Experimental Investigation on Shear Behavior of Dune Sand Reinforced Concrete Deep Beams

Abstract

An experimental study on the shear behavior of dune sand reinforced concrete (DSRC) deep beams was conducted to determine the feasibility of using dune sand (DS) in engineering. Nine DSRC deep beams were designed and thoroughly analyzed for failure modes, diagonal cracks, and load–deflection curves in this study. The results showed that the shear strength and ductility of DSRC deep beams increased when the DS replacement rate was 30%, but the opposite effect occurred when the DS replacement rate was 50%. To analyze the differences in the effects of the DS replacement rate, shear span-to-depth ratio, concrete strength, and stirrup ratio on the shear strength of DSRC and normal reinforced concrete (NRC) deep beams, a total of 227 shear experimental tests of NRC deep beams were conducted. Furthermore, four national codes were evaluated and compared based on experimental data. The evaluation results showed that the four codes underestimated the shear strength of DSRC and NRC deep beams. Among them, ACI 318–11 provided more reliable predictions for both NRC and DSRC deep beams. It is in this regard that a new empirical model for predicting the shear strength of DSRC deep beams is proposed, in which a reduction coefficient of the DS replacement rate is incorporated. The verification results indicates that the predicted results of the proposed model are in good agreement with the experimental results.

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.

2. Experimental Program

2.1. Materials

The concrete mixtures were made with 42.5 grade ordinary Portland cement (OPC) and grade I fly ash, in accordance with GB 175–2007 standards [44]. The high water absorption of dune sand and the fine particle gradation lead to a reduction in concrete strength, and so the easily available fly ash was selected as one of the concrete mixtures, which is shown in Figure 1a. The chemical composition of the OPC and fly ash are presented in

Table 1. The chemical composition of concrete mixtures (%).

Composition	CaO	SiO2	Al2O3	Fe2O3	SO3	MgO	R2O	K2O	Na2O	Loss
OPC	55.32	25.44	7.06	2.89	2.77	2.25	0.88	0.67	0.49	2.23
Fly ash	0.58	58.28	32.19	6.82	0.70	0.94	-	0.28	0.21	6.82

. The fine aggregate was river sand with a fineness modulus of 2.97 and an apparent density of 2487.5 kg/m³, and the coarse aggregate was river gravel ≤ 30 mm. The dune sand (DS) sample was collected from the Taklamakan Dune in the city of Korla, Xinjiang province of China, as shown in Figure 1b. The DS samples had an average particle size of 0.963 mm and a fineness modulus of 0.855. The chemical composition of the DS is presented in

Table 2. The chemical composition of Taklamakan Dune (%).

SiO2	Fe2O3	Al2O3	CaO	MgO	K2O	Na2O	TiO2	P2O5	MnO
55.61	2.44	9.56	14.38	2.54	2.32	2.08	0.36	0.14	0.06

. To improve the workability of DS concrete, the Q8081 polycarboxylic acid high-range water reducer (HRWR) agent with a water reduction rate of 37% was added. According to the suggestions of reference [15], DS replacement rate was chosen as one of the main variables in this paper and was set to 0, 30%, and 50%. Additionally, three sets of concrete of different strengths, each containing three cubic specimens (150 × 150 × 150 mm, and 150 × 150 × 300 mm), were cast from the concrete used in the specimens to measure the cubic concrete compressive strength and splitting tensile strength. The materials were thoroughly mixed in a standard rotating drum mixer before being poured into the mold. The specimens were demolded after one day and placed in a standard maintenance room at 20 ± 2 °C and >95% relative humidity to cure for four weeks. Then, the specimens were removed for concrete strength testing. The mix proportions of concrete with different strengths and different DS replacement rates and the measured results are shown in

Table 3. Mix proportions of concrete.

Number	Water (kg/m3)	Cement (kg/m3)	River Sand (kg/m3)	DS (kg/m3)	Coarse Aggregate (kg/m3)	Fly Ash (kg/m3)	HRWR (kg/m3)	fcu (Mpa)	ft (Mpa)
C30-30 a	146	257	547	234	1173	29	1.46	34.2	2.97
C40-0	146	293	768	0	1153	33	1.46	43.5	3.68
C40-30	146	293	538	230	1153	33	1.46	45.3	3.96
C40-50	146	293	384	384	1153	33	1.46	42.1	3.46
C50-30	146	402	510	218	1091	41	1.46	52.6	4.23

^a The first half of the number represents the target concrete compressive strength, and the second half represents the DS replacement rate (%).

