# Study the Fire Resistance of Desert Sand Concrete (DSC) with Interface Phase through Uniaxial Compression Tests and Analyses

Authors: Qian Zhang; Haifeng Liu; Qiang Liu; Jialing Che; Weiwu Yang; Jurong Ma; Shu Ing Doh; Kar Sing Lim
Journal: Advances in Civil Engineering
 (2021)

---

## Abstract

The shortage of sand resources and high-rise building fires are becoming increasingly prominent. Desert sand (DS) with smaller particles can effectively fill the concrete voids and further improve its working performance; it is used as a fine aggregate to produce concrete. This article studied the performance of desert sand concrete (DSC) against fire resistance by using mathematical modeling for simulation. The stress-strain curves of desert sand mortar (DSM) after elevated temperatures were tested, and the constitutive model was established. By comparing the experiment and simulation results, it was verified that the model is suitable to be adopted in this study. Data from experiment and past literature can serve as parameters for the subsequent simulation. The destruction process of DSC under uniaxial compression after elevated temperature was simulated by using ANSYS. The simulation results indicated that, after elevated temperature, compressive strength reduced with increase of interface thickness. The compressive strength of DSC had a substantially linear increase as the interface compressive strength increased. For two-grade coarse aggregate, the optimum volume content was 45%, and particle size of it showed a significant effect on the compressive strength of DSC. The DSM constitutive model and simulation results can provide a sound theoretical basis and technical support for DSC engineering applications.


---

## Body

## 1. Introduction

In recent years, the incidence of fires has soared in China. Fire disasters of high-rise buildings were recorded at alarming rates of 2499 cases in 2013 [1] (p. 329), 4989 in 2014 [2] (p. 365), and 5571 in 2015 [3] (p. 303). Compared to 2013, the fire growth rates in 2014 and 2015 were 99.64% and 122.93%, respectively. For high-rise buildings, due to the chimney effect, fire spreads rapidly, which may cause an increase in economic losses and casualties. Therefore, research on the fire resistance of concrete buildings after elevated temperature will help reduce unnecessary damage. Numerous researchers studied concrete after different elevated temperatures [4–7]. Pliya et al. [6] heated the recycled aggregate high-strength concrete to 550–600°C at different heating rates and observed a decline in compressive strength. Qiu [7] used a test to study C70 concrete failure behaviour after heating of 25–800°C. Initial crack toughness and instability toughness both decreased with temperature increase. In this paper, the target temperatures were set at 300°C, 500°C, and 700°C, while the room temperature (20°C) was used as a reference.Due to rapid development of construction and infrastructure, the shortage of medium sand in construction has become a global problem. Many researchers in China and abroad have started to find alternatives to substitute construction sand [8–10]. To reduce the dependency on nonrenewable sources while curbing environmental pollutions, desert sand was used as a substitute for medium sand. Many researchers are working on DSC [11–13]. The fineness modulus of DS is only 0.292, which is finer than fine sand (0.7–1.5 mm). It is classified as ultrafine sand. Zhang and Yang [14] used Mu Us DS and Tengger DS to produce DSC and suggested that DS could be used as fine aggregate for concrete production. Wang and Li [15] revealed that high-strength prestressed concrete of C50 [16] could be produced by mixing DS and medium sand. Thus, the use of desert sand can be widely applied for civil engineering near the desert region for better economic and social benefit. Yan et al. [17] applied statistical models to optimize the mix ratio for DSC, which replaced medium sand with a different proportion of DS obtained from Mu Us region.The macrolevel for concrete is an important aspect of concrete study. Concrete damage usually leads to a loss of concrete capacity. Concrete macroscopic failure is closely linked to nonuniformity of its microstructure. From macroscopic structure perspective, many investigations have been conducted to develop the mechanical models of concrete [18–21]. By modifying Drucker-Prager model, Yu et al. [18] proposed a new coupling function of concrete strength, which included temperature and strain rate in the model. Marsavina et al. [19] used transient finite element analysis to analyse chloride penetration in concrete. Albrifkani and Wang [20] proposed an explicit dynamic finite element simulation method to predict the nonlinear response of axial and rotational constraints of reinforced concrete beams at different temperatures. Morales-Alonso et al. [21] concluded that the high accuracy between experimental and simulated data can be produced using a cohesive crack model to study the fracture behaviour of concrete.Concrete was a three-phase mixture; as one phase of concrete, ITZ was also called interface phase [22]. Due to the large porosity, low strength, and heterogeneity in interface phase, interface phase became the weakest bond in concrete [23, 24], and the thickness was usually approximately 10–50 μm [25]. Scrivener et al. [26] suggested that the interface phase was a gradual transition region and was highly heterogeneous. Jin et al. [27] highlighted the influence of concrete compressive load based on one-way coupling of heat and force. Through Monte Carlo simulation, the impact of graded aggregate geometric characteristics on interface phase fraction was studied [28]. Thus, a further study of concrete interface phase is necessary.A lot of researchers have conducted many studies on mechanical properties of concrete. Nonetheless, few studies of DSC with interface phase after elevated temperature have been reported. Many existing models were relatively complicated and not suitable for DSC after elevated temperature. Considering the limitations of experiment, based on a random aggregate model, DSC was divided into coarse aggregate, DSM, and interface. The failure process of DSC under uniaxial compression after elevated temperature was simulated by using ANSYS. The effects of interface phase thickness, interface phase compressive strength, specimen size, coarse aggregate volume content, and particle size on compressive strength of DSC after elevated temperature treatment were analysed. Numerical simulation research can provide a support for DSC fire resistance after elevated temperature.


## 2. DSM Test

### 2.1. Materials of DSM Test

To simulate compressive strength of DSC, it is necessary to perform a uniaxial compressive test on DSM for validation purposes. Tables1–5 show the physical and chemical indexes of materials used in the study.Table 1
Physical and mechanical indexes of sands.
MaterialFineness modulus (%)Bulk density (g·cm−3)Apparent density (g·cm−3)Mud content (%)Void ratio (%)National standard (medium sand)2.3∼3.0≥1350≥2500≤1.0≤47Medium sand (artificial sand washing)2.38157026360.741.9Desert sand (Mu Us desert sand)0.29140026240.1440.95Table 2
Chemical components of sands.
MaterialComponent (%)Al2O3CaOFeOMgOSiO2K2ONa2OLoss on ignitionMedium sand9.740.960.981.0986.55———Desert sand8.722.001.851.5182.660.120.072.8Table 3
Physical indexes of cement.
Cement typeFinenessStandard consistency water consumption (%)StabilitySetting time (min)Compressive strength (MPa)P.O 42.5 R4.728Aptitude135 (initial)174 (final)33.4 (3d)54.8 (28d)Table 4
Physical indexes of fly ash.
Level (I)-fly ashWater content (%)Fineness (45μm sieve residue) (%)Water demand ratio (%)SO3 (%)Loss on ignition (%)Standard value≤1≤12≤95≤3≤5Measurements0.29.2940.22.8Table 5
Test results of water (tap water) quality.
Test itemsPrestressed concreteRCPlain concreteDetection valuepH value≥5.0≥4.5≥4.57.70Insolubles (mg·L−1)≤2000≤2000≤500032.65Solubles (mg·L−1)≤2000≤5000≤1000040.32Cl− (mg·L−1)≤500≤1000≤350018.92SO42− (mg·L−1)≤600≤2000≤270023.74Alkali content (mg·L−1)≤1500≤1500≤150010.34Figure1 shows the sieving curves of test materials. It was observed that the passing rate for DS was 100%, while it was only 55% for medium sand. Therefore, the particle size of DS was much smaller than that of medium sand. The w/c ratio of 0.45, cement-sand ratio of 0.5, and 0.3% superplasticizer of the cementitious materials were designed. A total of 10% fly ash was used to replace cement, while the medium sand was replaced with desert sand replacement rates (DSR) of 20%, 40%, 60%, 80%, and 100%.Figure 1
Sieving curve of the test materials.


