Experimental and Numerical Investigation of Shear Performance of RC Deep Beams Strengthened with Engineered Cementitious Composites

Abstract

Reinforced concrete (RC) deep beams constructed with low-strength concrete are susceptible to sudden splitting failures in the strut region due to shear–compression stresses. To mitigate this vulnerability, various strengthening techniques, including steel plates, fiber-reinforced polymer sheets, and cementitious composites, have been explored to confine the strut area. This study investigates the structural performance of RC deep beams with low-strength concrete, strengthened externally using an Engineered Cementitious Composite (ECC) layer. To ensure effective confinement and uniform shear distribution, shear reinforcement was provided at equal intervals with configurations of zero, one, and two vertical shear reinforcements. Four-point bending tests revealed that the ECC layer significantly enhanced the shear capacity, increasing load-carrying capacity by 51.6%, 54.7%, and 46.7% for beams with zero, one, and two shear reinforcements, respectively. Failure analysis through non-linear finite element modeling corroborated experimental observations, confirming shear–compression failure characterized by damage in the concrete struts. The strut-and-tie method, modified to incorporate the tensile strength of ECC and shear reinforcement actual stress values taken from the FE analysis, was used to predict the shear capacity. The predicted values were within 10% of the experimental results, underscoring the reliability of the analytical approach. Overall, this study demonstrates the effectiveness of ECC in improving shear performance and mitigating strut failure in RC deep beams made with low-strength concrete.

1. Introduction

The need to strengthen existing reinforced concrete (RC) structures has grown in response to increased service load demands and evolving structural requirements. RC deep beams are critical structural components in many construction applications. They are defined by the American Concrete Institute (ACI) code based on two key geometric criteria: (1) a shear span-to-overall depth ratio less than two, and (2) a clear span-to-overall depth ratio less than four [1,2]. These beams predominantly transfer loads through shear action and require appropriate shear reinforcement. Steel-reinforced low-strength concrete deep beams are particularly susceptible to brittle compression failure due to the poor confinement of the concrete strut and their inherently weak nature while carrying tensile loads [3]. To mitigate this, various strengthening techniques employing advanced materials like steel and fiber-reinforced polymers (FRPs) have been explored to confine the strut region and enhance the shear capacity [4,5,6].

The literature highlights significant ECC materials and technology advancements, leading to commercial and practical applications [7,8]. ECC, a distinctive fiber-reinforced material, was developed recently based on micromechanics principles [9]. ECC is designed to exhibit steady-state multiple cracking and strain-hardening behavior in tension by incorporating approximately 2% of randomly dispersed short polymeric fibers, such as polyethylene, polyvinyl alcohol (PVA), or polypropylene. These properties can be further enhanced through microstructural tailoring and material optimization techniques [10,11,12]. Due to the absence of coarse aggregates, ECC typically exhibits a lower elastic modulus than conventional concrete. However, it compensates with high tensile strain capacities ranging from 0.45% to 0.65% and compressive strengths between 30 MPa and 90 MPa, rendering its compressive performance comparable to or even exceeding that of ordinary cement concrete [13]. Furthermore, ECC demonstrates impressive tensile strength, ranging from 5.0 to 8.0 MPa, with failure strains between 3% and 5%.

