (Ministry of Housing and Urban-Rural Development of the People’s Republic of China, 2009). Four longitudinal strain gauges were uniformly attached to the outer surface of the steel formwork near the height of 56.5 mm, and the readings were checked during the loading to ensure concentric loading.

Figure 3.

Specimen mold.

Test setup and loading procedure

To ensure the specimen could bear loads very early (2 h after forming), the specimens were subjected to the sustained load within steel tube until the scheduled unload time, then the specimens were demold and loaded under axial compression to test the compressive strength and elastic modulus of concrete, as shown in Figure 4. The surfaces of the specimens were swiped and the upper and lower surfaces were polished to ensure a smooth surface. A set of three specimens were placed in the center of the lower plate of the test machine, as shown in Figure 5.

Figure 4.

Process of specimen preparation.

Figure 5.

Loading equipment.

Specimens were started to load at 2 h, 12 h, 1, 3, and 7 days after casting, while unloading and testing was done at different states at times 12 h, 1, 3, 7, and 28 days after the casting of concrete. The exact loading and testing times of different specimens are detailed in Table 3. For each loading start time-testing time configuration, three identical specimens were tested. For ease of reference, each specimen was given a name starting with an alphabetical letter (“A” for 2 h load start time, “B” for 12 h load start time, “C” for 1 day load start time, “D” for 3 days load start time, “E” for 7 days load start time, and “F” for no sustained loading), followed by a number to indicate the testing time (12 for 12 h, 1 for 1 day, 3 for 3 days, 7 for 7 days and 28 for 28 days), followed by a roman number to differentiate between three identical specimens. For an example, A-1-I means the first specimen loaded at 2 h after concrete casting and tested 1 day after concrete casting.

Table 3.

Specimen assignment.

Loading time	Unloading/testing time					Quantity*
Loading time	12 h	1 d	3 d	7 d	28 d	Quantity*
2 h	A-12	A-1	A-3	A-7	A-28	5 × 3
12 h	—	B-1	B-3	B-7	B-28	4 × 3
1 day	—	—	C-3	C-7	C-28	3 × 3
3 days	—	—	—	D-7	D-28	2 × 3
7 days	—	—	—	—	E-28	1 × 3
None	—	—	—	—	F-28	1 × 3
					Total:	48

a × b means the quantities of specimen in one group is b, and the number of groups is a.

Since concrete strength in the mold develops with time, it is difficult to determine a constant axial compression load. Therefore, following the study of Han and Yao (2003), 46.36 kN load was imposed on the specimens using loading machines as shown in Figure 5. 46.36 kN was 40% of the compressive bearing capacity of the steel tube. Each group of specimens were subjected to the sustained load until the scheduled unload time, then the external steel tubes were dismantled and concrete cylinders were loaded under axial compression to failure using an electro-hydraulic servo controlled pressure testing machine. When the testing machine started, upper pressure plate was adjusted to be close to but not touching the upper surface of the specimen, and then load was applied at a uniform speed until the specimen is failure. As the specimen is failure, the testing machine automatically stops and generates a stress-strain curve of compression test. The compressive strength of the concrete specimen can be obtained by the peak of the stress-strain curve and elastic modulus was also obtained from the experimental stress-strain curve slope.

Experimental results

Tables 4 and 5 show the compressive strength and elastic modulus test results of the concrete cylinders. Figures 6 and 7 show the measured concrete strength and elastic modulus development, respectively for specimens with sustained load applied at different stages. It can observed from Table 4 and Figure 6 that trend of the strength development under sustained loading is similar for concrete loaded at different age. The compressive strength of the specimens loaded after 2-h increases with time, and the compressive strength at age of 12 h, 1 day, 3 days and 7 days is 5.45%, 14.66%, 55.25% and 84.14% of that of 28 days, respectively. It can be seen that the strength increases sharply before 7 days, among which the strength increases most sharply from 1 to 3 days. With the increase of time, the growth rate decreases gradually and the strength tends to be stable. Difference in concrete 28 days compressive strength for specimens with sustained loading compared to that of unloaded specimens was found to be 0.91, 1.02, 1.03, 1.05, and 0.97 times for specimens loaded after 2 h, 12 h, 1 day, 3 days, and 7 days respectively.