### 2.2. DSM Test

The production of DSM specimens was carried out by complying with JCJ/T 70-2009 [29]. The test specimen was a prism of 40 × 40 × 160 (mm3). DSM with different DSR was heated at 300°C, 500°C, and 700°C for 3 hours. After the heating process, the specimens were cooled by natural cooling. From the test, the surface colour of DSM changed from dark grey to light grey with an increase of DSR. Besides that, the colour of specimen changed from red to white, as the temperature increased from 500°C to 700°C. Sun and Liu [30] have conducted an experiment of DSC using the same material. After elevated temperature, compared with the surface colour of test specimen at room temperature, it was found that the surface colour of test specimen at 500°C was pale and yellow, and the surface of test specimen at 700°C was grayish-yellow. The colour change was due to the presence of FeO in desert sand, which was roughly twice of FeO in medium sand. From Table 2, it was observed that FeO content in DS was approximately twice as that in medium sand. The relative amount of DS in DSM changed the specimens colour. Xu et al. [31] found that the colour of recycled mortar after elevated temperature changed from grey to light red and grey. The result was consistent with the findings of this research.The uniaxial compression test of specimen was performed by using CMT5305. The loading rate was 0.006 mm/s, and it was controlled by displacement. During the test, strain gages were fixed at both horizontal and vertical directions perpendicular to one another at the front and back surface of the specimen. Figure2 shows the details of the test setup.Figure 2
Loading setup.Figure3 shows the specimen failure characteristics of DSM with different DSR. It was observed that when specimen was compressed, part samples cracks started at the specimen edge and were destroyed along the diagonal direction, while the physical observation of the other damaged specimens showed that samples failed obliquely at different angles to the specimens centre and then cracked downward forming a Y-shape.Figure 3
Compression failure of DSM specimens after elevated temperature. (a) DSR-0%; (b) DSR-20%; (c) DSR-40%; (d) DSR-60%; (e) DSR-80%; (f) DSR-100%.
(a)(b)(c)(d)(e)(f)After elevated temperature, the DSM underwent crushing with different damage degrees. Figure4 shows the increase of failure angle with increasing temperature. It was found that the cones at 300°C, 500°C, and 700°C were relatively small as compared with the cone at room temperature. As temperature increases, the structure integrity was gradually deteriorated, and the overall structure was relatively loose at 700°C. This phenomenon was mainly caused by the moisture evaporation inside the concrete, C⟶S⟶H gel dehydration and decomposition, and CH chemical decomposition, as temperature rose from room temperature to 700°C [32].Figure 4
Destruction of DSM after elevated temperature. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)


### 2.3. Test Results of Uniaxial Compression Performance of DSM

The stress-strain curves of DSM with different DSR after elevated temperature were obtained through experimental research. Figure5 shows the DSM with DSR of 0% (ordinary mortar) and 100% (pure desert sand mortar) after elevated temperature. As shown in Figure 5, the peak stress of pure DSM at 300°C increased by about 5% in comparison with ordinary mortar. Meanwhile, the peak stress of pure DSM at room temperature, 500°C, and 700°C was lower than that of ordinary mortar. The optimal DSR was 40%. The peak stress, peak strain, elastic modulus, and Poisson’s ratio of DSM can be obtained from Figure 5. The secant modulus at 40% peak stress was taken as elastic modulus, and ratio of transverse strain to longitudinal strain at elastic stage of stress-strain curve was regarded as Poisson’s ratio.Figure 5
Stress-strain curve of DSM after elevated temperature. (a) DSR-0%; (b) DSR-100%.
(a)(b)According to the test results, the fitting relationship of DSM after elevated temperature is obtained. The determination coefficients (R2) of equations (1)–(4) were larger than 0.96. The fitting equations (1)–(4) were as follows: (1)σcS,Tσc=0.99+0.182T−20700+0.33S+0.018ST−20700−0.666T−207002−0.394S2,(2)εcS,Tεc=0.997+0.51T−20700−0.279S−0.118ST−20700+0.685T−207002+0.145S2,(3)ES,TE=1.02−1.385T−20700+0.167S+0.036ST−20700+0.487T−207002−0.185S2,(4)νS,Tν=0.99+0.55T−20700−0.13S+0.06ST−20700−4.28T−207002−0.02S2+3.61T−207003,where σcS,T, εcS,T, ES,T, and vS,T are the peak stress, peak strain, elastic modulus, and Poisson’s ratio of DSM after elevated temperature; σc, εc, E, and ν are the peak stress, peak strain, elastic modulus, and Poisson’s ratio of ordinary mortar at room temperature; T is temperature; S is the DSR.Based on the model [33], which belonged to concrete and mortar in Figure 6, the DSM stress-strain curve after elevated temperature can be obtained by test and was fitted, and the fitting results agree well, as shown in Figure 7.Figure 6
Constitutive model of concrete and mortar [33].Figure 7
Stress-strain fitting curves of DSM with different DSR after elevated temperature. (a) DSR-20%; (b) DSR-40%; (c) DSR-60%; (d) DSR-80%.
(a)(b)(c)(d)Therefore, equation (5) was suitable for DSM after elevated temperature in this study.(5)σσc=nεεcn−1+εεc−n.The parametern was obtained by fitting, which was the function of DSR, S, and temperature T. The range of T was 20–700°C. The coefficient of determination (R2) of equation (6) was 0.956, and the fitting was good. The fitting equation was as follows: (6)n=1.748+14.383T−20700+1.46S+3.31ST−20700−9.718T−207002.


## 2.1. Materials of DSM Test

To simulate compressive strength of DSC, it is necessary to perform a uniaxial compressive test on DSM for validation purposes. Tables1–5 show the physical and chemical indexes of materials used in the study.Table 1
Physical and mechanical indexes of sands.
MaterialFineness modulus (%)Bulk density (g·cm−3)Apparent density (g·cm−3)Mud content (%)Void ratio (%)National standard (medium sand)2.3∼3.0≥1350≥2500≤1.0≤47Medium sand (artificial sand washing)2.38157026360.741.9Desert sand (Mu Us desert sand)0.29140026240.1440.95Table 2
Chemical components of sands.
MaterialComponent (%)Al2O3CaOFeOMgOSiO2K2ONa2OLoss on ignitionMedium sand9.740.960.981.0986.55———Desert sand8.722.001.851.5182.660.120.072.8Table 3
Physical indexes of cement.
Cement typeFinenessStandard consistency water consumption (%)StabilitySetting time (min)Compressive strength (MPa)P.O 42.5 R4.728Aptitude135 (initial)174 (final)33.4 (3d)54.8 (28d)Table 4
Physical indexes of fly ash.
Level (I)-fly ashWater content (%)Fineness (45μm sieve residue) (%)Water demand ratio (%)SO3 (%)Loss on ignition (%)Standard value≤1≤12≤95≤3≤5Measurements0.29.2940.22.8Table 5
Test results of water (tap water) quality.
Test itemsPrestressed concreteRCPlain concreteDetection valuepH value≥5.0≥4.5≥4.57.70Insolubles (mg·L−1)≤2000≤2000≤500032.65Solubles (mg·L−1)≤2000≤5000≤1000040.32Cl− (mg·L−1)≤500≤1000≤350018.92SO42− (mg·L−1)≤600≤2000≤270023.74Alkali content (mg·L−1)≤1500≤1500≤150010.34Figure1 shows the sieving curves of test materials. It was observed that the passing rate for DS was 100%, while it was only 55% for medium sand. Therefore, the particle size of DS was much smaller than that of medium sand. The w/c ratio of 0.45, cement-sand ratio of 0.5, and 0.3% superplasticizer of the cementitious materials were designed. A total of 10% fly ash was used to replace cement, while the medium sand was replaced with desert sand replacement rates (DSR) of 20%, 40%, 60%, 80%, and 100%.Figure 1
Sieving curve of the test materials.