.

Smooth HPB300 bars with a nominal diameter of 6 mm were used as the stirrup, and ribbed HRB400 bars with nominal diameters of 12 mm and 16 mm were used as the longitudinal reinforcement. The joints between the longitudinal reinforcement and stirrup were protected with electrical tape and secured with plastic tape. The detailed mechanical properties of the reinforcing steel are reported in

Table 4. The properties of reinforcing bar.

Rebar	Nominal Diameter (mm)	Actual Cross-Section Area (mm2)	Yield Strength (MPa)	Ultimate Strength (MPa)	Elongation (%)
HPB300	8	49.8	357	561.4	13.3
HPB400	12	111.4	443	594.4	32.5
	16	202.6	454	621.8	39.7

.

2.2. Details of Test Specimens

Nine DSRC deep beams were designed and divided into four groups, and there was also a cross-control specimen. Group A contained two beams with DS replacement rate as a variable. Group B contained two beams with shear span-to-depth ratio as a variable. Group C contained two beams with stirrup rate as a variable. Group D contained two beams with concrete strength as a variable. Details of the DSRC deep beams with three different stirrup ratios are shown in Figure 2, Figure 3 and Figure 4. Stirrups were symmetrically reinforced on both sides of the beams. All test beams were 1800 mm long with a rectangular cross-section of 200 × 500 mm and an effective depth of 430 mm. Each specimen had six C16 longitudinal reinforcements in the bottom layer and two C12 longitudinal reinforcements in the top layer. Further details are presented in

Table 5. Details of test beams.

Series	Beam	b (mm)	a (mm)	h0 (mm)	l0 (mm)	fcu (MPa)	λ	DS (%)	ρsw (%)
Cross-control specimens	CC1	200	600	430	1500	45.3	1.4	30	0.168
A	A1	200	600	430	1500	43.5	1.4	0	0.168
	A2	200	600	430	1500	42.1	1.4	50	0.168
B	B1	200	450	430	1500	45.3	1.05	30	0.168
	B2	200	300	430	1500	45.3	0.7	30	0.168
C	C1	200	600	430	1500	45.3	1.4	30	0.252
	C2	200	600	430	1500	45.3	1.4	30	0
D	D1	200	600	430	1500	34.2	1.4	30	0.168
	D2	200	600	430	1500	52.6	1.4	30	0.168

, where b and a are the width and the shear span, h₀ and l₀ are the effective depth and the clear span, f_cu, λ, DS and ρ_sw are concrete strength, shear span-to-depth ratio, DS replacement rate, and stirrup rate, respectively.

2.3. Test Setup and Procedure

The experiment was conducted according to the procedure suggested by the standard method for testing concrete structures GB/T50152–2012 [45]. A 2000 kN servo-hydraulic actuator with a maximum displacement range of 100 mm was equipped for static loading. It applied a symmetrical four-point load to the beam at a displacement control rate of 0.1 mm/min. The beam was supported by a roller post and a pin bracket 150 mm from the end of beam, with a clear span of 1800 mm between the supports. Loading plates (size 150 × 200 mm) were placed at the loading point to prevent stress concentration damage. To measure the beam deflection at midspan, three linear variable differential transformers (LVDTs) were placed on both sides of the upper end of the beam and in the center of the lower section. Five pairs of strain gauges were placed at equal distances from the bottom of the beam’s longitudinal reinforcement. Each of the four stirrups on both sides of the beams with a smaller shear span-to-depth ratio (a/d = 0.7 and 1.05) and each of the six stirrups on both sides of the beams with a larger shear span-to-depth ratio (a/d = 1.4) received a pair of strain gauges. To measure concrete strain, strain gauges were installed at a 45° angle on both sides of the beam and vertically on the beam symmetry line. The details of the test setup are illustrated in Figure 5.

3. Results

3.1. Crack Pattern and Failure Mode

The crack propagation pattern and failure mode for each test beam are shown in Figure 6a–i. In Figure 6, the thickened line indicates the penetration diagonal crack, and the red line indicates the initial crack. The initial crack width and corresponding load, the first inclined crack width and corresponding load, the peak load, shear force, and failure mode for each specimen represented in

Table 6. Summary of test results for specimens.

