Shear Behavior of Ultra-High-Performance Concrete Deep Beams Reinforced with Fibers: A State-of-the-Art Review

Abstract

Ultra-high-performance concrete (UHPC) is considered a highly applicable composite material due to its exceptional mechanical properties, such as high compressive strength and ductility. UHPC deep beams are structural elements suitable for short spans, transfer girders, pile caps, offshore platforms, and bridge applications where they are designed to carry heavy loads. Several key factors significantly influence the shear behavior of UHPC deep beams, including the compressive strength of UHPC, the vertical web reinforcement (ρ_sv), horizontal web reinforcement (ρ_sh), and longitudinal reinforcement (ρ_s), as well as the shear span-to-depth ratio (λ), fiber type, fiber content (FC), and geometrical dimensions. In this paper, a comprehensive literature review was conducted to evaluate factors influencing the shear behavior of UHPC deep beams, with the aim of identifying research gaps and enhancing understanding of these influences. The findings from the literature were systematically classified and analyzed to clarify the impact and trends associated with each factor. The analyzed data highlight the effect of each factor on the shear behavior of UHPC deep beams, along with the overall trends. The findings indicate that an increase in compressive strength, FC, ρ_sv, ρ_s, and ρ_sh can enhance the shear capacity of UHPC-DBs by up to 63.36%, 63.24%, 38.14%, 19.02%, and 38.14%, respectively. Additionally, a reduction of 61.29% in λ resulted in a maximum increase of 49.29% in the shear capacity of UHPC-DBs.

1. Introduction

Ultra-high-performance concrete has drawn significant interest from researchers due to its exceptional mechanical properties, particularly its compressive strength, toughness, and durability [1]. According to ACI 318-14, concrete is generally categorized into three types based on compressive strength: normal-strength concrete (NSC), high-strength concrete (HSC), and ultra-high-performance concrete (UHPC), with compressive strengths ranging from 20 MPa to 50 MPa, 50 MPa to 120 MPa, and 120 MPa to 250 MPa, respectively [2,3,4].

Deep beams are commonly used in high-rise structures, bridges, offshore platforms, etc., to support heavy loads [5]. Notably, if the clear span of a beam (l) is less than four times its total depth (d), and a concentrated load is applied at a distance less than twice its depth, the beam can be considered a deep beam [4,6].

Researchers have reported that the compressive strength of UHPC is one of the most significant factors influencing the shear capacity of UHPC deep beams (UHPC-DBs) [7,8,9,10]. Findings indicate that increasing compressive strength can enhance the shear capacity of UHPC-DBs by up to 63.36%. Changes in vertical web reinforcement (ρ_sv) can influence the shear capacity of UHPC-DBs. Several research findings indicate that increasing the amount of (ρ_sv) can enhance the shear capacity of UHPC-DBs by up to 38.14% [7,8,10,11,12,13,14]. The impact of longitudinal reinforcement (ρ_s) on the shear capacity (SC) of UHPC-DBs has been studied by researchers. Experimental results indicate that increasing (ρ_s) leads to a maximum enhancement in the shear capacity of UHPC-DBs by up to 48.15% [7,9,10,15,16]. Another factor that can affect the shear capacity of UHPC-DBs is the amount of horizontal web reinforcement (ρ_sh). In recent years, researchers have evaluated the impact of ρ_sh on the shear capacity of UHPC-DBs. Their findings indicate that a maximum enhancement of 38.14% in the shear capacity of UHPC-DBs can be achieved with a higher amount of ρ_sh [7,8,9,16].

Additionally, the dimensions of UHPC-DBs, particularly the shear span-to-depth ratio (λ), play a crucial role in determining their shear capacity. Research findings indicate that a maximum increase of 49.29% in the shear capacity of UHPC-DBs can be achieved when λ decreases [7,9,10,13]. Incorporating fibers into UHPC mix designs is an effective solution for preventing single-crack failures in UHPC. Consequently, most UHPC mix designs include fibers, particularly steel fibers, due to their superior mechanical properties, especially tensile strength, which provides a crack-bridging effect. Fiber content (FC) is one of the most critical factors influencing the mechanical properties of UHPC, notably its compressive strength and the shear capacity of UHPC-DBs [17,18,19,20]. Research findings show that increasing steel fiber content up to a maximum of 3% can enhance both the compressive strength of UHPC and the shear capacity of UHPC-DBs [7,8,9,10].

However, the incorporation of steel fibers in UHPC mix designs may result in surface corrosion, particularly in harsh environments. As an alternative, synthetic fibers have been investigated, encouraging researchers to study their impact on the mechanical properties of UHPC [21,22,23,24,25,26,27,28].

The shear behavior of UHPC deep beams differs significantly from that of their counterparts with other types of fibers due to the inclusion of fibers in the mix design. Incorporating fibers into the UHPC mix results in strain-hardening behavior under tensile loading. This behavior leads to the formation of multiple cracks after the first crack appears, subsequently resulting in higher strain [29].