## 2.2. DSM Test

The production of DSM specimens was carried out by complying with JCJ/T 70-2009 [29]. The test specimen was a prism of 40 × 40 × 160 (mm3). DSM with different DSR was heated at 300°C, 500°C, and 700°C for 3 hours. After the heating process, the specimens were cooled by natural cooling. From the test, the surface colour of DSM changed from dark grey to light grey with an increase of DSR. Besides that, the colour of specimen changed from red to white, as the temperature increased from 500°C to 700°C. Sun and Liu [30] have conducted an experiment of DSC using the same material. After elevated temperature, compared with the surface colour of test specimen at room temperature, it was found that the surface colour of test specimen at 500°C was pale and yellow, and the surface of test specimen at 700°C was grayish-yellow. The colour change was due to the presence of FeO in desert sand, which was roughly twice of FeO in medium sand. From Table 2, it was observed that FeO content in DS was approximately twice as that in medium sand. The relative amount of DS in DSM changed the specimens colour. Xu et al. [31] found that the colour of recycled mortar after elevated temperature changed from grey to light red and grey. The result was consistent with the findings of this research.The uniaxial compression test of specimen was performed by using CMT5305. The loading rate was 0.006 mm/s, and it was controlled by displacement. During the test, strain gages were fixed at both horizontal and vertical directions perpendicular to one another at the front and back surface of the specimen. Figure2 shows the details of the test setup.Figure 2
Loading setup.Figure3 shows the specimen failure characteristics of DSM with different DSR. It was observed that when specimen was compressed, part samples cracks started at the specimen edge and were destroyed along the diagonal direction, while the physical observation of the other damaged specimens showed that samples failed obliquely at different angles to the specimens centre and then cracked downward forming a Y-shape.Figure 3
Compression failure of DSM specimens after elevated temperature. (a) DSR-0%; (b) DSR-20%; (c) DSR-40%; (d) DSR-60%; (e) DSR-80%; (f) DSR-100%.
(a)(b)(c)(d)(e)(f)After elevated temperature, the DSM underwent crushing with different damage degrees. Figure4 shows the increase of failure angle with increasing temperature. It was found that the cones at 300°C, 500°C, and 700°C were relatively small as compared with the cone at room temperature. As temperature increases, the structure integrity was gradually deteriorated, and the overall structure was relatively loose at 700°C. This phenomenon was mainly caused by the moisture evaporation inside the concrete, C⟶S⟶H gel dehydration and decomposition, and CH chemical decomposition, as temperature rose from room temperature to 700°C [32].Figure 4
Destruction of DSM after elevated temperature. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)


## 2.3. Test Results of Uniaxial Compression Performance of DSM

The stress-strain curves of DSM with different DSR after elevated temperature were obtained through experimental research. Figure5 shows the DSM with DSR of 0% (ordinary mortar) and 100% (pure desert sand mortar) after elevated temperature. As shown in Figure 5, the peak stress of pure DSM at 300°C increased by about 5% in comparison with ordinary mortar. Meanwhile, the peak stress of pure DSM at room temperature, 500°C, and 700°C was lower than that of ordinary mortar. The optimal DSR was 40%. The peak stress, peak strain, elastic modulus, and Poisson’s ratio of DSM can be obtained from Figure 5. The secant modulus at 40% peak stress was taken as elastic modulus, and ratio of transverse strain to longitudinal strain at elastic stage of stress-strain curve was regarded as Poisson’s ratio.Figure 5
Stress-strain curve of DSM after elevated temperature. (a) DSR-0%; (b) DSR-100%.
(a)(b)According to the test results, the fitting relationship of DSM after elevated temperature is obtained. The determination coefficients (R2) of equations (1)–(4) were larger than 0.96. The fitting equations (1)–(4) were as follows: (1)σcS,Tσc=0.99+0.182T−20700+0.33S+0.018ST−20700−0.666T−207002−0.394S2,(2)εcS,Tεc=0.997+0.51T−20700−0.279S−0.118ST−20700+0.685T−207002+0.145S2,(3)ES,TE=1.02−1.385T−20700+0.167S+0.036ST−20700+0.487T−207002−0.185S2,(4)νS,Tν=0.99+0.55T−20700−0.13S+0.06ST−20700−4.28T−207002−0.02S2+3.61T−207003,where σcS,T, εcS,T, ES,T, and vS,T are the peak stress, peak strain, elastic modulus, and Poisson’s ratio of DSM after elevated temperature; σc, εc, E, and ν are the peak stress, peak strain, elastic modulus, and Poisson’s ratio of ordinary mortar at room temperature; T is temperature; S is the DSR.Based on the model [33], which belonged to concrete and mortar in Figure 6, the DSM stress-strain curve after elevated temperature can be obtained by test and was fitted, and the fitting results agree well, as shown in Figure 7.Figure 6
Constitutive model of concrete and mortar [33].Figure 7
Stress-strain fitting curves of DSM with different DSR after elevated temperature. (a) DSR-20%; (b) DSR-40%; (c) DSR-60%; (d) DSR-80%.
(a)(b)(c)(d)Therefore, equation (5) was suitable for DSM after elevated temperature in this study.(5)σσc=nεεcn−1+εεc−n.The parametern was obtained by fitting, which was the function of DSR, S, and temperature T. The range of T was 20–700°C. The coefficient of determination (R2) of equation (6) was 0.956, and the fitting was good. The fitting equation was as follows: (6)n=1.748+14.383T−20700+1.46S+3.31ST−20700−9.718T−207002.


## 3. Computational Model of DSC

### 3.1. Material Model and Failure Criteria

#### 3.1.1. Constitutive Model and Parameters of Coarse Aggregate after Elevated Temperatures

The elevated temperature had a little negative effect on coarse aggregates. The coarse aggregate was hardly damaged during loading process. Concrete damage was mainly due to the insufficient bearing capacity of mortar. Thus, the elastoplastic model of coarse aggregate as shown in Table6 was selected.Table 6
Model parameters of coarse aggregate after elevated temperatures [34].
T (°C)Elastic modulus (GPa)Peak strain (10−3)Poisson’s ratio204560.253005060.257003060.25


#### 3.1.2. Parameters of Interface Phase after Elevated Temperatures

Interface phase was the weakest phase in the overall structure of concrete. It will affect the concrete strength. The corresponding parameters of interface phase were relatively small as compared with mortar strength and elastic modulus. Generally, the elastic modulus of interface phase was within 30–70% of mortar elastic modulus [35, 36]. Based on the mortar mechanical parameters, the strain and Poisson’s ratio were kept constant, and the stress and elastic modulus were multiplied by a coefficient (<1) as the stress and elastic modulus of interface phase. In this study, the mortar elastic modulus was taken as the interface phase elastic modulus according to an arithmetic sequence of 60%, 70%, 80%, and 90%, respectively.