Recent research has investigated innovative strengthening techniques that integrate ECC with other materials to enhance the shear performance of reinforced concrete beams. For instance, Emara et al. examined the combined application of ECC and carbon fiber reinforced polymer (CFRP) sheets, reporting a significant increase in shear capacity ranging from 61.1% to 160.1%, compared to control specimen capacities [14]. This hybrid system provided better crack control and enhanced load capacity than conventional strengthening methods. Similarly, Yuan et al. [15] anticipated a unique strengthening technique by integrating high-strength steel wire with ECC layers, yielding promising results in strength enhancement and ductility improvement. This hybrid approach addresses some limitations that ECCs have: superior ductility, crack control, and enhanced bond characteristics provide a promising alternative to conventional methods, mitigating brittle failure risks while improving structural resilience. Wei et al. utilized a 10 mm-thick ECC layer as a strengthening material within the shear span of RC beams, demonstrating its effectiveness in significantly enhancing shear strength and providing a practical strengthening solution [16]. ECC layers’ high tensile load-carrying capacity makes them well-suited for structural applications such as ECC-concrete composite beams. This study reported that composite beams with a height replacement ratio of 0.4 and a steel reinforcement ratio of 1.70% exhibited superior load-carrying performance [17]. Li et al. [18] explored highly ductile fiber-reinforced concrete (HDC) jacketing for shear strengthening of RC beams by varying parameters, including the shear-span-to-effective-depth ratio, internal shear reinforcement, and HDC jacket thickness. Their results indicated improvements in shear capacity ranging from 13.6% to 145.5%, highlighting that targeted placement of ECC in critical regions can substantially enhance structural performance without necessitating full beam jacketing.

Furthermore, Zhu et al. [19] investigated two advanced forms of ECC: a high-strength engineered cementitious composite (HS-ECC), with compressive strengths ranging from 80 to 150 MPa, and an ultra-high-strength engineered cementitious composite (UHS-ECC), characterized by compressive strengths exceeding 150 MPa. Their study reviewed recent progress in developing and applying a UHS-ECC, from material formulation to structural performance. Additionally, in parallel, research has also explored the use of lightweight ECC for strengthening RC beams. Findings revealed that normal-weight and lightweight ECC (LWECC) beams incorporating PVA fibers outperformed those with polypropylene fibers. Furthermore, an LWECC developed using slate aggregate, achieving densities and strengths comparable to lightweight concrete, demonstrated significant improvements in structural behavior, including 57.8% higher energy absorption, 64% greater resistance to post-diagonal cracking, 45.9% increase in normalized shear strength, and a 112.1% enhancement in deformability index [20].

All these studies demonstrate that the ECC strengthening of RC beams continues to evolve, with promising innovations in applying techniques, materials, and applications [21,22]. Combining ECC with other strengthening materials and developing specialized ECC has significant potential for future applications. However, continued research is required to address existing challenges: material cost, type of fiber, strengthening technique, bonding, and interface behavior. Additionally, the absence of standardized design guidelines and construction complexities poses practical challenges. Addressing these issues through continued research is crucial for the widespread implementation of ECC in structural strengthening.

Research Gap and Significance

A review of the existing literature highlights a significant gap in the application of externally applied ECC layers for strengthening RC deep beams, particularly in realistic conditions. Most prior studies have focused on moderate-strength concrete and have frequently employed irregular, asymmetrical, or absent vertical shear reinforcement configurations, as shown in

Table 1. Arrangements of shear reinforcement with ECC strengthening of deep beams.

References	fc’	a/d	Arrangement of Shear Reinforcement	Remarks
Wei et al. [16]	36	1.5		The shear reinforcement was not arranged equally along the shear span.
Li et al. [18]	32.13	2		Moderate-strength concrete is used.
Khalil et al. [21]	26.4	1		The shear reinforcement was not provided in the shear span.
Present study	15.9	1.5		The shear reinforcement is arranged equally along the shear span.