This paper critically reviews the literature on the shear behavior of UHPC-DBs to analyze the influence of key factors, including compressive strength, ρ_sv, ρ_sh, ρ_s, λ, and FC on their shear capacity. Additionally, it aims to identify overall trends associated with each factor’s effect on the shear capacity of UHPC-DBs and highlight existing research gaps in this area.

2. Shear Behavior of UHPC Deep Beams in International Standards

2.1. Minimum Shear Reinforcement

There are international standards that specify the minimum reinforcement requirements for UHPC deep beams. The following standards have been thoroughly reviewed, and the reinforcement requirements outlined in each have been summarized.

2.1.1. ACI 318-19 [30]

The minimum areas of horizontal and vertical reinforcement, A_h,min and A_v,min, can be calculated using Equations (1) and (2), respectively, as follows:

A_h,min = 0.025 b S_h

(1)

A_v,min = 0.025 b S_v

(2)

where S_h and S_v represent the spacing of horizontal and vertical web reinforcements, respectively. The beam width is denoted by b.

2.1.2. Eurocode 2 (EC-2) [31]

The minimum areas of vertical and horizontal web reinforcements, A_v,min and A_h,min, can be calculated using Equations (3) and (4), respectively, as follows:

A_v,min = 0.001 A_c

(3)

A_h,min = 0.001 A_c

(4)

where the concrete section area is represented by A_c. Notably, S_v and S_h should not exceed the smaller value of 300 mm or 2b in this case.

2.2. Recommended Shear Design Guidelines for UHPC Deep Beams

2.2.1. France Association of Civil Engineering (AFGC-13) [32]

The shear capacity of UHPC deep beams can be calculated using Equation (5), as follows:

V_d = V_c + V_fb + V_s

(5)

where Vc represents the shear strength of concrete can be calculated using Equation (6), as follows:

$$V_c=(0.21/{\mathsf{\gamma }}_{cf}{\mathsf{\gamma }}_E)k\sqrt{f_c^{\prime }}bd$$

(6)

where the cylindrical compressive strength of concrete is denoted by $f_c^{\prime }$. Additionally, a partial safety factor on fibers and a safety coefficient are represent by γ_cf and γ_E, respectively.

Moreover, the impact of steel fiber (V_fb) on the shear capacity of UHPC deep beams can be calculated using Equation (7), as follows:

V_fb = (A_fv σ_Rd,f/tanθ)

(7)

where the fiber effect area is represented by A_fv and the residual tensile strength is denoted by σ_Rd,f, which can be calculated using the following equation:

$$\sigma =(1/k{\sigma }_{c,f})\times (1/w_{lim}){\int }_0^{wlim}{\sigma }_f\left(w\right)dw$$

(8)

where the maximum crack width is represented by w_max, and w_lim is the greater value between w_max and w_u. Additionally, the fiber orientation factor, k, is taken as 1.25.

The shear strength of vertical shear reinforcement, V_s, can be calculated using the following equation:

V_s = A_v/s_v z f_yv cot θ

(9)

2.2.2. Korea Concrete Institute (KCI-2012) [33]

In this standard, the design shear strength can similarly be calculated through Equation (5). However, in this case, V_c is determined using Equation (10), as flows:

$$V_c={\phi }_{b}0.18\sqrt{f_c^{\prime }}bd$$

(10)

where the member reduction factor, φ_b, is represented and taken as 0.77. Additionally, V_s can be calculated using the following equation:

V_s = φ_b (A_v f_yv (sin α_s + cos α_s)/S) d

(11)

The angle between the longitudinal beam axis and the shear reinforcement is denoted by α_s.

Finally, V_fb is calculated using Equation (12), as follows:

V_fb = φ_b (f_vd/tan β_u) bz

(12)

where the angle between the beam’s axial direction and the diagonal tensile crack plane is represented by β_u and is approximately greater than 30°. The design average tensile strength, which is perpendicular to the diagonal tensile crack, is denoted by f_vd and can be calculated using Equation (13), as follows:

$$f_{\mathrm{vd}}=(1/w_v){\int }_0^{w_v}{\phi }_c{\sigma }_k\left(w\right)dw=(1/w_v){\int }_0^{w_v}{\sigma }_d\left(w\right)dw$$

(13)

where the material reduction factor is represented by ${\phi }_c$ and is taken as 0.8. The ultimate crack width at the peak stress on the outer fiber is denoted by w_u, and w_v is the maximum value between w_u and 0.3 mm. The tension softening curve is also represented by ${\sigma }_k\left(w\right)$ [13].

2.2.3. Federal Highway Administration Research and Technology (FHWA) [34]

This standard does not include any publication on the development length of shear reinforcement in UHPC deep beams. However, it is advised that, due to the high compressive and tensile strength of UHPC, the existing AASHTO LRFD Bridge Design Specifications [35] can be applied in this case.