#### 3.1.3. Failure Criteria

Concrete was generally regarded as a brittle material, and only a small deformation under external force may cause the component to break and fracture. In this study, the maximum principal strain failure criterion was adopted. When the strain value of finite element unit reaches the maximum principal strain value, the unit is regarded as a failure and cannot continue to bear the load.


### 3.2. Material Model and Failure Criteria

#### 3.2.1. Random Aggregate Model

Fuller and Thompson [37] proposed a maximum compactness rational grading curve to achieve best compactness and strength. The Fuller-grading curve expression was as follows: (7)P=100%DhDMAX0.5,where Dh is screen hole diameter; P is percentage of coarse aggregate passing diameter Dh; DMAX is coarse aggregate maximum particle size.Based on Fuller-grading curve, Walaraven and Reinhardt [38] converted a three-dimensional grading curve into a two-dimensional grading curve with equation (8). The number of coarse aggregates can be calculated by equation (9).(8)PD<D0=PK1.065D0DMAX0.5−0.053D0DMAX4−0.012D0DMAX6−0.0045D0DMAX8−0.0025D0DMAX10,(9)N=4AπD¯,where PK is percentage of coarse aggregate total volume to the concrete total volume; D0 is smallest diameter of the coarse aggregate; A is area occupied by coarse aggregate; D¯ is average diameter of coarse aggregate; and N is number of coarse aggregates.


#### 3.2.2. A Finite-Element Model of DSC

To produce an acceptable result, at least three test blocks need to be prepared for each case in experiment. In this study, the two-dimensional random aggregate program was written and used. Taking the particle size group with a volume content of 55% and a gradation of 5–10–20 mm as an example, the area occupied by coarse aggregates of 5–10 mm and 10–20 mm can be calculated, respectively. Then, the number of aggregates can be obtained. Therefore, the volume content was ultimately expressed by the number of large and small aggregates. According to Figures8(a)–8(c), the distribution of large aggregates on the plane was conducted randomly. Figure 8(d) shows the model details. Both cement mortar and coarse aggregate material unit could adopt a quadrilateral four-node plane82 unit, which was divided by a mapped grid.Figure 8
Finite element models of DSC. (a) Random distribution—I. (b) Random distribution—II. (c) Random distribution—III. (d) Model details.
(a)(b)(c)(d)


#### 3.2.3. Comparative Analysis between Experiment and Numerical Simulation

For simulation, the specimen size was 100 × 100 × 100 (mm3). The coarse aggregate volume content, coarse aggregate particle size, and interface thickness were 55%, 5–10–20 (mm), and 0.6 mm, respectively. Table 7 shows the errors between experimental and simulated results. The errors were tiny and were within ±5%.Table 7
Error between experimental and simulated value (test dates from [39]).
T (°C)DSR (100% (test-simulation)/test)0%20%40%60%80%100%Room temperature0.310.160.000.620.700.07300−0.291.50−1.150.760.942.265001.890.04−0.203.020.433.607004.053.44−1.590.701.492.37Ghannam et al. [40] and Prabhu et al. [41] replaced fine sand with blended granite, iron powder, and foundry sand and found that the optimal replacement rate was 10% and 20%, respectively. In comparison, Al-Jabri et al. [42] suggested that the optimal replacement was 40–50%, when the sand was replaced by copper slag. Therefore, the optimum of fine aggregate was highly dependent on the material type, which was used as a replacement. In Figure 9, the optimal DSR is 40%; it is also shown that the simulated values agree well with the experimental values. Thus, this model was suitable to simulate the uniaxial compression performance of DSC with interface phase after elevated temperature.Figure 9
Compressive strength of DSC after elevated temperature.In DSC compression process, the initial position of failure was located at the interface inside DSC. With the growth of compressive stress, the DSC specimen was broken in diagonal direction. For failure angle measurement, the lowest failure angle as shown in Figure10(a) was regarded as failure surface. As shown in Figure 10, after 300°C, the failure modes of DSC in experiments and simulations were compared. The result shows little difference of failure angle between DSC experiment (46.7–49.3°) and simulation (46.6–48.8°), respectively. In three-dimensional view, the failure form of DSC obtained from experiment and simulation was similar to an inverted triangular pyramid.Figure 10
Failure form of DSC. (a) Test; (b) simulation.
(a)(b)


## 3.1. Material Model and Failure Criteria

### 3.1.1. Constitutive Model and Parameters of Coarse Aggregate after Elevated Temperatures

The elevated temperature had a little negative effect on coarse aggregates. The coarse aggregate was hardly damaged during loading process. Concrete damage was mainly due to the insufficient bearing capacity of mortar. Thus, the elastoplastic model of coarse aggregate as shown in Table6 was selected.Table 6
Model parameters of coarse aggregate after elevated temperatures [34].
T (°C)Elastic modulus (GPa)Peak strain (10−3)Poisson’s ratio204560.253005060.257003060.25


### 3.1.2. Parameters of Interface Phase after Elevated Temperatures

Interface phase was the weakest phase in the overall structure of concrete. It will affect the concrete strength. The corresponding parameters of interface phase were relatively small as compared with mortar strength and elastic modulus. Generally, the elastic modulus of interface phase was within 30–70% of mortar elastic modulus [35, 36]. Based on the mortar mechanical parameters, the strain and Poisson’s ratio were kept constant, and the stress and elastic modulus were multiplied by a coefficient (<1) as the stress and elastic modulus of interface phase. In this study, the mortar elastic modulus was taken as the interface phase elastic modulus according to an arithmetic sequence of 60%, 70%, 80%, and 90%, respectively.


### 3.1.3. Failure Criteria

Concrete was generally regarded as a brittle material, and only a small deformation under external force may cause the component to break and fracture. In this study, the maximum principal strain failure criterion was adopted. When the strain value of finite element unit reaches the maximum principal strain value, the unit is regarded as a failure and cannot continue to bear the load.


## 3.1.1. Constitutive Model and Parameters of Coarse Aggregate after Elevated Temperatures

The elevated temperature had a little negative effect on coarse aggregates. The coarse aggregate was hardly damaged during loading process. Concrete damage was mainly due to the insufficient bearing capacity of mortar. Thus, the elastoplastic model of coarse aggregate as shown in Table6 was selected.Table 6
Model parameters of coarse aggregate after elevated temperatures [34].
T (°C)Elastic modulus (GPa)Peak strain (10−3)Poisson’s ratio204560.253005060.257003060.25


## 3.1.2. Parameters of Interface Phase after Elevated Temperatures

Interface phase was the weakest phase in the overall structure of concrete. It will affect the concrete strength. The corresponding parameters of interface phase were relatively small as compared with mortar strength and elastic modulus. Generally, the elastic modulus of interface phase was within 30–70% of mortar elastic modulus [35, 36]. Based on the mortar mechanical parameters, the strain and Poisson’s ratio were kept constant, and the stress and elastic modulus were multiplied by a coefficient (<1) as the stress and elastic modulus of interface phase. In this study, the mortar elastic modulus was taken as the interface phase elastic modulus according to an arithmetic sequence of 60%, 70%, 80%, and 90%, respectively.


## 3.1.3. Failure Criteria

Concrete was generally regarded as a brittle material, and only a small deformation under external force may cause the component to break and fracture. In this study, the maximum principal strain failure criterion was adopted. When the strain value of finite element unit reaches the maximum principal strain value, the unit is regarded as a failure and cannot continue to bear the load.