. The confinement of the concrete strut plays a critical role in enhancing the strength and ductility of RC deep beams. It is well established that improved confinement delays crushing of concrete, enhances energy dissipation, and transforms brittle failure into a more ductile response. In this study, the application of ECC on the side faces of the beams provided an effective passive confinement mechanism. This contributed to a more uniform stress distribution and controlled the propagation of diagonal cracks. Particularly in low-strength concrete beams, such confinement is essential to resist localized crushing and improve overall shear capacity. The fiber bridging effect of ECC further augmented this behavior by maintaining crack continuity and preventing sudden loss of load-carrying capacity [23]. These configurations do not accurately reflect the confinement efficiency of ECC, especially for RC deep beams with a shear span-to-depth ratio (a/d) of 1.5. Additionally, the presence of non-uniform reinforcement layouts within the critical diagonal strut region can lead to uneven crack patterns and localized stress concentrations, making it difficult to isolate and assess the true contribution of ECC. The novelty of the present study lies in addressing these limitations by experimentally investigating RC deep beams constructed with low-strength concrete, a consistent a/d ratio of 1.5, and a symmetrical vertical shear reinforcement layout. The shear reinforcement is uniformly distributed along the span, including at mid-span and key shear regions, to ensure uniform confinement and controlled crack propagation. This approach allows for a more accurate and reliable assessment of the ECC layer’s contribution to shear performance. This study aims to provide clearer insights into the effectiveness of ECC strengthening under practical and representative conditions, contributing to the advancement of standardized design practices, particularly relevant for regions where low-strength concrete is commonly used.

There is also a need for more experimental and numerical validation to understand the behavior of ECC-strengthened RC deep beams. Furthermore, the lack of standardized design guidelines and practical implementation highlights the need for multiple research investigations. This study focuses on experimentally evaluating the structural behavior and shear strength enhancement of reinforced concrete deep beams equipped with uniformly distributed shear reinforcements and externally strengthened using an ECC layer. A non-linear finite element (FE) analysis supplements the experimental investigation to validate the load–deflection behavior and failure modes. Additionally, the shear capacity of the deep beams is predicted using the strut-and-tie (ST) method, with modifications to account for the tensile contribution of the ECC layer.

2. Experimental Investigation

2.1. Materials

In this present study, the materials used for the preparation of ECC were ordinary Portland cement (OPC) of 43 grade, conforming to IS 8112:2013 [24], Class F fly ash, complying with IS 3812:2003 [25], silica fume, with an average particle size of 0.2 microns, silica sand, with a particle size of 200 microns, polycarboxylate ether-based superplasticizer, specifically Auramix 350 manufactured by Fosroc (Bangalore, India), and potable water. Polyvinyl alcohol (PVA) fibers procured from Kuraray India Pvt. Ltd. (Uttar Pradesh, India) were also used in this research for preparing the ECC.

Table 2. Properties of PVA fiber.

Tensile Strength (MPa)	Diameter (μm)	Fiber Length (mm)	Young’s Modulus (GPa)	Density (g/cm3)
1600	40	12	40	1.3

shows the properties of the PVA fibers. The deep beams were cast with the materials, which include OPC of 43 grade, M-sand complying with zone II of IS 383:1970 (reaffirmed 2002) [26], crushed gravel with a nominal size of 20 mm as coarse aggregates, and potable water. The reinforcement for the deep beams was provided with high yield strength deformed (HYSD) bars of diameter 20 mm and 25 mm for the top and bottom, respectively. Stirrups were provided with 6 mm bars with uniform spacing. The mechanical properties of the steel reinforcement are given in

Table 3. Properties of steel reinforcement.

Diameter (mm)	Yield Strength (MPa)	Young’s Modulus (GPa)
6	464	200
20	550	203
25	550	203

.

2.2. Mix Proportion, Preparation and Testing of ECC

The preparation of the ECC mix follows a systematic sequence, as illustrated in Figure 1. Initially, the dry mixing of cement, fly ash, and silica fume was carried out to achieve a uniform texture in a mixer machine for about 2 to 3 min. Silica sand was then added to the mixture as a fine aggregate, followed by adding water gradually in the mixer machine along with superplasticizer to improve workability. Subsequently, PVA fibers were slowly introduced into the mix. Mixing continued for another 3 to 5 min until a uniform, fiber-dispersed ECC mix with smooth consistency was achieved and suitable for casting. This thorough mixing process ensures a homogeneous ECC matrix to enhance mechanical performance. The mix was cast into cubes of size 70 mm to test the compressive strength of the ECC after a 28-day curing period. The summary of the mixture proportion is provided in

Table 4. Mixture proportion of ECC.