3. Significance of Study

Among the 63 tested UHPC-DBs available in the literature, the percentage of studies evaluating the impact of ρ_sv, ρ_sh, λ, FC, and ρ_s were 23.8%, 12.7%, 20.6%, 20.6%, and 22.2%, respectively, as illustrated in Figure 1. This graph indicates that all these factors have approximately the same degree of importance in evaluating the shear capacity of UHPC deep beams.

To provide a better understanding of vertical web reinforcement (ρ_sv), horizontal web reinforcement (ρ_sh), longitudinal reinforcement (ρ_s), and shear span-to-depth ratio (λ), each of these factors is illustrated in Figure 2.

Since researchers have studied the influence of only certain factors, not all key factors, on the shear capacity of UHPC-DBs, a comprehensive state-of-the-art review is crucial. This review should analyze the shear capacity of UHPC-DBs, focusing on influential factors such as compressive strength, ρ_sv, ρ_sh, ρ_s, λ, and FC.

Table 1. Comprehensive dataset from literature review.

References	Compressive Strength (MPa)	Beam Dimensions (l × w × d) (mm)	ρs (%)	ρsv (%)	ρsh (%)	λ	a/mm	Fiber Type		Fiber Content (kg/m3)		Fiber Aspect Ratio (Length/Diameter)		Fiber Tensile Strength (MPa)		Ultimate Shear Capacity (kN)	Mid-span Deflection (mm)	Failure Mode	FEA	Loading Conditions
								Steel	Syn	Steel	Syn	Steel	Syn	Steel	Syn
[7]	86.5	1200 × 150 × 600	3.62	0.19	0.16	0.923	500	-	-	0	0	-	-	-	-	609.42	2.25	Diagonal compression failure	N	Three-point loading
	113.4							S		0.5		65		2300		873.31	3.25	Shear compression (SC) failure
	125.6									1						1089.40	3.5
	151.4									2						1356.96	3.70
	173.6									3						1407.18	3.75
	138.5					0.554	300			1						1409.21	4.45	Diagonal compression failure
						0.739	400									1411.80	4.60	Shear compression failure
						0.923	500									1208.20	4.30
			3.19													1150.70	4.14
			3.35													1176.40	4.25
			3.62	0												1056.30	3.35
				0.38												1392.24	6.9
				0.15												1180.60	4.27
				0.19	0.24											1270.6	4.80
					0.31											1358.70	7.2
[8]	114.2	1000 × 100 × 500	3.49	0.6	0.33	0.8	400	-	-	0	0	-	-	-	-	915	6.1	Shear compression (SC) failure	N	Three-point loading
	88.1			0	0			HE	PP	1	0.25	50	480	1100	350	566	8.2
	84.7									2	0.5					571	7.8
[11]	139	1000 × 150 × 300	2.01	0	0	0.961	250	HE	-	1.5	0	54.55	-	1345	-	1115	4.40	Diagonal shear crack	N	Four-point loading
				0.78												1260	8
[15]	60	1500 × 150 × 500	0.42 (BFRP)	0.6	0.349	0.87	400	-	-	0	0	-	-	-	-	583	22	Diagonal cracks	Ansys software (v19): 10% difference compared to EXP results	Four-point loading
			0.51 (BFRP)													659	14.8	Compression cracks and BFRP failure rupture
			0.81 (BFRP)													720	13.4
			0.51													511	14.4	Flexural tension failure
[36]	67	750 × 150 × 400	1.38%	0.419	0	0.75	300	-	PP	0	1	-	480	-	350	85.32	7.79	Diagonal shear crack	Abaqus software: 3% difference compared to EXP results	Three-point loading
[37]	132.5	1900 × 80 × 400	9.5	0.708	0.236	0.875	350	HE	-	1.5	0	65	-	828	-	1140	3.25	Diagonal shear crack	Abaqus software (v6.14): 7% difference compared to EXP results	Continuous beam
[12]	139	1000 × 150 × 300	2.01	0	0	0.961	250	HE	-	1.5	0	54.55	-	1345	-	1104.9	4.35	Splitting shear failure	N	Four-point loading
				0.78												1334.0	8.1
[16]	73.16	1600 × 200 × 600	0.67	0.33	0.33	0.13	75	-	-	0	0	-	-	-	-	1321	2.51	Splitting	N	Uniform load
			1.05													1401	3.18	Local pressure
			1.27													1409	3.43	Diagonal-compression
			1.05		0.25											1226	2.03
					0.5											1531	2.42
[13]	172.9	1000 × 80 × 400	3.67	0.47	0	0.79	276.5	HE	-	1.5	0	25	-	828.3	-	890	1.9	Diagonal shear crack	Abaqus software (v6.9): 10% difference compared to EXP results	Four-point loading
				0.84												1060	2
				0.47		0.94	329									830	1.7
				0.84												910	1.8
				1.68												1010	1.85
[38]	150	2700 × 200 × 500	3.44	0.5	0	2.7	1350	S		2.5	0	80	-	2500	-	717	12	Diagonal shear crack	Abaqus software- 3% difference compared to EXP results	Three-point loading
[39]	84.63	1200 × 150 × 400	1.05	0	0	1	400	S	-	1.5	0	65	-	2300	-	361	4.03	Diagonal shear crack	N	Three-point loading
[9]	158.8	800 × 150 × 300	7.05	0	0	1.2	293.4	S	-	2	0	-	-	-	-	737.5	2.97	Shear compression failure	N	Three-point loading
		1100 × 150 × 300				1.8	440.1									538	5.00
		1700 × 150 × 300				3.1	758.0									374	21.59	Flexural failure
	126.1	800 × 150 × 300				1.2	293.4	-		0						434	2.73	Diagonal compression failure
	126.1	1100 × 150 × 300				1.8	440.1									112.5	1.84	Diagonal tension failure
	126.1	1700 × 150 × 300				3.1	758.0									173	5.98
	160.3	1800 × 200 × 350	7.62			2	582	S		2						1250	5.56	Shear compression failure
	155									1.5						931	4.23
	113.8							-		0						459.5	2.55	Diagonal compression failure
	160.3	1800 × 200 × 400	6.67			2	682	S		2						1083.5	4.69	Shear compression failure
	155									1.5						801.5	4.25
	113.8							-		0						397	2.75	Diagonal tension failure
[10]	140	2000 × 150 × 225	2.62	2.33	0	1.8	328.5	S	-	1	0	59	-	2500	-	172.5	21.14	Shear tension failure	N	Four-point loading
	150									2						186	23.30	Shear compression failure
	140			1.40						1						147.5	16.10	Shear tension failure
	150									2						176	18.06	Shear compression failure
	140		3.67							1						155.5	17.85	Shear tension failure
	150									2						182.8	19.86	Shear compression failure
	140		2.62			2.6	474.5			1						104.0	14.19	Shear tension failure
			3.67													114.5	13.18
	150		2.62							2						116	15.03	Shear compression failure
			3.67													125.05	16.18
[14]	132.10	1000 × 80 × 400	5.46	0.35	0	0.79	276.5	HE	-	1.5	-	25	-	828.3	-	760	2.5	Shear compression failure	N	Four-point loading

