1. Introduction
With the growth in the scale of infrastructure construction, the demand for river sand is continuing to increase. The lack of fresh water resources in several desert areas has led to a severe scarcity of river sand and consequently increased construction and transportation costs [
1,
2,
3]. The use of dune sand (DS), which is abundant in those areas [
4], as a fine aggregate to replace some of the river sand in the production of structural elements may be promising.
Sand could reduce the volume change of cementitious materials caused by environmental effects to a certain extent, and plays a skeletal role in the concrete. There are many studies on the replacement of river sand by recycled aggregate for concrete production [
5,
6], such as recycled plastic aggregates [
7], metal lathe waste [
8,
9], waste glass [
10], and rubber tree seed shells [
11]. DS is a very fine aggregate with a mineral composition dominated by quartz, and it is therefore unsuitable as a construction aggregate when used alone [
12]. However, mixing it with natural sand improves the gradation and gives the concrete a certain bearing capacity in dry or waterlogged conditions [
13,
14,
15]. Therefore, a number of scholars around the world have conducted a lot of research on the feasibility of using DS instead of river sand in the production of concrete. These studies have mainly focused on the engineering properties [
16,
17,
18], the mechanical properties [
17,
19,
20,
21], durability [
22,
23], and workability [
24,
25,
26] of DSC. Most of the available studies show that the replacement of river sand by DS as fine aggregate has a positive effect on the performance of concrete. Therefore, some researches on the effect of DS on structural member performance have been carried out. Wang et al. [
27] conducted an experimental study on the mechanical properties of DS concrete-filled steel tubular stub columns and beams. Results showed that the failure pattern of the DS concrete-filled steel tubular stub specimens with a DS replacement rate of 10% were similar to those of normal members. The damage mode and mechanism of DSRC beam–column joints were investigated by Li et al. [
28]. The results of the experiment revealed that when the DS replacement ratio was 20%, the ductility of the specimens increased to some extent. Li et al. [
29] also performed shear strength tests on DSRC beams from the Gurbantunggut Desert to assess the feasibility of partially replacing river sand with DS in RC beams. The results of flexural strength tests conducted on beams by Djeridane [
30] showed that cementitious mortar based on DS could be used for improving the flexural strength and stiffness, as well as the ductility of RC beams.
The shear transfer mechanism of RC deep beams is relatively complicated and no longer in compliance with the classical plane sectional theory. Numerous studies on the influence of key parameters on the shear performance of CRC beams have been carried out. Chen [
31] proposed an optimal strut-and-tie model (STM) by using evolutionary structural optimization and conducted an experiment on eight RC deep beams based on this model. The results showed that the optimal STM could retard the crack expansion and reduce the amount of steel. The experimental results of Lu et al. [
32] showed that the shear strength of deep beams increased with decreasing shear span-to-depth ratio. Li et al. [
33] found that the increase in reinforcement area limited the tensile strength of the compression strut and thus improved the compressive strength of the compression strut, which improved the shear strength of the deep beam. Hussein et al. [
34] pointed out that the shear strength of RC deep beams can be improved to some extent by reducing the size effect through proper configuration of loading and supporting areas. Kondalraj and Rao [
35] found that the diagonal crack width of RC deep beams can be reduced to a certain extent by increasing the number of web reinforcements. Chen et al. [
36] studied the shear strength of steel reinforced concrete deep beams. The results showed that the shape and depth of the wide flange have a great impact on the shear strength of deep beams. Husem et al. [
37] studied the shear strength of RC deep beams under different reinforcement arrangements. The results showed that the diagonal reinforcement could improve the bearing capacity, energy absorption capacity, and displacement ductility of RC deep beams. In recent years, some studies on the shear performance of RC deep beams with special aggregate have also been carried out [
38,
39,
40,
41,
42,
43]. However, the research on the shear behavior of RC deep beams with DS as fine aggregate is very limited [
29].
In this paper, an experimental study on the shear performance of DSRC deep beams was carried out. The failure mode and damage mechanism of DSRC deep beams were assessed with the shear span-to-depth ratio, DS replacement rate, stirrup rate, and concrete strength as the main parameters. A detailed comparative analysis of the effect of DS on various parameters of beam shear strength was performed by comparing the experimental data from 227 normal reinforced concrete (NRC) deep beams with DSRC deep beams. The accuracy of the existing national codes for predicting the shear strength of NRC and DSRC deep beams was then comprehensively compared and evaluated. Based on the results of the analysis, a modified model for the shear strength of DSRC beams was proposed.
5. Prediction of the Shear Strength of the DSRC Beam
The effects of the key parameters on DSRC beams were similar to those of normal beams. Therefore, DSRC beams use the same shear resistance mechanism as standard beams. There is no domestic or international code for shear design of DSRC deep beams. To compute the shear strength of DSRC deep beams, the shear strength prediction method for normal RC beams can be improved. The experimental data were compared to the predicted values provided by four national codes in this section. The details of the selected codes are shown below.