Binder			Silica Sand (kg/m3)	Water (kg/m3)	Superplasticizer (kg/m3)	PVA Fibers (kg/m3)
Cement (kg/m3)	Fly Ash (kg/m3)	Silica Fume (kg/m3)
257.4	772.2	257.4	450.45	347.49	2.57	26

.

Determining the tensile strength of ECC accurately is critical due to its strain-hardening behavior and multiple cracking characteristics. Various experimental methods have been developed and standardized to evaluate the tensile properties of ECC. The direct tensile test using dog-bone specimens, first standardized by Li et al. [27], directly measures the tensile properties of ECC. However, the method requires highly accurate alignment and gripping to prevent stress concentrations and premature failures, making it technically demanding and sensitive to setup imperfections. An alternative approach, the four-point bending test described by Kanakubo [28], indirectly assesses tensile behavior through flexural performance. However, this study was also excluded, focusing on direct tensile response rather than flexural analysis for inverse modeling. Instead, the four bending test method, which was developed at Heriot-Watt University (HWU) and proposed by Suryanto et al. [29], was adopted. This technique utilizes simple rectangular prism specimens with dimensions of 30 × 75 × 270 mm³, streamlining the testing process while effectively capturing stable multiple cracking and strain-hardening behavior. Its ease of implementation, reliability, and reduced setup complexity made it suitable for the present investigation into the tensile strength of ECC. It also introduced a virtual testing platform for simulating tensile behavior and calibrating ECC performance parameters. This advancement helps reduce material waste and experimental variability, reflecting the continuous evolution and increasing precision required for characterizing the tensile properties of ECC [30]. The HWU method was applied to evaluate the tensile behavior of an ECC specimen subjected to a four-point bending test, as shown in Figure 2. The setup identifies the pure bending zone between the loading points. Within this region, multiple fine cracks are observed, indicating ECC’s characteristic strain-hardening and multiple-cracking behavior.

The mechanical response of ECC specimens was evaluated using the HWU method under a four-point bending test. Three identical specimens were cast and tested. The results were used to generate the average response curve [30]. The average load–displacement curve obtained from the three tested specimens is shown in Figure 3a. The curve displays an initial linear response followed by a non-linear region, indicating the onset of matrix cracking. After reaching the first peak, multiple fluctuations are observed, corresponding to the progressive formation of multiple cracks. The load drops are associated with the initiation of new micro-cracks within the ECC layer. Following these drops, the load increases again as the fibers engage in bridging the cracks, helping to redistribute stresses and restore part of the load-carrying capacity. This behavior reflects the strain-hardening nature of ECC, which improves overall ductility and energy dissipation, leading to the characteristic fluctuations seen in the load–displacement response. The curve ultimately reaches a peak load of approximately 1.3 kN before gradually declining, reflecting the post-cracking behavior characteristic of ECC. The tensile stress–strain curve is derived from the experimental results, as shown in Figure 3b. The curve initially rises steeply, indicating elastic behavior, and then gradually increases beyond the first cracking point, demonstrating the strain-hardening phase. A maximum tensile stress of around 4.9 MPa is observed, followed by a sharp drop, marking the onset of localized failure. The extended strain capacity was beyond 4% before failure. The ECC cube samples were tested in a universal testing machine of capacity 1000 kN and exhibited an average compressive strength of 39.1 MPa.

2.3. Details of Deep Beam Specimens

The mix proportion for the deep beams is given in

Table 5. Mixture proportion for deep beam specimens.