l: length of deep beam; w: width of deep beam; d: depth of deep beam; a: distance between concentrated load and nearest beam support; Syn: synesthetic; FEA: finite element analysis; S: steel fiber; HE: hooked-end steel fiber; N: no; BFRP: basalt fiber-reinforced polymer bars.

summarizes the comprehensive dataset, including the compressive strength of UHPC-DBs, beam dimensions, ρ_sv, ρ_sh, ρ_s, λ, FC, fiber type, fiber aspect ratio, fiber tensile strength, ultimate shear capacity with associated mid-span deflection, failure modes, finite element analysis results with percentage differences from experimental results, and loading conditions.

Table 1 illustrates the impact of various fibers, including hooked-end steel fiber, polypropylene fiber, and steel fiber, on the shear capacity of UHPC-DBs, as investigated by researchers [36,37,38,39].

4. Influence of Effective Factors on the Shear Capacity of UHPC-DBs

4.1. Influence of Fiber Content (FC)

The shear behavior of UHPC deep beams (UHPC-DBs) is significantly influenced by fiber content in the UHPC mix design. This enhancement is attributed to the fiber’s crack-bridging effect and increased tensile strength, resulting in up to a 35.58% improvement in shear capacity when comparing specimens without fiber to those with 1% steel fiber [40].

4.2. Influence of Vertical Web Reinforcement (ρ_sv)

Vertical web reinforcement enhances the shear capacity and structural integrity of UHPC deep beams (UHPC-DBs). This improvement is attributed to the concrete confinement provided by ρ_sv, which helps control crack propagation. The design of ρ_sv in UHPC-DBs can be based on the strut-tie model (STM) using FHWA-RC-24-0004 [41].

4.3. Influence of Horizontal Web Reinforcement (ρ_sh)

The shear capacity of UHPC-DBs can be enhanced by incorporating horizontal web reinforcements, as they help transfer tensile stress across the beam’s depth and reduce crack propagation [42].

4.4. Influence of Longitudinal Reinforcement (ρ_s)

Incorporating ρ_s into UHPC-DBs enhances their shear capacity due to its role as a tension tie in the STM. It effectively transfers tensile stresses and helps UHPC-DB resist shear forces. This reinforcement also controls crack propagation and enhances the structural integrity of UHPC-DBs [41].

4.5. Influence of Shear Span-to-Depth Ratio (λ)

According to the STM, as λ decreases, the area near the applied load positions and supports is treated as a diagonal compression strut, which effectively transfers shear forces to the support. Research findings indicate that decreasing λ from 0.9 to 0.3 enhances the shear capacity by up to 19.33% [43].