Beam	Initial Crack		Incline Crack		Ultimate Load (kN)	Shear Stress (MPa)	Failure Mode
	Width (mm)	Load (kN)	Width (mm)	Load (kN)
CC1	0.05	168.8	0.10	392.4	856.0	4.98	S-C
A1	0.04	180.5	0.15	351.0	812.0	4.72	S-C
A2	0.06	179.0	0.14	379.5	787.0	4.58	S-C
B1	0.03	192.5	0.13	418.6	922.4	5.36	B-S
B2	0.03	253.4	0.09	531.6	1179.0	6.85	B-S
C1	0.04	156.4	0.12	361.4	782.0	4.55	S-C
C2	0.02	127.0	0.13	335.4	715.0	4.16	S-C
D1	0.03	100.9	0.11	323.0	721.0	4.19	S-C
D2	0.03	201.6	0.40	452.3	944.0	5.49	S-C

. The shear span-to-depth ratio had a significant effect on the damage patterns of DSRC deep beams. Specimens B1 and B2 failed in bending shear, and all other specimens failed in compression shear when the shear span-to-depth ratio was increased.

The specimens were in the elastic stress phase at the start of the test, and there were no cracks on the surface. When the load reached 14–22.7% of the ultimate load, initial cracking occurred at the midspan of the beams, with the initial width varying from 0.01 to 0.05 mm. Bending cracks appeared near the pure bending zone of the beam as the external load was increased further. When the external load was around 45% of the ultimate load, the first diagonal crack appeared. With an initial width ranging from 0.1 to 0.5 mm, the crack expanded from the support to the loading point. The maximum failure crack width ranged between 1.50 and 4.00 mm. Finally, after the load was increased to the peak load, the load-carrying capacity dropped sharply, and the main diagonal crack suddenly penetrated the beam, and the specimen exhibited shear failure mode.

The cracks in the specimen A2 had a denser distribution than the sparse cracks in the normal specimens or the specimens A1. This difference occurred probably because DS has extremely fine grains. The pores between the coarse and fine aggregates were filled, which increased the density of the specimen and strengthened the concrete to some extent. In this way, stress can be transferred within the beam effectively, which can help in avoiding stress concentrations.

3.2. Load–Displacement Behavior

The load–displacement curves of the specimens are presented in Figure 7a–d. At the beginning of the test, the concrete was not cracked, the specimen was in the elastic phase, and the load–displacement curve showed a linear relationship. As the load increased until the specimen cracked, the slope of the load–displacement curve decreased with an increase in displacement. Eventually, the load increased until shear failure occurred, and the load–displacement curve showed a horizontal linear relationship during the failure phase, followed by a sharp drop.

The load–displacement relationship for specimens with various DS replacement ratios is shown in Figure 7a. The load–displacement curve for the specimen CC1 was similar to that of the specimen A1. The initial crack load of the specimen CC1 was approximately 18% of the maximum load. The ultimate load and the corresponding displacement of the specimen A1 were significantly smaller than those of the specimen CC1, which were 94.7% and 72.6% of specimen CC1, respectively. Additionally, the slope of the load–deflection curve of specimen A2 before the initial crack load was significantly smaller than that of the other two beams. When the displacement was increased, the ultimate load and displacement of A2 were slightly lower than in specimen A1. These findings suggested that when the DS replacement rate was 30%, the bearing capacity and ductility of deep beams were greater relative to those of the NRC deep beam, while the opposite phenomenon occurred when the DS replacement rate was 50%. This is mainly due to the fact that the elastic modulus of concrete with a DS replacement rate of 50% is lower than that of ordinary concrete, resulting in poor resistance to deformation and reduced flexural stiffness of DSC. Besides, the lower tensile strength of DSC leads to weaker crack resistance and bond strength of reinforcement than ordinary concrete, so the deflection of DSRC beams is greater than that of NRC beams.

The load–displacement relationship for specimens with different shear span-to-depth ratios is shown in Figure 7b. Before the specimens cracked, the load–displacement curves of the three specimens were similar. The monitored cracking load range was about 20% of the maximum load. Before the diagonal cracking load was applied, all three beams had similar load–deflection curves. After the initial crack appeared in the beam, the slope of the load–displacement curve of B2 was significantly greater than that of the other two beams, and the slope decreased as the shear span-to-depth ratio increased. Specimen B2 had the highest ultimate load of the three beams, measuring 588.3 kN. The ultimate loads of specimens B1 and CC1 were 21.0% and 27.7% of the specimen B2 ultimate load, respectively. The initial crack and corresponding displacement of B2 were slightly larger than those of the other two specimens, but the ultimate displacements were significantly smaller, and were 76% and 55% of those of B1 and CC1, respectively. This difference occurred because an increase in the shear span-to-depth ratio increased the length of the force arm, which in turn increased the bending moment. Furthermore, as the bending effect of the specimens weakened, the stiffness decreased significantly, and the failure mode shifted from bending–shear failure to shear failure.