Table 4.

Compressive strength test results of concrete cylinders under sustained stress.

No.	Loading age	Testing age	Compressive strength (MPa)
A-I	2 h	12 h	1.81
A-II	2 h	1 day	4.87
A-III	2 h	3 days	18.36
A-IV	2 h	7 days	27.96
A-V	2 h	28 days	33.23
B-I	12 h	1 day	6.73
B-II	12 h	3 days	22.55
B-III	12 h	7 days	29.62
B-IV	12 h	28 days	37.41
C-I	1 days	3 days	23.42
C-II	1 days	7 days	30.86
C-III	1 days	28 days	37.80
D-I	3 days	7 days	30.49
D-II	3 days	28 days	38.22
E-I	7 days	28 days	35.76
F-I	—	28 days	36.54

Table 5.

Elastic modulus test results of concrete cylinders under sustained stress.

No.	Loading age	Testing age	Elastic modulus (GPa)
A-I	2 h	12 h	2.36
A-II	2 h	1 day	2.65
A-III	2 h	3 days	17.22
A-IV	2 h	7 days	22.83
A-V	2 h	28 days	26.50
B-I	12 h	1 day	5.80
B-II	12 h	3 days	17.92
B-III	12 h	7 days	24.65
B-IV	12 h	28 days	29.98
C-I	1 day	3 days	19.04
C-II	1 day	7 days	25.42
C-III	1 day	28 days	29.25
D-I	3 days	7 days	25.01
D-II	3 days	28 days	28.72
E-I	7 days	28 days	27.91
F-I	—	28 days	28.22

Figure 6.

Concrete compressive strength development for different loading ages.

Figure 7.

Concrete elastic modulus development for different loading ages.

The similar phenomenon can be found for elastic modulus from Table 5 and Figure 7. The elastic modulus of the specimens loaded after 2-h increases with time, and the elastic modulus after 12 h, 1 day, 3 days and 7 days is 8.91%, 10.00%, 64.98% and 86.15% of that of 28 days, respectively. It can be seen that the elastic modulus increases sharply before 7 days and the growth rate decreases gradually and the elastic modulus tends to be stable. Difference in concrete 28 days elastic modulus for specimens with sustained loading compared to that of unloaded specimens was found to be 0.93, 1.06, 1.04, 1.02, and 0.99 for specimens loaded after 2 h, 12 h, 1 day, 3 days, and 7 days respectively.

Therefore, loading influence on concrete strength and elastic modulus development may be neglected for load commencement after 12 h. Therefore, only the data related to specimens “A” are considered hereafter.

Parameter regression and model validation

Strength development model

Experimental data from specimens A was used to calibrate the parameters K_g, k, and $φ$ in equation (18). Values of the other parameters used for regression analysis to determine K_g, k, and $φ$ are given in Table 6. Least squares multiple nonlinear regression was adopted to quantify the three parameters. Considering the physical interpretation of each parameter, optimal value was searched in a given interval. The regression analysis was conducted using MATLAB software (MathWorks, 2014). The fitted parameter values are shown in Table 7, and the coefficient of multiple determination of the obtained result was 0.9646.

Table 6.

Parameters determined before regression.

Fly ash content	$ρ_{c}$ (kg/m³)	$V_{w}$ (m³)	$V_{a}$ (m³)	$CS$ (mL/g)	$w / b$	$d$ (mm)
10%	3100	0.1625	0	0.07	0.387	25
$R_{c 28}$ (MPa)	$\bar{σ}$ (MPa)	f _exp	$c$ (kg)	MPT (mm)	$a / c$
52.5	4.62	1.15	378	2.0	3.07

Table 7.

Regressed parameters.