5. Effect of Compressive Strength on the Shear Capacity of UHPC Deep Beams

The compressive strength of UHPC can significantly affect the shear capacity of UHPC-DBs. Chen et al. [7] evaluated the impact of various UHPC compressive strengths on the shear capacity of UHPC-DBs. The experimental results indicated that shear capacity increased with higher compressive strengths, as shown in Figure 3a. Specifically, for UHPC deep beams with compressive strengths of 132.3 MPa and 198.6 MPa, the shear capacities were 873.31 kN and 1407.18 kN, respectively, demonstrating a 37.9% increase in shear capacity when the compressive strength was raised by 33.38%.

In a study by Smarzewski [8], the impact of UHPC compressive strength on shear capacity was assessed experimentally. The results showed that specimens with a compressive strength of 114.2 MPa exhibited a shear capacity approximately 38% higher than those with a compressive strength of 88.1 MPa, indicating that a 22.85% increase in compressive strength resulted in a 38.14% improvement in shear capacity.

Additionally, the influence of compressive strength on the shear capacity of three different UHPC-DBs with varying dimensions was evaluated by Deng et al. [9]. Figure 3b demonstrates that for the first series of deep beams with dimensions of 800 × 150 × 300 mm, shear capacity increased by 37.9% when the compressive strength of UHPC was enhanced by 33.38%. In the second series, for the UHPC-DB with dimensions of 1800 × 200 × 400 mm, the shear capacity improved by 63.36% when the compressive strength was increased by 29%. Finally, for the third type of deep beam with dimensions of 1800 × 200 × 350 mm, shear capacity increased by 63.24% with a 29% increase in compressive strength. It is noteworthy that in the second and third series, the length and width of the UHPC-DBs are identical. However, despite the difference in their depths, which are 400 mm and 350 mm, respectively, their shear span-to-depth ratios (λ) are equal to 2. This is attributed to the varying distances between the concentrated load and the nearest beam support (a), which are 682 mm and 582 mm, respectively. Overall, it can be concluded that when all other parameters remain constant, the UHPC-DB with a smaller depth exhibits higher shear capacity compared to those with greater depth.

Moreover, in another study conducted by Ahmad et al. [10], the shear capacity of the UHPC-DB improved by 7.25% when the compressive strength of UHPC was increased by 6.66%.

The overall trend between the percentage increase in UHPC compressive strength and the percentage increase in the shear capacity of UHPC-DBs approximately follows a linear relationship with a slope of 1.55, as illustrated in Figure 3c.

Figure 3a demonstrates that increasing the compressive strength of UHPC-DBs enhances their shear capacity, with a trend line exhibiting an R² value of 0.96. Figure 3b indicates that beams measuring 1800 mm × 200 mm × 350 mm exhibit slightly higher shear capacities than those measuring 1800 mm × 200 mm × 400 mm, suggesting that beam depth influences shear performance. Finally, Figure 3c presents an overall trend line, incorporating data from various studies with differing beam dimensions and reinforcement ratios, resulting in an R² value of 0.63. This variability underscores the impact of beam geometry and reinforcement configurations on shear capacity.

6. Effect of Vertical Web Reinforcement (ρ_sv) on the Shear Capacity of UHPC Deep Beams

The amount of ρ_sv is one of the most influential factors affecting the shear capacity of UHPC-DBs.

Chen et al. [7] assessed the influence of ρ_sv on the shear capacity of UHPC-DBs. In their study, four different ρ_sv regimes were evaluated: 0%, 0.15%, 0.19%, and 0.38%. The findings revealed that the shear capacity of UHPC-DBs increased by up to 24.13% when comparing UHPC-DBs reinforced with 0.38% ρ_sv to those without any ρ_sv. The increasing trend in the shear capacity of the UHPC-DBs with varying ρ_sv regimes is illustrated in Figure 4a.

In another study, two different ρ_sv regimes were considered, and their impact on the shear capacity of UHPC-DBs was evaluated by Smarzewski [8]. The findings revealed a 38.14% improvement in the shear capacity of UHPC deep beams when specimens with no ρ_sv were reinforced with 0.6% ρ_sv.

Furthermore, the impact of two different ρ_sv regimes, including 0% and 0.78%, on the shear capacity of UHPC-DBs was assessed by Abadel et al. [11]. The research findings indicated that the shear capacity of the UHPC-DBs increased by up to 11.5% when comparing specimens without ρ_sv to those reinforced with 0.78% ρ_sv.

Similarly, two different ρ_sv regimes, including 0% and 0.78%, were considered, and their impact on the shear capacity of UHPC-DB was evaluated by Abadel et al. [12]. Based on their findings, a 17.17% improvement in shear capacity was achieved when specimens reinforced with 0.78% ρ_sv were compared to those without ρ_sv.