Cement (kg/m3)	M-Sand (kg/m3)	Coarse Aggregate (kg/m3)	Water (kg/m3)
323.5	704	1320	146

. M15 grade concrete with a characteristic compressive strength of 15.9 MPa was adopted for the preparation of deep beams. The geometric configuration, dimensions, and reinforcement layout of the beam specimens are shown in Figure 4. A total of twelve RC deep beams were cast for this study, which are grouped as set I and set II, to observe the replication of similar results with a minor change, only in the shear span. The slight variation in a/d was introduced to examine the influence of a more critical shear span condition on the effectiveness of ECC strengthening. Despite the difference, both sets exhibit deep beam behavior, and the comparison was made to evaluate performance trends rather than direct equivalence. Within a set, three specimens have acted as control specimens, and the other three are strengthened beams with an ECC layer. All beams were tested under simply supported boundary conditions. Each beam measured 1500 mm in length (L), 150 mm in breadth (B), and 400 mm in depth (D). The number of shear reinforcements within the shear span was distributed equally; either one or two were provided in two different sets with different shear spans. Details of all the specimens and nomenclature used in this study are summarized in

Table 6. Details of test specimens.

S. No.	Experimental Set	Specimen ID	Beam Dimensions (mm)			Shear Span (mm)	Number of Shear Reinforcements	ECC Layer Thickness (mm)
			L	B	D
1	Set-I	CDB-100-0	1500	150	400	550	-	-
2		CDB-100-1					1	-
3		CDB-100-2					2	-
4		SDB-100-0					-	20
5		SDB-100-1					1	20
6		SDB-100-2					2	20
7	Set-II	CDB-200-0	1500	150	400	500	-	-
8		CDB-200-1					1	-
9		CDB-200-2					2	-
10		SDB-200-0					-	20
11		SDB-200-1					1	20
12		SDB-200-2					2	20

. CDB refers to control deep beams, while SDB denotes strengthened deep beams. The numbers 100 and 200 represent the distance between the two-point loads, corresponding to 550 mm and 500 mm shear spans, respectively. The digits 1 and 2 indicate the number of shear reinforcements distributed equally within the shear span. An ECC layer with a uniform thickness of 20 mm was applied to the strengthened specimens on both sides. The primary diagonal shear cracks typically initiate and propagate from the surface and are predominantly concentrated within the outer regions of the beam cross-section. By applying a 20 mm ECC layer, the design specifically targets these critical surface-initiated cracks, effectively enhancing crack bridging and delaying crack propagation.

2.4. Strengthening Procedure

The sequence of steps for strengthening RC deep beams with ECC is shown in Figure 5. Initially, the molds were prepared, reinforcement cages with shear reinforcements were placed, and fresh concrete was poured into the wooden mold to achieve a uniform surface on top of the beam. Once the concrete becomes hardened, the formwork can be removed. Wet curing of the cast beams enhances hydration and develops adequate strength. After the curing process, surface marking and preparation of the beam specimens were carried out to define the shear span region designated for applying ECC. To improve the bonding interface for applying the ECC, mechanical surface roughening using a cutting machine was carried out. Then, the loose concrete particles were removed using a chisel tool to ensure a clean and rough surface. Additionally, no chemical bonding agents were used to replicate a conservative field condition without artificial bond enhancement. Throughout the experimental loading, no visible signs of interface debonding or delamination were observed, and failure occurred predominantly through the concrete core or at expected shear zones, indicating a reliable bond transfer. Finally, ECC was applied manually over the treated surface of the beam specimen and leveled to obtain a smooth surface. At last, the completed ECC strengthened beam specimens following the overlay process were cured to facilitate proper setting and strength development.

2.5. Experimental Test Setup

Static loading was applied using a four-point bending configuration, as depicted in Figure 6. The experimental tests were conducted using a servo-controlled hydraulic loading system with a maximum capacity of 500 kN. The load was applied monotonically under a load-controlled test setup with a constant displacement rate of 0.2 mm/min. Vertical deflections were measured using dial gauges placed directly beneath the loading points and at mid-span. Steel bearing plates measuring 100 mm in width and 20 mm in thickness were positioned at both the loading points and supports to ensure uniform load distribution and prevent local crushing of the concrete, as shown in the figure.