## 3.2. Material Model and Failure Criteria

### 3.2.1. Random Aggregate Model

Fuller and Thompson [37] proposed a maximum compactness rational grading curve to achieve best compactness and strength. The Fuller-grading curve expression was as follows: (7)P=100%DhDMAX0.5,where Dh is screen hole diameter; P is percentage of coarse aggregate passing diameter Dh; DMAX is coarse aggregate maximum particle size.Based on Fuller-grading curve, Walaraven and Reinhardt [38] converted a three-dimensional grading curve into a two-dimensional grading curve with equation (8). The number of coarse aggregates can be calculated by equation (9).(8)PD<D0=PK1.065D0DMAX0.5−0.053D0DMAX4−0.012D0DMAX6−0.0045D0DMAX8−0.0025D0DMAX10,(9)N=4AπD¯,where PK is percentage of coarse aggregate total volume to the concrete total volume; D0 is smallest diameter of the coarse aggregate; A is area occupied by coarse aggregate; D¯ is average diameter of coarse aggregate; and N is number of coarse aggregates.


### 3.2.2. A Finite-Element Model of DSC

To produce an acceptable result, at least three test blocks need to be prepared for each case in experiment. In this study, the two-dimensional random aggregate program was written and used. Taking the particle size group with a volume content of 55% and a gradation of 5–10–20 mm as an example, the area occupied by coarse aggregates of 5–10 mm and 10–20 mm can be calculated, respectively. Then, the number of aggregates can be obtained. Therefore, the volume content was ultimately expressed by the number of large and small aggregates. According to Figures8(a)–8(c), the distribution of large aggregates on the plane was conducted randomly. Figure 8(d) shows the model details. Both cement mortar and coarse aggregate material unit could adopt a quadrilateral four-node plane82 unit, which was divided by a mapped grid.Figure 8
Finite element models of DSC. (a) Random distribution—I. (b) Random distribution—II. (c) Random distribution—III. (d) Model details.
(a)(b)(c)(d)


### 3.2.3. Comparative Analysis between Experiment and Numerical Simulation

For simulation, the specimen size was 100 × 100 × 100 (mm3). The coarse aggregate volume content, coarse aggregate particle size, and interface thickness were 55%, 5–10–20 (mm), and 0.6 mm, respectively. Table 7 shows the errors between experimental and simulated results. The errors were tiny and were within ±5%.Table 7
Error between experimental and simulated value (test dates from [39]).
T (°C)DSR (100% (test-simulation)/test)0%20%40%60%80%100%Room temperature0.310.160.000.620.700.07300−0.291.50−1.150.760.942.265001.890.04−0.203.020.433.607004.053.44−1.590.701.492.37Ghannam et al. [40] and Prabhu et al. [41] replaced fine sand with blended granite, iron powder, and foundry sand and found that the optimal replacement rate was 10% and 20%, respectively. In comparison, Al-Jabri et al. [42] suggested that the optimal replacement was 40–50%, when the sand was replaced by copper slag. Therefore, the optimum of fine aggregate was highly dependent on the material type, which was used as a replacement. In Figure 9, the optimal DSR is 40%; it is also shown that the simulated values agree well with the experimental values. Thus, this model was suitable to simulate the uniaxial compression performance of DSC with interface phase after elevated temperature.Figure 9
Compressive strength of DSC after elevated temperature.In DSC compression process, the initial position of failure was located at the interface inside DSC. With the growth of compressive stress, the DSC specimen was broken in diagonal direction. For failure angle measurement, the lowest failure angle as shown in Figure10(a) was regarded as failure surface. As shown in Figure 10, after 300°C, the failure modes of DSC in experiments and simulations were compared. The result shows little difference of failure angle between DSC experiment (46.7–49.3°) and simulation (46.6–48.8°), respectively. In three-dimensional view, the failure form of DSC obtained from experiment and simulation was similar to an inverted triangular pyramid.Figure 10
Failure form of DSC. (a) Test; (b) simulation.
(a)(b)


## 3.2.1. Random Aggregate Model

Fuller and Thompson [37] proposed a maximum compactness rational grading curve to achieve best compactness and strength. The Fuller-grading curve expression was as follows: (7)P=100%DhDMAX0.5,where Dh is screen hole diameter; P is percentage of coarse aggregate passing diameter Dh; DMAX is coarse aggregate maximum particle size.Based on Fuller-grading curve, Walaraven and Reinhardt [38] converted a three-dimensional grading curve into a two-dimensional grading curve with equation (8). The number of coarse aggregates can be calculated by equation (9).(8)PD<D0=PK1.065D0DMAX0.5−0.053D0DMAX4−0.012D0DMAX6−0.0045D0DMAX8−0.0025D0DMAX10,(9)N=4AπD¯,where PK is percentage of coarse aggregate total volume to the concrete total volume; D0 is smallest diameter of the coarse aggregate; A is area occupied by coarse aggregate; D¯ is average diameter of coarse aggregate; and N is number of coarse aggregates.


## 3.2.2. A Finite-Element Model of DSC

To produce an acceptable result, at least three test blocks need to be prepared for each case in experiment. In this study, the two-dimensional random aggregate program was written and used. Taking the particle size group with a volume content of 55% and a gradation of 5–10–20 mm as an example, the area occupied by coarse aggregates of 5–10 mm and 10–20 mm can be calculated, respectively. Then, the number of aggregates can be obtained. Therefore, the volume content was ultimately expressed by the number of large and small aggregates. According to Figures8(a)–8(c), the distribution of large aggregates on the plane was conducted randomly. Figure 8(d) shows the model details. Both cement mortar and coarse aggregate material unit could adopt a quadrilateral four-node plane82 unit, which was divided by a mapped grid.Figure 8
Finite element models of DSC. (a) Random distribution—I. (b) Random distribution—II. (c) Random distribution—III. (d) Model details.
(a)(b)(c)(d)


## 3.2.3. Comparative Analysis between Experiment and Numerical Simulation

For simulation, the specimen size was 100 × 100 × 100 (mm3). The coarse aggregate volume content, coarse aggregate particle size, and interface thickness were 55%, 5–10–20 (mm), and 0.6 mm, respectively. Table 7 shows the errors between experimental and simulated results. The errors were tiny and were within ±5%.Table 7
Error between experimental and simulated value (test dates from [39]).
T (°C)DSR (100% (test-simulation)/test)0%20%40%60%80%100%Room temperature0.310.160.000.620.700.07300−0.291.50−1.150.760.942.265001.890.04−0.203.020.433.607004.053.44−1.590.701.492.37Ghannam et al. [40] and Prabhu et al. [41] replaced fine sand with blended granite, iron powder, and foundry sand and found that the optimal replacement rate was 10% and 20%, respectively. In comparison, Al-Jabri et al. [42] suggested that the optimal replacement was 40–50%, when the sand was replaced by copper slag. Therefore, the optimum of fine aggregate was highly dependent on the material type, which was used as a replacement. In Figure 9, the optimal DSR is 40%; it is also shown that the simulated values agree well with the experimental values. Thus, this model was suitable to simulate the uniaxial compression performance of DSC with interface phase after elevated temperature.Figure 9
Compressive strength of DSC after elevated temperature.In DSC compression process, the initial position of failure was located at the interface inside DSC. With the growth of compressive stress, the DSC specimen was broken in diagonal direction. For failure angle measurement, the lowest failure angle as shown in Figure10(a) was regarded as failure surface. As shown in Figure 10, after 300°C, the failure modes of DSC in experiments and simulations were compared. The result shows little difference of failure angle between DSC experiment (46.7–49.3°) and simulation (46.6–48.8°), respectively. In three-dimensional view, the failure form of DSC obtained from experiment and simulation was similar to an inverted triangular pyramid.Figure 10
Failure form of DSC. (a) Test; (b) simulation.
(a)(b)