Parameter	K_g	k	$φ$
Fitting value	4.714	0.9798	171.3

Predictions from the proposed model and the predictions from CEB-FIP Model Code (fib, 2012) without (fib, 2012) and with (fib, 2012 sus) sustained load are compared with the test results in Jiao et al. (2020) and test results of specimens “A” in this experiment in Figure 8. Proposed model shows the best agreement with the data, which is expected as the same data was used to determine the model parameters. The CEB-FIP model with sustained loading provide good accuracy at early stage, but over predicts the strength at 28 days. CEB-FIP model without sustained loading, significantly over predicts the compressive strength development but is most close to the test results in Jiao et al. (2020), which does not consider the influence of sustained load at early age, either. Therefore, in terms of 28 days compressive strength, CEB-FIP models provide non-conservative results, while proposed model can provide more accurate predictions.

Figure 8.

Comparison of strength development models for early sustained loaded concrete.

Elastic modulus model

Figure 9 compares the experimental elastic modulus with fib (2012), fib (2012) sus, test results in Jiao et al. (2020), and proposed model. The trend is similar to that in Figure 8. It can be seen that the test results in Jiao et al. (2020) is significant larger than the test results in this study due to ignoring the effect of sustained loading at early age. The proposed model shows the best agreement with experimental outcomes, and the fib (2012) model shows the largest deviation. However, in terms of elastic modulus at 28 days, CEB-FIP model with sustained loading only slightly over predicts the elastic modulus than the proposed model.

Figure 9.

Comparison of elastic modulus development for early sustained loaded concrete.

Discussion

When concrete is under sustained load, the strength and elastic modulus development of the concrete are subject to two distinct effects: increasing caused by solidification and decreasing caused by damage. Stress level of the applied load determines which of the two is dominant. In this study, specimens “A” were subjected to sustained loaded after 2 h to simulate the working state of CFST members that the concrete core did not have enough strength after concrete pouring. In this case, setting and hardening process of the concrete core is affected by external forces, which means early age loading leads to the slowing down of cement hydration process, thus hindering the development strength and elastic modulus of concrete core. According to the experimental results, the strength and elastic modulus of concrete decrease under early-age loading, indicating that the decreasing effect of 2-h early-age loading on the compressive strength and elastic modulus of concrete is dominant. It can be observed from Figures 8 and 9 that the test results in Jiao et al. (2020) are significant larger than that of this study due to ignoring the effect of sustained loading at early age, which demonstrates that early-age and sustained loads are two major factors that must be considered in modeling concrete strength and elastic modulus development.

Figure 10 shows concrete stress-to-strength ratio, $σ' (t) / f_{c} (t)$ , where $f_{c} (t)$ is the concrete strength at age t. The 2 h loaded specimens reached 45% of the 12-h strength of the specimens, showing that early damage occurred because the applied stress exceeded the concrete proportional elastic limit (approximately 40%). Thus, the experiments verified that concrete has insufficient early strength. Current practice to avoid concrete cracking early usually employs high strength concrete in structures likely to be exposed to early loading. However, the proposed model, validated experimentally, shows that high strength concrete will still have relatively low early strength. Therefore, reducing early stress will be more effective than increasing concrete strength, for example, by providing temporary structural support for the first several days after concrete pouring.

Figure 10.

Concrete stress-to-strength ratio at different ages.

The other specimens showed stress levels <25%, which suggest these specimens strengths would not be influenced by such low stress levels. However, 28 days strengths of specimens loaded at 12 h, 1 day, and 3 days were higher than non-loaded specimens, as shown in Figure 6. Thus, early but low stress could strengthen concrete, which is consistent with Reference (Han et al., 2016).

Figures 6 and 7 also show that 2 h loaded specimen strength and elastic modulus were lower than all other specimens at 28 days. This shows that the relative high stress to strength ratio resulting from the very early loading (2 h) influenced strength and elastic modulus development in later periods.

The proposed models depended on test time, similar to other concrete strength models. Model verification was limited to the specific experiment range of this study, and more test data is required to validate the obtained parameter values to ensure model stability.