2.6. Results and Discussions

The experimental results of all the tested deep beams are presented and analyzed to assess the effectiveness of the proposed ECC layer strengthening system in enhancing shear capacity and controlling crack development. The evaluation emphasizes key performance indicators, including load-bearing capacity, ductility, and failure modes.

2.6.1. Load-Carrying Capacity

From the observation, the control beams exhibited brittle failure, with diagonal shear cracks propagating rapidly from the loading points toward the supports, indicating a diagonal-tension failure mechanism [31]. The peak load capacities of CDB and SDB tested under static loading are shown in Figure 7. The plots illustrate the influence of shear reinforcement on the tested beam specimens. The control deep beams exhibit a gradual increase in load-carrying capacity with additional shear reinforcement. For CDB-100, the maximum load increases from approximately 176 kN (with no shear reinforcement) to around 229 kN with two shear reinforcements. Similarly, for CDB-200, the peak load improves from about 183 kN to roughly 236 kN as the reinforcement increases. It is evident that the shorter shear span CDB-100 enhances shear resistance, resulting in higher peak loads compared to CDB-200, which has a longer shear span.

The strengthened beams show a significant improvement in both stiffness and load capacity over the control specimens. In SDB-100, the load-carrying capacity rises from nearly 270 kN for the unreinforced beam to around 339 kN when two shear reinforcements are added. For SDB-200, the maximum load increases from approximately 270 kN to over 349 kN with two reinforcements. Notably, SDB specimens consistently outperform their CDB counterparts, highlighting the effectiveness of the strengthening technique in enhancing load-carrying capacity. In all cases, the addition of shear reinforcement and reduction in shear span length lead to increased strength. The improved post-peak behavior in SDB specimens further indicates better crack control.

2.6.2. Load–Deflection Characteristics and Ductility Index

The load–deflection responses of both CDB and SDB beams with shear spans are shown in Figure 8. From the figure, it is clear that the ECC-strengthened specimen exhibited an improved deformation when compared with specimens without ECC. It may also be noted that the specimens show an improved deformation as the number of shear reinforcements increases. Ductility is a critical parameter in assessing the deformation capacity of reinforced concrete beams, especially under extreme loading conditions. In deep beams, due to their shear-dominated behavior and limited moment arm, the development of large plastic rotations is restricted, resulting in relatively lower ductility compared to slender beams. However, ECC and the reinforcement detailing can improve their overall ductile response. To quantify this behavior, the ductility index, defined as the ratio of ultimate deflection to yield deflection, was evaluated for all tested specimens [32]. The results are presented in

Table 7. Ductility index of the tested specimens.

Specimen ID	Ductility Index
CDB-100-0	1.27
CDB-100-1	1.28
CDB-100-2	1.30
SDB-100-0	1.30
SDB-100-1	1.33
SDB-100-2	1.32
CDB-200-0	1.32
CDB-200-1	1.35
CDB-200-2	1.37
SDB-200-0	1.37
SDB-200-1	1.46
SDB-200-2	1.50

.

The ductility indices of the tested deep beam specimens ranged from 1.27 to 1.50, indicating a moderate level of deformation capacity prior to failure. As deep beams are primarily shear-dominant members, they inherently exhibit lower ductility compared to flexure-dominated slender beams. The results show a gradual increase in ductility with the incorporation of ECC and shear reinforcement, particularly in the SDB-200 series, where the maximum ductility index of 1.50 was recorded. In contrast, the CDB-100 series without ECC contribution exhibited the lowest ductility values, ranging between 1.27 and 1.30. These findings confirm that while deep beams typically fall within a ductility range of 1.2 to 2.0, strategic use of high-performance materials such as ECC can enhance ductile behavior by delaying the onset of brittle failure. These results confirm that the ECC layer significantly improves the ductility of deep beams, making them more resilient under shear-dominated loading.