Yousef et al. [13] evaluated the impact of ρ_sv on two series of UHPC-DBs with λ of 0.79 and 0.94. The first series, with λ = 0.79, employed two ρ_sv regimes (0.47% and 0.84%), while the second series, with λ = 0.94, used three regimes (0.47%, 0.84%, and 1.68%). The findings revealed a 16.03% improvement in shear capacity for the first series when comparing specimens with 0.47% and 0.84% ρ_sv. For the second series, a 17.82% improvement was observed when comparing specimens with 0.47% and 1.68% ρ_sv. The increasing trend in shear capacity for these two series, considering the increase in their compressive strength, is illustrated in Figure 4b. Additionally, Figure 4b illustrates that, under identical conditions of ρ_sv, the improvement in shear capacity is more pronounced in specimens with lower λ compared to those with higher λ, indicating that reducing λ can enhance the shear capacity of UHPC-DBs.

In another study, Ahmad et al. [10] investigated the impact of ρ_sv on the shear capacity of UHPC-DBs. Two different ρ_sv regimes, 1.4% and 2.33%, were considered for two distinct mix designs. For the first mix design, the shear capacity improved by up to 14.92% when comparing specimens reinforced with ρ_sv of 1.4% and 2.33%. For the second mix design, the shear capacity improvement was 5.37%. As the compressive strengths of mix designs one and two were 140 MPa and 150 MPa, respectively, it can be concluded that the influence of ρ_sv on the shear capacity is more pronounced in UHPC mix designs with slightly lower compressive strengths compared to those with higher compressive strengths. The increasing trend in the shear capacity of the UHPC-DBs, considering their ρ_sv, is illustrated in Figure 4c. Furthermore, Figure 4c shows that, under identical conditions of ρ_sv, specimens with higher compressive strength exhibit greater shear capacity compared to those with lower compressive strength.

Considering all previous studies [7,8,10,11,12,13] on the impact of ρ_sv on the shear capacity of UHPC-DBs, it can be concluded that the overall relationship between normalized ρ_sv and the corresponding normalized shear capacity exhibits an increasing trend, as illustrated in Figure 4d.

Figure 4a shows that increasing ρ_sv in a UHPC-DB [7] enhances its shear capacity, with an R² value of 0.99. In another study [9], this improvement was 0.98, suggesting that ρ_sv significantly influences the shear capacity of UHPC-DBs.

7. Effect of Longitudinal Reinforcement (ρ_s) on the Shear Capacity of UHPC Deep Beams

Since ρ_s is another factor affecting the shear capacity of UHPC-DBs, it has attracted researchers’ attention to investigate its impact. The impact of ρ_s with three different regimes, 3.19%, 3.35%, and 3.62%, on the shear capacity of UHPC-DB was assessed by Chen et al. [7]. Their findings revealed that the shear capacity of UHPC-DB increases with a higher amount of ρ_s. As illustrated in Figure 5a, an increase in ρ_s by 11.88% resulted in an improvement in shear capacity of up to 4.76%.

In another study by Erfan et al. [15], the impact of varying ρ_s on the shear behavior of UHPC-DBs was investigated. The researchers examined three different ρ_s values: 0.42%, 0.51%, and 0.81%. Their findings revealed that increasing ρ_s by 48.15% led to a 19.02% enhancement in the shear capacity of UHPC-DBs, as illustrated in Figure 5b.

In a study by Si et al. [16], the impact of ρ_s on the shear capacity of UHPC-DBs was investigated. The researchers examined three different ρ_s values: 0.67%, 1.05%, and 1.27%. Their findings demonstrated that increasing ρ_s by 47.24% resulted in a 6.25% improvement in the shear capacity of UHPC-DBs, as illustrated in Figure 5c.

Moreover, the impact of ρ_s on the shear capacity of UHPC-DBs with various ρ_s regimes, including 2.62% and 3.67%, was investigated by Ahmad et al. [10]. The study was conducted under two different compressive strengths, 140 MPa and 150 MPa. Their findings indicated that the shear capacity of UHPC-DBs improved by 5.14% for the 140 MPa beams and 3.72% for the 150 MPa beams with a 28.61% increase in ρ_s, suggesting that the impact of ρ_s on shear capacity is more pronounced in UHPC-DBs with lower compressive strength, as illustrated in Figure 5d.

Considering previous research [7,10,15,16] on the impact of ρ_s on the shear capacity of UHPC-DBs, there is a relationship indicating that an increase in ρ_s leads to an enhancement in shear capacity. This relationship can be represented by a linear trend line with a slope of 0.25, as illustrated in Figure 5e.

Figure 5a–c show that an increase in ρ_s in UHPC-DBs, as reported in three references [7,15,16], resulted in an improvement in shear capacity, with R² values of 0.99, 0.87, and 0.92, respectively.