The load–displacement relationship for specimens with various stirrup ratios is shown in Figure 7c. When the external load was small, the slope of the load–displacement curve increased with an increase in the stirrup ratio. When the initial crack appeared, the curve for the M-30–1.4–0.252 specimen slowed down significantly, and the appearance of the diagonal crack was delayed. The maximum mid-span deflection of the specimen increased as the stirrup ratio increased. This occurred because the stirrup was effective in retarding the appearance of cracks, thus, increasing the deformation capacity and the load-carrying capacity of the beam.

The load–displacement relationship for specimens with different values of concrete strength is shown in Figure 7d. The concrete strength had a greater effect on the initial crack displacement. The initial crack displacement of specimen D2 was 21.4% and 104.7% larger than the crack displacement of specimens CC1 and D1, respectively. After the diagonal cracks were formed, the displacement of the diagonal cracks of CC1 became the largest, which was 21.4% and 58.7% larger than those of specimens D1 and D2, respectively. As the concrete strength increased, the ultimate load also increased. However, the ultimate displacement of specimen CC1 was the largest (6.53 mm).

4. Discussion

To determine the effect of the main parameters on the shear strength of DSRC deep beams, the experimental results from NRC deep beams were compared to those of DSRC deep beams. The shear strength was denoted as the normalized shear strength v_u = V_u/f_tbh₀, in which f_t denotes the concrete tensile strength, b denotes the cross-sectional width, and h₀ denotes the effective beam depth, given for each of the main parameters. The relationship between the main parameters and the normalized shear strength are shown in Figure 8.

4.1. Effect of Shear Span-to-Depth Ratio

Figure 8a shows the relationship between shear stress and shear span-to-depth ratio for DSRC deep beams and NRC deep beams. All NRC deep beam specimens in Figure 8a are shown with shear span-to-depth ratio as the variable, including: 32 sets from Rogowsky et al. [46], 16 sets from Lu et al. [47], 13 sets from Foster et al. [48], 12 sets from Tan and Lu [49] and 17 sets from Tan et al. [50]. For DSRC beams, the variation in shear strength with shear span-to-depth ratio was similar to that for NRC beams. The ultimate shear stress decreased as the shear span-to-depth ratio increased. The shear strength of specimens B1 and B2 decreased by 21.8% and 27.4%, respectively, when compared to the specimen B2 (ultimate shear stress v_n = 6.85 MPa). This decrease occurred because as the shear span-to-depth ratio of the deep beam increased, the angle between the strut and tie increased, the arch effect weakened, the shear mechanism gradually transitioned from arch action dominant to beam action dominant, and the role of concrete struts to improve the shear strength gradually disappeared.

4.2. Effect of Concrete Strength

The normalized ultimate shear stress (v_u) versus the concrete strength is shown in Figure 8b. All the specimens of NRC deep beams in Figure 8 are shown with concrete strength as the variable, including: 12 sets from Febres et al. [51], 26 sets from Rogowsky et al. [46], 12 sets from Tan and Lu [49] and 17 sets from Tan et al. [50]. Shear stress increased gradually as concrete strength increased. The shear stress of the specimen with a concrete strength of 30 MPa was 4.19 MPa, while the shear stress of the specimen with a concrete strength of 40 and 50 MPa increased by 18.7% and 30.9%, respectively. In comparison to the increase in shear strength of NRC deep beams, the shear strength of DSRC deep beams increased to a lesser extent as concrete strength increased. This meant that the increase in concrete strength was greater than the increase in ultimate shear stress of dune sand RC deep beams. As shown in Table 3, DS admixture increased low-grade concrete strength slightly but had no effect on high-grade concrete strength. Before diagonal concrete cracks developed in the shear span section, the shear load capacity was mostly borne by the concrete in the whole section. As the load increased, diagonal cracks appeared in the shear span section, and the stress was redistributed in the beam. The shear mechanism was described as a strut and tie mechanism with compression concrete arch ribs and tension longitudinal reinforcement. Under these conditions, the concrete arch ribs in the abdomen of deep beams within the shear span section carried the majority of the shear load capacity of the shorter beam.