The code GB50010–2010 [
39], based on the strut and tie model, considers the shear span-to-depth ratio, the tensile strength of the stirrup and horizontal reinforcement, the concrete strength, and the span-to-height ratio. The shear strength for the NRC beam is calculated using the following equation:
where
refers to the shear span-to-depth ratio,
represents the concrete tensile strength,
represents the beam section width,
represents the effective depth,
represents the effective span-to-height ratio,
represents the yield strength of vertical reinforcement,
represents the area of vertical reinforcement,
represents the spacing of vertical reinforcement,
represents the yield strength of horizontal reinforcement,
represents the area of horizontal reinforcement, and
represents the spacing of horizontal reinforcement.
The code ACI318–11 [
56], based on the strut-and-tie model, considers the effects of shear-to-span ratio, concrete strength, reinforcement ratio, and other factors. The shear strength for the normal RC deep beam was computed using the following equation:
where the effective compressive strength of concrete is
,
represents the concrete strut strength factor,
represents the concrete compressive strength,
represents the beam section width,
refers to the width of the concrete strut, and
refers to the angle between concrete struts and the longitudinal axis.
The code EN 1992–1–1 (EC2) [
57] modified the effective compressive strength of concrete based on ACI 318–11, as shown below:
The code CSA A23.3–04 [
58] also modifies the effective compressive strength of concrete in ACI 318–11, as shown below:
where
represents the principal tensile strain,
represents the concrete strut strength factor,
represents the concrete compressive strength,
represents the beam section width,
represents the width of the concrete strut, and
represents the angle between concrete struts and the longitudinal axis.
5.1. Comparison of Experimental Data and Predictions
The comparison of the experimental results of the DSRC beams and 10 previous studies [
46,
48,
49,
50,
51,
52,
53,
54,
55,
59] with the predictions of the selected four national codes are presented in
Figure 9a–d. The ratios between the experimental results and predictions (
Vu/
Vpred) and corresponding mean, standard deviation, and coefficient of variation (COV) are also reported in
Figure 9. The diagonal line (
y =
x) indicated that the predicted and experimental values were equal. In the upper region of the diagonal line, the predicted value was greater than the experimental value, and correspondingly, in the lower region of the diagonal, the predicted value was less than the experimental value.
Most of the scatter of the NRC beams and DSRC beams were distributed below the diagonal line
y =
x, indicating that all four codes underestimated the experimental values, producing mean values of 1.15–1.75. Among them, CSA offered conservative estimates and the maximum dispersion for NRC and DSRC deep beams and predicted a mean value and standard deviation of 1.75 and 0.58 for NRC beams and a mean value and standard deviation of 1.38 and 0.26 for DSRC beams. Additionally, the predictions for DSRC beams provided by GB50018 were less accurate and more discrete than the predictions provided by the other three codes, with an average strength ratio and standard deviation of 1.57 and 0.10, respectively. The data points were highly scattered around the diagonal line
y =
x for ACI and EC2 (see
Figure 9a,c). The shear strength of NRC beams was rationally expected by ACI and EC2 with mean values of 1.15 and 1.19, respectively. However, the predicted values obtained by EC2 greatly underestimated the experimental values for DSRC beams. In contrast, when predicting the shear strength of DSRC beams, the mean value, standard deviation and COV of the ACI are lower than those of EC2, which equal 1.17, 0.10 and 0.09, respectively. It is believed that ACI exhibited better predictive performance than the other three national codes.
5.2. Prediction of the Shear Strength of DSRC Beams
The above comparisons indicate that ACI was the most suitable for predicting the shear behavior of DSRC beams. Hence, ACI was modified to predict the shear strength of DSRC beams. The DSC strength was higher than the normal concrete strength due to the inclusion of the appropriate amount of DS to partly fill the pores in concrete. The coefficient
λ of DSC can be calculated using the following equation:
where
ft represents the concrete tensile strength, and
fc′ represents the cylinder concrete compressive strength.
The method for predicting the shear strength of DSRC beams was improved as follows:
where
represents the concrete strength effect factor, which is 0.75 at C30 and 1.0 at C40 and C50;
represents the dune sand impact factor, which is 0.85 for a dune sand replacement rate of 50% and 1.0 for 40% and below.
The predicted results for experimental DSRC beams are presented in
Table 7. It can be observed from
Table 7 that the predictions of the shear load capacity of DSRC beams provided by the proposed model were direct and efficient with mean value and standard deviation of 1.018 and 0.066, respectively. Overall, it can be concluded that the proposed model significantly reduced the variability of predictions and accurately estimate the shear strength of the DSRC beams.