8. Effect of Horizontal Web Reinforcement (ρ_sh) on the Shear Capacity of UHPC Deep Beams

Another factor affecting the shear capacity of UHPC-DBs is ρ_sh. Several studies have evaluated its impact on the shear capacity of UHPC-DBs. For instance, Chen et al. [7] investigated various ρ_sh regimes, including 0.16%, 0.24%, and 0.31%. Their findings revealed that the shear capacity increased by up to 11.07% with a 48.38% increase in ρ_sh, as illustrated in Figure 6a.

In another study, Smarzewski et al. [8] investigated the effect of two different ρ_sh regimes, 0% and 0.33%, on the shear capacity of UHPC-DBs. Their findings revealed that reinforcing a specimen without ρ_sh with 0.33% ρ_sh increased its shear capacity by up to 38.14%.

Si et al. [16] investigated three ρ_sh regimes (0.25%, 0.33%, and 0.5%) to reinforce UHPC-DBs. Their findings revealed a 19.92% improvement in shear capacity when ρ_sh was increased by up to 50%, as illustrated in Figure 6b.

Considering all previous studies [7,8,16] on the impact of ρ_sh on the shear capacity of UHPC-DBs, the relationship between ρ_sh and SC generally follows an increasing trend, represented by a linear trend line with a slope of 0.45, as illustrated in Figure 6c.

As illustrated in Figure 6, an increase in ρ_sh in studies [7,16] led to an improvement in the shear capacity of UHPC-DBs, with R² values of 0.98 and 0.90, respectively. This suggests that the increasing trends are approximately similar, with an overall R² value of 0.91.

9. Effect of Shear Span-to-Depth Ratio (λ) on the Shear Capacity of UHPC Deep Beams

The shear span-to-depth ratio (λ) significantly affects the shear capacity of UHPC-DBs. Previous research has extensively examined this relationship. Chen et al. [7] investigated the impact of λ on the shear capacity of UHPC-DBs using three ratios: 0.554, 0.739, and 0.923. As shown in Figure 7a, their findings revealed that reducing λ enhances the shear capacity of UHPC-DBs. Specifically, a reduction in λ of up to 39.98% led to an improvement in shear capacity by as much as 14.42%.

In a study by Yousef et al. [13], the effect of two λ, 0.79 and 0.94, was examined under two ρ_sv of 0.47% and 0.84%. Their findings revealed that a 15.96% reduction in λ increased the shear capacity of UHPC-DBs by 6.74% and 14.15% for ρ_sv values of 0.47% and 0.84%, respectively. These results emphasize that the influence of λ on shear capacity is more pronounced in specimens with higher ρ_sv, as illustrated in Figure 7b.

Furthermore, Deng et al. [9] investigated the shear behavior of UHPC-DBs with three different λ: 1.2, 1.8, and 3.1. Their results showed that reducing λ by up to 61.29% increased the shear capacity of UHPC-DB by as much as 49.29%, as illustrated in Figure 7c.

Considering all previous research findings, the overall relationship between λ and shear capacity exhibits a decreasing trend, indicating that as λ increases, shear capacity decreases linearly with a slope of 0.5, as illustrated in Figure 7d.

Figure 7 shows that in studies [7,9], an increase in λ leads to a decreasing trend in shear capacity, with R² values of 0.73 and 0.93, respectively. This results in an overall decreasing trend, with R² values of 0.75, as illustrated in Figure 7d.

10. Effect of Fiber Content (FC) on the Shear Capacity of UHPC Deep Beams

A review of the literature on the impact of fiber content on the shear capacity of UHPC-DBs suggests that increasing steel fiber content up to 3% significantly enhances shear capacity. Chen et al. [7] investigated the effects of four fiber contents (0.5%, 1%, 2%, and 3%) on the shear capacity of UHPC-DBs. Their findings revealed that the shear capacity could increase by up to 37.93% when fiber content was raised from 0.5% to 3%, as illustrated in Figure 8a. Additionally, Smarzewski [8] investigated the effect of two fiber contents on the shear behavior of UHPC-DBs. The findings revealed a shear capacity improvement of 0.88% when deep beams were reinforced with 2% steel and 0.5% polypropylene fibers, compared to those reinforced with 1% steel and 0.25% polypropylene fibers.

In another study, Deng et al. [9] evaluated the impact of three fiber contents, 0%, 1.5%, and 2%, on the shear capacity of UHPC-DBs. Their findings demonstrated that the shear capacity of UHPC-DBs could be enhanced by up to 63.24% when specimens without fiber reinforcement were compared to those reinforced with 2% steel fibers, as shown in Figure 8b. Additionally, Ahmad et al. [10] assessed the impact of two fiber content levels, 1% and 2%, under two different ρ_s regimes and two distinct λ values. Their findings indicated that the shear capacity could be improved by up to 16.19% when deep beams reinforced with 1% fiber were compared to those reinforced with 2%, with ρ_s and λ being 2.62% and 1.8, respectively. This improvement in shear capacity was reduced to 14.93% under the same λ when ρ_s was 3.67%, suggesting that the effect of fiber content on the shear capacity of UHPC-DBs is more pronounced at lower ρ_s values, as illustrated in Figure 8c. The shear capacity improvement of reinforced UHPC-DBs was 10.34% when reinforced with 1% and 2% fiber content, with ρ_s and λ being 2.62% and 2.6, respectively. This indicates that the effect of fiber content is more significant at lower λ values, as shown in Figure 8d.