## 4. Simulation of Compressive Strength

### 4.1. Effect of Thickness of Interface Phase on Compressive Strength

Due to computational efficiency problem, it was difficult to adopt micrometers unit scale as the scale of concrete finite element mesoscopic calculation analysis. The thickness of interface phase was 0.2–0.8 mm [25, 43, 44]. Quite a few researchers [27, 45] even assumed that the interface phase thickness was 1 mm or 2 mm in the process of numerical simulation and believed that if the parameters were reasonable enough, it was feasible to expand the thickness of interfacial phase. Zhou and Hao [25] found that the concrete tensile strength declined with increasing interface phase thickness. However, very few studies have been reported on the influence of interface phase thickness on concrete compressive strength. 2D random aggregate distribution program was written and run in ANSYS, which can simulate the uniaxial compressive failure process of DSC with different interface phase thicknesses. The influence of interface phase thickness on the DSC compressive strength is illustrated in Figure 11. The DSC compressive strength was decreased when interface phase thickness increased.Figure 11
Effect of thickness of interface phase on compressive strength of DSC.Through the fitting analysis of three-dimensional surface in Figure12, for DSC after elevated temperature, the empirical formula between interface phase thickness, temperature, and compressive strength is obtained. As shown in equation (10), the coefficient of determination (R2) is 0.998, which shows a high degree of fit.Figure 12
Three-dimensional diagram of interface phase thickness, temperature, and compressive strength of DSC.(10)fT,tfc=1.018+0.53T−20700−0.026ttc−0.888T−207002,where fT,t is DSC compressive strength with different interface phase thickness after elevated temperature; fc is DSC compressive strength at room temperature; t is interface phase thickness; tc is maximum value of interface phase thickness.


### 4.2. Effect of Compressive Strength of Interface Phase on Compressive Strength of DSC

The mortar compressive strength was obtained from test determining the interface phase compressive strength. It was considered that the strains of mortar and interface phase remained the same, and the interface phase strength was changed by changing the interface phase’s elastic modulus. In this study, the interface phase’s elastic modulus was assumed to be in the range of 60–90% of the mortar elastic modulus. Table8 shows the specific values of elastic modulus of interface phase.Table 8
Compressive strength of interface phase (I-from test; II-for simulation).
T (°C)Mortar (I)Interface phase (II)0.60.70.80.9Room temperature46.9128.1532.8437.5342.2230044.626.7631.2235.6840.1450037.9122.7826.5830.3834.1770026.4915.8918.5421.1923.84The interface phase’s thickness was 0.6 mm, particle size group was 5–10–20(mm), DSR was 40%, and coarse aggregate volume content was 45%. According to Figure13, after elevated temperature, the DSC compressive strength increased with the increase of interface phase’s compressive strength. The coefficients of determination (R2) were larger than 0.99 at different temperatures, which concluded that the interface phase’s compressive strength affected the DSC strength significantly.Figure 13
Effect of compressive strength of interface phase on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)


### 4.3. Effect of Specimen Size on Compressive Strength

Jin [46] studied the concrete size effect subjected to different strain rates. In the finite element model, volume content of coarse aggregate and particle size were 45% and 5–10–20 mm, respectively. Different sizes of cubes, namely, 100 mm, 150 mm, and 200 mm, were chosen. The uniaxial compression failure processes of DSC after elevated temperatures with varying sizes of specimen were simulated and analysed. In Figure 14, the compressive strength of DSC specimens at different exposure temperatures reduced with the increase of specimen size.Figure 14
Effect of specimen size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)


### 4.4. Effect of Coarse Aggregate Volume Content on Compressive Strength

Meddah et al. [36] found that the coarse aggregate optimal volume content was 45-46%. In Figure 15, the compressive strength of test specimen increased initially and then decreased with the increase of volume content. When the coarse aggregate content was 45%, the DSC compressive strength reached the maximum value.Figure 15
Effect of volume content on compressive strength of DSC. (a) Room temperature; (b)300°C; (c)500°C; (d) 700°C.
(a)(b)(c)(d)


### 4.5. Effect of Particle Size of Coarse Aggregate on Compressive Strength

When the aggregate size was selected reasonably, the concrete can obtain good mixing performance, physical properties, and durability [47, 48]. Coarse aggregate particle size had a greater impact on the concrete compressive strength. Ogundipe et al. [49] used single-size aggregates to produce concrete cubes with sizes of 6 mm, 10 mm, 12.5 mm, 20 mm, and 25 mm. The results revealed that the compressive strength began to increase until the aggregate size reached 12.5 mm, and the concrete produced with aggregate size of 20 mm had higher compressive strength than 25 mm. Therefore, the rationality of the choice of aggregate particle size has an important influence on concrete application. The two-graded DSC was prepared, and the effect of minimum, intermediate, and maximum particle sizes on compressive strength of DSC was investigated.


#### 4.5.1. Effect of Minimum Particle Size of Coarse Aggregate on Compressive Strength

The influence of coarse aggregate minimum particle size on the DSC compressive strength was analysed. The particle size was 5–20–25 mm, 10–20–25 mm, and 15–20–25 mm. Therefore, the minimum particle size was 5 mm, 10 mm, and 15 mm, respectively. Figure16 shows that the DSC compressive strength has the same trend with the rise of minimum size after exposure to different temperatures. The DSC compressive strength declined with increasing the minimum coarse aggregate size.Figure 16
Effect of minimum particle size on compressive strength of DSC. (a) Room temperature; (b)300°C; (c)500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure17, for DSC after elevated temperature, the empirical formula between minimum particle size, temperature, volume content, and compressive strength is obtained, as shown in equation (11). The determination coefficient (R2) is 0.999, which has a high degree of fit.Figure 17
Cube diagram of temperature, volume content, minimum particle size, and compressive strength.(11)fT,Dmin,Vfc=0.99+0.59T−20700−0.01DDc−0.0003V−0.02T−20700DDc−0.94T−207002+0.01DDc2,where fT,Dmin,V is compressive strength considering the influence of temperature, minimum particle size, and volume content; Dmin is minimum particle size of two-stage coarse aggregate; V is coarse aggregate volume content; D is particle size of coarse aggregate; Dc is maximum particle size of coarse aggregate in the control group.


#### 4.5.2. Effect of Intermediate Particle Size of Coarse Aggregate on Compressive Strength

The particle size was 5–10–25 mm, 5–15–25 mm, and 5–20–25 mm. Therefore, the intermediate particle size was 10 mm, 15 mm, and 20 mm, respectively. Figure18 shows the influence of intermediate particle size on the compressive strength of DSC after exposure to elevated temperatures. As the intermediate particle size gets larger, the compressive strength of DSC increases firstly and then decreases.Figure 18
Effect of intermediate particle size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure19, the empirical formula between intermediate particle size, temperature, volume content, and compressive strength is obtained, as shown in equation (12). The determination coefficient (R2) is 0.999, which has a high degree of fit.Figure 19
Cube diagram of temperature, volume content, intermediate particle size, and compressive strength.(12)fT,Dmid,Vfc=1+0.56T−20700+0.04DDc−0.0003V+0.01T−20700DDc−0.93T−207002−0.03DDc2,where fT,Dmid,V is compressive strength considering the influence of temperature, intermediate particle size, and volume content. Dmid is intermediate particle size of two-stage coarse aggregate.