Conclusions

Early and sustained loads are two major factors that must be considered in modeling concrete strength and elastic modulus development. Therefore, compressible packing model (CPM) based models were proposed to predict concrete strength and elastic modulus explicitly incorporating considerations for early and sustained load. The proposed models in this paper are simple and efficient, and can be easily modified to suit various structural design codes for practical design purposes. The developed models were compared against experimental outcomes and models suggested in CEB-FIP Code. The proposed model showed superior agreement to experimental outcomes for all early loading ages investigated.

Very early age loading (e.g. loading just 2 h after casting) significantly influenced concrete strength development, mainly because the stress to strength ratio for very early age loaded concrete was relative high (reaching 45% for 2 h loading age), thus resulting in damage, and had a significant effect on strength and elastic modulus development.

Footnotes

Acknowledgements

The authors appreciate LetPub () for its linguistic assistance during the preparation of this manuscript.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research received funding from the China National Natural Science Foundation (Grant Nos. 51678030 and 51708020), and the Transportation science and technology program of Hebei Province (Grant No. QG2018-8).

ORCID iDs

Yuying Jiao

Dilum Fernando

References

Baron

Bascoul

Escadeillas

, et al. (1993) From clinker to concrete-An overall modeling. Materials and Structures 26(6): 319–327.

Bentz

(1997) Three-dimensional computer simulation of Portland cement hydration and microstructure development. Journal of the American Ceramic Society 80(1): 3–21.

Bentz

(2006) Influence of water-to-cement ratio on hydration kinetics: Simple models based on spatial considerations. Cement and Concrete Research 36(2): 238–244.

Bergström

Byfors

(1980) Properties of concrete at early ages. Materials and Structures 13(3): 265–274.

Beushausen

Alexander

Ballim

(2012) Early-age properties, strength development and heat of hydration of concrete containing various South African slags at different replacement ratios. Construction and Building Materials 29: 533–540.

De Larrard

(1999) Concrete Mixture Proportioning: A Scientific Approach. London: E & FN.

De Larrard

Belloc

(1997) The influence of aggregate on the compressive strength of normal and high-strength concrete. ACI Material Journal 94(5): 417–426.

Fédération Internationale du Béton (fib) (2012) Model code 2010 final draft. vol. 1, Bulletin 65, and vol. 2, Bulletin 66, Lausanne, Switzerland.

Gencoglu

Uygunoglu

Demir

, et al. (2012) Prediction of elastic modulus of steel-fiber reinforced concrete (SFRC) using fuzzy logic. Computers and Concrete 9(5): 389–402.

10.

Féret

(1892) Sur la compacité des mortiers hydrauliques [On the compactness of hydraulic mortars]. Annales des Ponts et Chaussées 7(4): 5–164.

11.

Han

Liu

Xie

, et al. (2016) A strength developing model of concrete under sustained loads. Construction and Building Materials 105: 189–195.

12.

Han

Yao

(2003) Effect of initial stress on bearing capacity of concrete-filled steel tubular beam-columns. China Civil Engineering Journal 36(4): 9–18.

13.

Han

(2010) Some recent developments of concrete filled steel tubular (CFST) structures in China. In: Proceedings of the 4th international conference on steel & composite structures, Sydney, NSW, Australia, 21–23 July.

14.

Huang

Chen

, et al. (2016) Study on preloading reduction of ultimate load of circular concrete-filled steel tubular columns. Thin-Walled Structures 98(1):454–464.

15.

ICS (2009) Testing hardened concrete, Part 3: Compressive strength of test specimens (BS EN 12390-3:2009). Brussels: European Committee for Standardization Management Centre.

16.

Jiao

Han

Xie

, et al. (2020) Early-age creep behavior of concrete-filled steel tubular members subjected to axial compression. Journal of Constructional Steel Research 166: 105939.

17.

Jin

Seung

Choi

, et al. (2017) Prediction of early-age compressive strength of epoxy resin concrete using the maturity method. Construction and Building Materials 152: 990–998.