Considering all previous studies [7,8,9,10] that evaluated the impact of fiber content on the shear capacity of UHPC-DBs, it can be observed that increasing fibers content up to 3% enhances shear capacity of UHPC-DBs, following a linear trend with a slope of 0.5, as illustrated in Figure 8e.

An increase in fiber content in studies [7,9] resulted in an increasing trend, with R² values of 0.89 and 0.97, respectively. This suggests that the optimal steel fiber content in UHPC mix design for enhancing the shear capacity of UHPC-DBs is 2%.

11. Finite Element Analysis of Shear Behavior in UHPC-DBs

A thorough review of the literature reveals several studies in which finite element analysis (FEA) was used to model and simulate the shear behavior of UHPC-DBs [13,15,36,37,38]. Two advanced FEA tools, ANSYS and ABAQUS, are commonly used to simulate UHPC-DBs reinforced with fibers. The literature shows only one study [15] in which ANSYS was employed to simulate the shear behavior of fiber-reinforced UHPC-DBs, with a difference of approximately 10% between the experimental and FEA results.

In contrast, several studies [13,36,37,38] utilized ABAQUS to simulate the shear behavior of UHPC-DBs, with differences of 10%, 3%, 7%, and 3%, between experimental and FEA results, as reported in [13,36,37,38], respectively.

12. Conclusions and Recommendations

This paper critically reviewed the effective factors influencing the shear capacity of UHPC-DBs, including compressive strength, vertical web reinforcement (ρ_sv), horizontal web reinforcement (ρ_sh), longitudinal web reinforcement (ρ_s), shear span-to-depth ratio (λ), and fiber content (FC). A review of the literature indicates that an increase in compressive strength, ρ_sv, ρ_sh, ρ_s, and FC leads to a corresponding increase in the shear capacity of UHPC-DBs, following linear trends with slopes of 1.55, 0.06, 0.45, 0.25, and 186.8, respectively. Conversely, an increase in λ results in a reduction in the shear capacity of UHPC-DBs, following a decreasing linear trend with a slope of −0.98. The maximum influence of each factor on the shear capacity of UHPC-DBs is as follows:

• In terms of the impact of compressive strength on the shear capacity of UHPC deep beams, a 63.36% improvement, the maximum observed, occurs when compressive strength increases by up to 29%.
• The shear capacity of UHPC-DBs can be enhanced by up to 38.14% by incorporating ρ_sv of 0.6, compared to those without any ρ_sv.
• An increase in ρ_s by up to 48.15% results in a maximum improvement of 19.02% in the shear capacity of UHPC-DBs.
• A maximum improvement of 38.14% in the shear capacity of UHPC-DBs can be achieved when ρ_sh increases by up to 0.33.
• A reduction of 61.29% in λ resulted in a maximum increase of 49.29% in the shear capacity of UHPC-DBs.
• Incorporating steel fiber with a content of 2% resulted in a maximum improvement of 63.24% in the shear capacity of UHPC-DBs, compared to those reinforced with no fibers.

A review of the literature reveals a significant research gap in evaluating the shear behavior of UHPC-DBs reinforced with synthetic fibers, with only one study available on this topic. To address this, it is essential to investigate the impact of various factors, including compressive strength, ρ_sv, ρ_sh, ρ_s, λ, FC, and geometrical dimensions, to better understand the shear behavior of UHPC-DBs reinforced with synthetic fibers. Additionally, the effect of fiber aspect ratio on the shear behavior of UHPC-DBs warrants further investigation. Exploring the impact of hybrid fibers on the shear behavior of UHPC-DBs is also highly recommended. Furthermore, evaluating the simultaneous influence of two or more factors on the shear behavior of UHPC-DBs is crucial, as current standards have not adequately addressed this complexity.

In terms of finite element analysis (FEA), previous studies have predominantly modelled concrete reinforced with steel rebars without incorporating fibers as distinct elements. Modelling UHPC-DBs with integrated elements, including concrete, steel reinforcement, and fibers, could provide a more accurate and comprehensive understanding of the shear behavior of UHPC-DBs reinforced with fibers.

Finally, the application of machine learning (ML) techniques, such as artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs), or a combination of these, offers potential for developing predictive models for the shear behavior of UHPC-DBs. Employing optimization algorithms, such as particle swarm optimization (PSO), could further enable the optimization of factors to maximize shear capacity. Notably, no research to date has explored the use of ML in predicting the shear behavior of UHPC-DBs reinforced with fibers or in optimizing the effective factors.