#### 4.5.3. Effect of Maximum Particle Size of Coarse Aggregate on Compressive Strength

The particle size was 5–10–15 mm, 5–10–20 mm, 5–10–25 mm, 5–10–30 mm, and 5–10–35 mm. Therefore, the maximum particle size was 15 mm, 20 mm, 25 mm, 30 mm, and 35 mm, respectively. Figure20 illustrates the influence of the maximum particle size of coarse aggregate on the DSC compressive strength. In Figure 20, as the maximum particle size gets bigger, the compressive strength increases initially and then decreases. When the particle size is 20 mm, the compressive strength reaches the optimal value.Figure 20
Effect of maximum particle size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure21, the empirical formula between minimum particle size and temperature, volume content, and compressive strength is obtained, as shown in equation (13). The determination coefficient (R2) is 0.998, which has a high degree of fit.Figure 21
Cube diagram of temperature, volume content, maximum particle size, and compressive strength.(13)fT,Dmax,Vfc=1+0.59T−20700−0.04DDc−0.0002V−0.02T−20700DDc−0.93T−207002+0.03DDc2,where fT,Dmax,V is compressive strength considering the influence of temperature, maximum particle size, and volume content. Dmax is maximum particle size of a two-stage coarse aggregate.


## 4.1. Effect of Thickness of Interface Phase on Compressive Strength

Due to computational efficiency problem, it was difficult to adopt micrometers unit scale as the scale of concrete finite element mesoscopic calculation analysis. The thickness of interface phase was 0.2–0.8 mm [25, 43, 44]. Quite a few researchers [27, 45] even assumed that the interface phase thickness was 1 mm or 2 mm in the process of numerical simulation and believed that if the parameters were reasonable enough, it was feasible to expand the thickness of interfacial phase. Zhou and Hao [25] found that the concrete tensile strength declined with increasing interface phase thickness. However, very few studies have been reported on the influence of interface phase thickness on concrete compressive strength. 2D random aggregate distribution program was written and run in ANSYS, which can simulate the uniaxial compressive failure process of DSC with different interface phase thicknesses. The influence of interface phase thickness on the DSC compressive strength is illustrated in Figure 11. The DSC compressive strength was decreased when interface phase thickness increased.Figure 11
Effect of thickness of interface phase on compressive strength of DSC.Through the fitting analysis of three-dimensional surface in Figure12, for DSC after elevated temperature, the empirical formula between interface phase thickness, temperature, and compressive strength is obtained. As shown in equation (10), the coefficient of determination (R2) is 0.998, which shows a high degree of fit.Figure 12
Three-dimensional diagram of interface phase thickness, temperature, and compressive strength of DSC.(10)fT,tfc=1.018+0.53T−20700−0.026ttc−0.888T−207002,where fT,t is DSC compressive strength with different interface phase thickness after elevated temperature; fc is DSC compressive strength at room temperature; t is interface phase thickness; tc is maximum value of interface phase thickness.


## 4.2. Effect of Compressive Strength of Interface Phase on Compressive Strength of DSC

The mortar compressive strength was obtained from test determining the interface phase compressive strength. It was considered that the strains of mortar and interface phase remained the same, and the interface phase strength was changed by changing the interface phase’s elastic modulus. In this study, the interface phase’s elastic modulus was assumed to be in the range of 60–90% of the mortar elastic modulus. Table8 shows the specific values of elastic modulus of interface phase.Table 8
Compressive strength of interface phase (I-from test; II-for simulation).
T (°C)Mortar (I)Interface phase (II)0.60.70.80.9Room temperature46.9128.1532.8437.5342.2230044.626.7631.2235.6840.1450037.9122.7826.5830.3834.1770026.4915.8918.5421.1923.84The interface phase’s thickness was 0.6 mm, particle size group was 5–10–20(mm), DSR was 40%, and coarse aggregate volume content was 45%. According to Figure13, after elevated temperature, the DSC compressive strength increased with the increase of interface phase’s compressive strength. The coefficients of determination (R2) were larger than 0.99 at different temperatures, which concluded that the interface phase’s compressive strength affected the DSC strength significantly.Figure 13
Effect of compressive strength of interface phase on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)


## 4.3. Effect of Specimen Size on Compressive Strength

Jin [46] studied the concrete size effect subjected to different strain rates. In the finite element model, volume content of coarse aggregate and particle size were 45% and 5–10–20 mm, respectively. Different sizes of cubes, namely, 100 mm, 150 mm, and 200 mm, were chosen. The uniaxial compression failure processes of DSC after elevated temperatures with varying sizes of specimen were simulated and analysed. In Figure 14, the compressive strength of DSC specimens at different exposure temperatures reduced with the increase of specimen size.Figure 14
Effect of specimen size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)


## 4.4. Effect of Coarse Aggregate Volume Content on Compressive Strength

Meddah et al. [36] found that the coarse aggregate optimal volume content was 45-46%. In Figure 15, the compressive strength of test specimen increased initially and then decreased with the increase of volume content. When the coarse aggregate content was 45%, the DSC compressive strength reached the maximum value.Figure 15
Effect of volume content on compressive strength of DSC. (a) Room temperature; (b)300°C; (c)500°C; (d) 700°C.
(a)(b)(c)(d)


## 4.5. Effect of Particle Size of Coarse Aggregate on Compressive Strength

When the aggregate size was selected reasonably, the concrete can obtain good mixing performance, physical properties, and durability [47, 48]. Coarse aggregate particle size had a greater impact on the concrete compressive strength. Ogundipe et al. [49] used single-size aggregates to produce concrete cubes with sizes of 6 mm, 10 mm, 12.5 mm, 20 mm, and 25 mm. The results revealed that the compressive strength began to increase until the aggregate size reached 12.5 mm, and the concrete produced with aggregate size of 20 mm had higher compressive strength than 25 mm. Therefore, the rationality of the choice of aggregate particle size has an important influence on concrete application. The two-graded DSC was prepared, and the effect of minimum, intermediate, and maximum particle sizes on compressive strength of DSC was investigated.


### 4.5.1. Effect of Minimum Particle Size of Coarse Aggregate on Compressive Strength

The influence of coarse aggregate minimum particle size on the DSC compressive strength was analysed. The particle size was 5–20–25 mm, 10–20–25 mm, and 15–20–25 mm. Therefore, the minimum particle size was 5 mm, 10 mm, and 15 mm, respectively. Figure16 shows that the DSC compressive strength has the same trend with the rise of minimum size after exposure to different temperatures. The DSC compressive strength declined with increasing the minimum coarse aggregate size.Figure 16
Effect of minimum particle size on compressive strength of DSC. (a) Room temperature; (b)300°C; (c)500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure17, for DSC after elevated temperature, the empirical formula between minimum particle size, temperature, volume content, and compressive strength is obtained, as shown in equation (11). The determination coefficient (R2) is 0.999, which has a high degree of fit.Figure 17
Cube diagram of temperature, volume content, minimum particle size, and compressive strength.(11)fT,Dmin,Vfc=0.99+0.59T−20700−0.01DDc−0.0003V−0.02T−20700DDc−0.94T−207002+0.01DDc2,where fT,Dmin,V is compressive strength considering the influence of temperature, minimum particle size, and volume content; Dmin is minimum particle size of two-stage coarse aggregate; V is coarse aggregate volume content; D is particle size of coarse aggregate; Dc is maximum particle size of coarse aggregate in the control group.