18.

Kim

Han

Song

(2002a) Effect of temperature and aging on the mechanical properties of concrete: Part I. Experimental results. Cement and Concrete Research 32(7): 1087–1094.

19.

Kim

Han

Park

(2002b) Effect of temperature and aging on the mechanical properties of concrete: Part II. Prediction model. Cement and Concrete Research 32(7):1095–1100.

20.

Kirby

Biernacki

(2012) The effect of water-to-cement ratio on the hydration kinetics of tricalcium silicate cements: Testing the two-step hydration hypothesis. Cement and Concrete Research 42(8): 1147–1156.

21.

Chen

, et al. (2018) Cyclic behavior of concrete-filled steel tubular column–reinforced concrete beam frames incorporating 100% recycled concrete aggregates. Advances in Structural Engineering 21(12):1802–1814.

22.

Hou

, et al. (2019) Long-term experimental behavior of concrete-encased CFST with preload on the inner CFST. Journal of Constructional Steel Research 155(4): 355–369.

23.

Liew

JYR

Xiong

(2009) Effect of preload on the axial capacity of concrete-filled composite columns. Journal of Constructional Steel Research 65(3):709–722.

24.

Liew

JYR

Xiong

(2012) Ultra-high strength concrete filled composite columns for multi-storey building construction. Advances in Structural Engineering 15(9): 1487–1503.

25.

Mander

JAB

Priestley

MJN

(1988) Theoretical stress-strain model for confined concrete. Journal of Structural Engineering 114(8): 1804–1826.

26.

MathWorks

Inc

. (2014). MATLAB for Windows, Version 2014b. Natick, MA: MathWorks, Inc.

27.

Ministry of Housing and Urban-Rural Development of the People’s Republic of China (2009). Standard for Test Method of Mechanical Properties on Ordinary Concrete (GB/T 50082-2009), Beijing, China.

28.

Papanikolaou

Stefanidou

Kappos

(2013) The effect of preloading on the strength of jacketed R/C columns. Construction & Building Materials 38(1): 54–63.

29.

Patel

Liang

Hadi

MNS

(2013) Numerical analysis of circular concrete-filled steel tubular slender beam-columns with preload affects. International Journal of Structural Stability & Dynamics 13(3): 1250065.

30.

Patel

Liang

Hadi

MNS

(2014) Behavior of biaxially-loaded rectangular concrete-filled steel tubular slender beam-columns with preload effects. Thin-Walled Structures 79(6): 166–177.

31.

Shen

Shi

Zhu

, et al. (2016) Relationship between tensile Young’s modulus and strength of fly ash high strength concrete at early age. Construction and Building Materials 123: 317–326.

32.

Snyder

Bentz

(2004) Suspended hydration and loss of freezable water in cement pastes exposed to 90% relative humidity. Cement and Concrete Research 34(11): 2045–2056.

33.

Taerwe

Caspeele

(2012) Quantitative comparison of estimation methods for determining the in situ characteristic concrete compressive strength. Structural Engineering International 22(2): 215–222.

34.

Valentini

Parisatto

Russo

, et al. (2014) Simulation of the hydration kinetics and elastic moduli of cement mortars by microstructural modelling. Cement and Concrete Composites 52(9): 54–63.

35.

Wang

Luan

(2018) Modeling of hydration, strength development, and optimum combinations of cement-slag-limestone ternary concrete. International Journal of Concrete Structures and Materials 12(1): 12.

36.

Xie

Chen

Sun

, et al. (2018) Behaviour of concrete-filled steel tubular members under pure bending and acid rain attack: Test simulation. Advances in Structural Engineering 22(1): 240–253.

37.

Yazdani

Mckinnie

Haroon

(2006) Modeling compressive strength development in Florida concrete. Journal of Materials in Civil Engineering 18(6): 868–870.

38.

Zhang

Sun

(2006) Hydration process of Portland cement-fly ash pastes. Journal Southeast University. (Natural Science Ed.) 36(1): 118–123.