4.3. Effect of the Stirrup Rate

The variation in ultimate shear stress (v_u) with the stirrup rate for normal RC deep beams and dune sand RC deep beams is shown in Figure 8c. All the specimens of NRC deep beams in Figure 8c are shown with concrete strength as the variable, including: 25 sets from Smith and Vantsiotis [52], 28 sets from Tanimura and Sato [53], 6 sets from Garay and Lubell [54], 30 sets from Oh and Shin [55]. The pattern of variation in the stirrup rate was similar for DSRC deep beam specimens and NRC deep beam specimens; the ultimate shear stress increased continuously with an increase in the stirrup rate. This indicated that the addition of DS had no effect on the shear contribution of the stirrup. The ultimate shear stress of the specimens increased by 9.37% and 19.72% when the stirrup rates increased from 0% to 0.168% and 0.252%, respectively, according to a comparison of test data from three specimens with different stirrup rates. This change occurred because as the stirrup rate increased, the stirrup could bear greater tensile stress, slowing down the rate of damage to the concrete strut. This inhibited the expansion of cracks and increased the area of the tensile region, thus, increasing the ultimate shear stress.

4.4. Effect of Dune Sand Replacement Rate

The correlation between the ultimate shear stress and the DS replacement rate is shown in Figure 8d. When the shear span-to-depth ratio, concrete strength and stirrup ratio remain constant, the ultimate shear stress increased by 5.5% and decreased by 3.0% for the specimens with DS replacement rates of 30% and 50%, respectively, compared to the ultimate shear stress of the normal specimens (v_u = 4.72 MPa). This indicated that the dune sand replacement rate strongly affected the shear strength of the RC beam. The pores between the coarse and fine aggregates are filled with DS, a very fine aggregate. Therefore, a small amount of dune sand can improve the compactness and compressive strength of concrete. A large amount of DS, on the other hand, reduces mortar strength and the bond between the mortar and the coarse aggregate. The shear strength contribution of DSRC beams is mainly composed of stirrup and concrete. When diagonal cracks were observed in the DSRC deep beams, the DSC failed earlier and the stirrup took up most part of the shear force.

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:

$$V_{\mathrm{u}}=\frac{1.75}{\lambda +1}{f}_{\mathrm{t}}b{h}_0+\frac{(l_0/h-2)}{3}{f}_{\mathrm{yv}}\frac{A_{\mathrm{sv}}}{s_{\mathrm{v}}}{h}_0+\frac{(5-l_0/h)}{6}{f}_{\mathrm{yh}}\frac{A_{\mathrm{sh}}}{s_{\mathrm{h}}}{h}_0$$

(1)

where $\lambda$ refers to the shear span-to-depth ratio, $f_{\mathrm{t}}$ represents the concrete tensile strength, $b$ represents the beam section width, $h_0$ represents the effective depth, $l_0/h$ represents the effective span-to-height ratio, $f_{\mathrm{yv}}$ represents the yield strength of vertical reinforcement, $A_{\mathrm{sv}}$ represents the area of vertical reinforcement, $s_{\mathrm{v}}$ represents the spacing of vertical reinforcement, $f_{\mathrm{yh}}$ represents the yield strength of horizontal reinforcement, $A_{\mathrm{sh}}$ represents the area of horizontal reinforcement, and $s_{\mathrm{h}}$ 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:

$$V_{\mathrm{u}}={ f}_{\mathrm{ce}}^{ }{b}_{\mathrm{w}}{w}_{\mathrm{s}}\sin {\theta }_{\mathrm{s}}$$

(2)

where the effective compressive strength of concrete is $f_{\mathrm{ce}}^{ }=0.85{\beta }_{\mathrm{s}}{f}_c^{\prime }$, ${\beta }_{\mathrm{s}}$ represents the concrete strut strength factor, $f_c^{\prime }$ represents the concrete compressive strength, $b$ represents the beam section width, $w_{\mathrm{s}}$ refers to the width of the concrete strut, and ${\theta }_{\mathrm{s}}$ 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:

$$f_{\mathrm{ce}}=0.60(1-\frac{f_{\mathrm{c}}^{\prime }}{250})\frac{{\alpha }_{\mathrm{cc}}{f}_{\mathrm{c}}^{\prime }}{{\gamma }_{\mathrm{c}}}$$

(3)