### 4.5.2. Effect of Intermediate Particle Size of Coarse Aggregate on Compressive Strength

The particle size was 5–10–25 mm, 5–15–25 mm, and 5–20–25 mm. Therefore, the intermediate particle size was 10 mm, 15 mm, and 20 mm, respectively. Figure18 shows the influence of intermediate particle size on the compressive strength of DSC after exposure to elevated temperatures. As the intermediate particle size gets larger, the compressive strength of DSC increases firstly and then decreases.Figure 18
Effect of intermediate particle size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure19, the empirical formula between intermediate particle size, temperature, volume content, and compressive strength is obtained, as shown in equation (12). The determination coefficient (R2) is 0.999, which has a high degree of fit.Figure 19
Cube diagram of temperature, volume content, intermediate particle size, and compressive strength.(12)fT,Dmid,Vfc=1+0.56T−20700+0.04DDc−0.0003V+0.01T−20700DDc−0.93T−207002−0.03DDc2,where fT,Dmid,V is compressive strength considering the influence of temperature, intermediate particle size, and volume content. Dmid is intermediate particle size of two-stage coarse aggregate.


### 4.5.3. Effect of Maximum Particle Size of Coarse Aggregate on Compressive Strength

The particle size was 5–10–15 mm, 5–10–20 mm, 5–10–25 mm, 5–10–30 mm, and 5–10–35 mm. Therefore, the maximum particle size was 15 mm, 20 mm, 25 mm, 30 mm, and 35 mm, respectively. Figure20 illustrates the influence of the maximum particle size of coarse aggregate on the DSC compressive strength. In Figure 20, as the maximum particle size gets bigger, the compressive strength increases initially and then decreases. When the particle size is 20 mm, the compressive strength reaches the optimal value.Figure 20
Effect of maximum particle size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure21, the empirical formula between minimum particle size and temperature, volume content, and compressive strength is obtained, as shown in equation (13). The determination coefficient (R2) is 0.998, which has a high degree of fit.Figure 21
Cube diagram of temperature, volume content, maximum particle size, and compressive strength.(13)fT,Dmax,Vfc=1+0.59T−20700−0.04DDc−0.0002V−0.02T−20700DDc−0.93T−207002+0.03DDc2,where fT,Dmax,V is compressive strength considering the influence of temperature, maximum particle size, and volume content. Dmax is maximum particle size of a two-stage coarse aggregate.


## 4.5.1. Effect of Minimum Particle Size of Coarse Aggregate on Compressive Strength

The influence of coarse aggregate minimum particle size on the DSC compressive strength was analysed. The particle size was 5–20–25 mm, 10–20–25 mm, and 15–20–25 mm. Therefore, the minimum particle size was 5 mm, 10 mm, and 15 mm, respectively. Figure16 shows that the DSC compressive strength has the same trend with the rise of minimum size after exposure to different temperatures. The DSC compressive strength declined with increasing the minimum coarse aggregate size.Figure 16
Effect of minimum particle size on compressive strength of DSC. (a) Room temperature; (b)300°C; (c)500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure17, for DSC after elevated temperature, the empirical formula between minimum particle size, temperature, volume content, and compressive strength is obtained, as shown in equation (11). The determination coefficient (R2) is 0.999, which has a high degree of fit.Figure 17
Cube diagram of temperature, volume content, minimum particle size, and compressive strength.(11)fT,Dmin,Vfc=0.99+0.59T−20700−0.01DDc−0.0003V−0.02T−20700DDc−0.94T−207002+0.01DDc2,where fT,Dmin,V is compressive strength considering the influence of temperature, minimum particle size, and volume content; Dmin is minimum particle size of two-stage coarse aggregate; V is coarse aggregate volume content; D is particle size of coarse aggregate; Dc is maximum particle size of coarse aggregate in the control group.


## 4.5.2. Effect of Intermediate Particle Size of Coarse Aggregate on Compressive Strength

The particle size was 5–10–25 mm, 5–15–25 mm, and 5–20–25 mm. Therefore, the intermediate particle size was 10 mm, 15 mm, and 20 mm, respectively. Figure18 shows the influence of intermediate particle size on the compressive strength of DSC after exposure to elevated temperatures. As the intermediate particle size gets larger, the compressive strength of DSC increases firstly and then decreases.Figure 18
Effect of intermediate particle size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure19, the empirical formula between intermediate particle size, temperature, volume content, and compressive strength is obtained, as shown in equation (12). The determination coefficient (R2) is 0.999, which has a high degree of fit.Figure 19
Cube diagram of temperature, volume content, intermediate particle size, and compressive strength.(12)fT,Dmid,Vfc=1+0.56T−20700+0.04DDc−0.0003V+0.01T−20700DDc−0.93T−207002−0.03DDc2,where fT,Dmid,V is compressive strength considering the influence of temperature, intermediate particle size, and volume content. Dmid is intermediate particle size of two-stage coarse aggregate.


## 4.5.3. Effect of Maximum Particle Size of Coarse Aggregate on Compressive Strength

The particle size was 5–10–15 mm, 5–10–20 mm, 5–10–25 mm, 5–10–30 mm, and 5–10–35 mm. Therefore, the maximum particle size was 15 mm, 20 mm, 25 mm, 30 mm, and 35 mm, respectively. Figure20 illustrates the influence of the maximum particle size of coarse aggregate on the DSC compressive strength. In Figure 20, as the maximum particle size gets bigger, the compressive strength increases initially and then decreases. When the particle size is 20 mm, the compressive strength reaches the optimal value.Figure 20
Effect of maximum particle size on compressive strength of DSC. (a) Room temperature; (b) 300°C; (c) 500°C; (d) 700°C.
(a)(b)(c)(d)By fitting the cubic diagram in Figure21, the empirical formula between minimum particle size and temperature, volume content, and compressive strength is obtained, as shown in equation (13). The determination coefficient (R2) is 0.998, which has a high degree of fit.Figure 21
Cube diagram of temperature, volume content, maximum particle size, and compressive strength.(13)fT,Dmax,Vfc=1+0.59T−20700−0.04DDc−0.0002V−0.02T−20700DDc−0.93T−207002+0.03DDc2,where fT,Dmax,V is compressive strength considering the influence of temperature, maximum particle size, and volume content. Dmax is maximum particle size of a two-stage coarse aggregate.


## 5. Conclusions

The mechanical properties and model of DSM after elevated temperature were obtained through experiments, which provided material parameters for subsequent simulation, and ANSYS software was used to research compression failure process of DSC with interface phase. The effects of interface phase thickness, interface phase compressive strength, test specimen size, volume content, and particle size on the DSC compressive strength after elevated temperature were analysed. The conclusions were as follows:(1)
The DSC compressive strength decreased when the thickness of interface phase changed from 0.3 mm to 0.9 mm. After elevated temperature, the DSC compressive strength had a linearly increasing relationship with the interface phase’s compressive strength. The DSC compressive strength decreased with the increase of specimen size.(2)
The compressive strength of specimen at different temperatures increased firstly and then decreased with increasing coarse aggregate volume. The compressive strength reached the peak value when the volume content was 45%. When the temperature reached 700°C, the effect of volume content of coarse aggregate on compressive strength of DSC was significantly weakened.(3)
The DSC compressive strength reduced with increasing minimum particle size. With the growth of coarse aggregate intermediate and maximum particle size, the compressive strength increased firstly and then decreased. For maximum particle size, when the particle size was 20 mm, the compressive strength reached the optimal value. Compared to the intermediate particle size, the minimum and maximum particle sizes had more significant impacts on the DSC compressive strength.Based on this study, the constitutive model of DSM and numerical simulation results can provide the support for the fire resistance of DSC.



---

*Source: 8863136-2021-02-25.xml*