The code CSA A23.3–04 [58] also modifies the effective compressive strength of concrete in ACI 318–11, as shown below:

$$\begin{gathered} f_{\mathrm{ce}}=\frac{f_c^{\prime }}{0.8+170{\epsilon }_1} \\ {\epsilon }_1={\epsilon }_{\mathrm{s}}+({\epsilon }_{\mathrm{s}}+0.002){\cot }^2{\theta }_{\mathrm{s}} \end{gathered}$$

(4)

where ${\epsilon }_1$ represents the principal tensile strain, ${\beta }_{\mathrm{s}}$ represents the concrete strut strength factor, $f_c^{\prime }$ represents the concrete compressive strength, $b$ represents the beam section width, $w_{\mathrm{s}}$ represents the width of the concrete strut, and ${\theta }_{\mathrm{s}}$ 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 (V_u/V_pred) 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:

$$\lambda =1.7\frac{f_{\mathrm{t}}}{\sqrt{f_c^{\mathrm{\prime }}}}$$

(5)

where f_t represents the concrete tensile strength, and f_c′ represents the cylinder concrete compressive strength.

The method for predicting the shear strength of DSRC beams was improved as follows:

$$V_{\mathrm{u}}=1.445f_{\mathrm{t}}\varphi \delta {\beta }_{\mathrm{s}}\sqrt{f_c^{\mathrm{\prime }}}{b}_{\mathrm{w}}{w}_{\mathrm{s}}\sin {\theta }_{\mathrm{s}}$$

(6)

where $\varphi$ represents the concrete strength effect factor, which is 0.75 at C30 and 1.0 at C40 and C50; $\delta$ 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. Validation results of the proposed model.

Number	Vu (kN)	Vpred,proposed (kN)	Vu/Vpred,proposed
CC1	428	390.72	1.10
A1	383.5	355.80	1.08
A2	406	329.13	1.05
B1	461	489.30	0.94
B2	589.5	607.12	0.97
C1	391	390.72	1.00
C2	357.5	390.72	0.91
D1	360.5	254.69	1.06
D2	472	449.78	1.05
Mean			1.018
Standard deviation			0.066

. 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.

6. Conclusions

In this experimental and analytical study, the effect of various influencing parameters on the shear strength of nine DSRC deep beams was investigated. The applicability of four existing national codes was evaluated, and ACI was improved to predict the shear strength of DSRC beams. The following conclusions were drawn:

• Compared to NRC deep beams, a small amount of dune sand can improve the load-carrying capacity and ductility of RC beams, but too much of it has the opposite effect. When the DS replacement rate was 30%, the load-carrying capacity and ductility of beams were 5.3% and 27.4% higher than that of NRC deep beams, respectively. When the DS replacement rate increased to 50%, the load-carrying capacity and ductility of beams were 5.9% and 3.5% lower than that of the NRC deep beams, respectively.
• The effect of shear span-to-depth ratio on shear strength of DSRC deep beams was similar to that of NRC deep beams. As the shear-to-span ratio increases, the shear load capacity decreases and the failure mode of the DSRC beam changes from bending shear to compression shear. Similarly, the effect of the stirrup ratio on the shear strength of DSRC deep beams was similar to that of NRC deep beams; the shear strength increased with an increase in the stirrup ratio.
• Relative to NRC deep beams, the shear strength of DSRC deep beams increased to a lesser extent with an increase in concrete strength. The shear stress in the specimens with concrete strengths of 40 and 50 MPa increased by 18.7% and 30.9%, respectively, compared to the shear stress in the specimens with concrete strength of 30 MPa.
• Based on the results of the statistical parameters, the selected four national codes give conservative prediction results. The shear strength predictions for both DSRC deep beams and NRC deep beams yielded by the ACI approach were closer to the experimental results than other national codes. For NRC deep beams, ACI318 yielded an average strength ratio and standard deviation of 1.15 and 0.31, respectively, with a COV of 29%, while for DSRC deep beams, ACI318 yielded an average strength ratio and standard deviation of 1.17 and 0.10, respectively, with a COV of 9%.
• As the effect of dune sand on the concrete strength and shear strength of RC beams were both considered, the modified ACI318 approach in this paper provided accurate predictions with a mean and standard deviation of 1.018 and 0.066, respectively, which shows that the proposed formula agrees well with the experimental results of the DSRC deep beams. The model proposed in this study may provide a reference for shear strength prediction of DSRC deep beams.
• It should be noted that these conclusion are obtained based on the test results from limited specimens with multiple variables. More deep and fine studies on the DSRC beams with different DS replacement rate are required in the further.