2.6.3. Crack Patterns and Failure Mode

The crack patterns of the control beams and ECC-strengthened beam specimens, as classified in Table 6, are shown in Figure 9. A prominent diagonal crack was developed near the support region of the beam specimen during the loading process, as shown in the figure. This crack initiated from the bottom edge of the beam and propagated diagonally upward towards the load point, indicating a typical shear failure mode. Several secondary cracks branched out from the main crack line, further confirming the dominance of shear stresses in this region. The appearance of these cracks occurred when the specimens reached close to the failure load and suggests that the beam experienced significant diagonal shear tension before failure. At the final loading stage, the control specimens exhibited prominent diagonal shear cracks extending from the loading points toward the supports. The failure of the control specimen was characterized by a brittle shear failure without yielding in the longitudinal tensile reinforcement. In specimens C-100 series, the cracks are wide and sharply inclined, splitting the concrete due to diagonal tension stress. The crack was characterized by a single dominant crack forming at approximately 45° to the beam’s longitudinal axis, indicating a critical shear failure zone due to the longer shear span. Similarly, in the C-200 series, diagonal cracks are also visible, although slightly flatter due to the shorter shear span. No secondary crack distribution is visible, and the failure appears sudden. There was no evidence of crack bridging or distributed cracking.

In contrast, the strengthened beams show a well-distributed network of fine micro-cracks, especially near the loading and support regions. Specimens such as S-100-1 and S-100-2 exhibited multiple narrow cracks along the shear region, reflecting improved crack control and a strain-hardening failure mode. The S-200 series also demonstrates similar behavior, with micro-cracks forming rather than a dominant major crack. Multiple fine cracks suggest effective stress redistribution and enhanced load capacity.

3. Numerical Investigation

3.1. Non-Linear Finite Element Evaluation

This study aims to investigate the shear behavior of strengthened deep beams through a non-linear finite element (FE) analysis, which was performed to understand the failure mechanisms. This analysis can support the unavailability of proper instrumentation, and to avoid the experimental errors, which are crucial for validating the results against experimental observations [33,34]. The simulation is carried out using the concrete damage plasticity (CDP) model available in the ABAQUS (Version 2019) software. The model accounts for both tensile cracking and compressive crushing, making it suitable for simulating the complex behavior of ECC and concrete. Material properties such as strain hardening, strain softening, and appropriate damage parameters are incorporated to replicate the non-linear response observed in experimental testing accurately.

The tensile stress–strain response of the concrete and ECC is plotted in Figure 10. The cracking strain ${(\epsilon }_t^{~ck})$ is estimated from the tensile strain (${\epsilon }_t$) and elastic strain (${\epsilon }_{ot}^{el}$), as represented in Figure 10. The cracking strain ${(\epsilon }_t^{~ck})$ and elastic strain (${\epsilon }_{ot}^{el}$) are mathematically expressed as in Equations (1) and (2), respectively [35],

$${\epsilon }_t^{~ck}={\epsilon }_t-{\epsilon }_{ot}^{el}$$

(1)

$${\epsilon }_{ot}^{el}={\displaystyle \frac{{\sigma }_t}{E_o}}$$

(2)

The tensile damage variable represents the degree of material stiffness deterioration ($d_t$) and the correlation is given in Equation (3),

$${ d}_t=1-{\displaystyle \frac{{\sigma }_t}{{\sigma }_{to}}}$$

(3)

where, ${\sigma }_{to}$ and ${\sigma }_t$ are peak tensile yield stress and instantaneous tensile yield stress [36].

The compressive stress–strain response of the concrete and ECC is plotted in Figure 11. The inelastic or crushing strain (${\epsilon }_c^{~in}$) is estimated from the compressive strain $\left({\epsilon }_c\right)$ and the elastic strain $({\epsilon }_{oc}^{el}$), as represented in Equations (4) and (5), respectively [37].

$${\epsilon }_c^{~in}={\epsilon }_c-{\epsilon }_{oc}^{el}$$

(4)

$${\epsilon }_{oc}^{el}={\displaystyle \frac{{\sigma }_c}{E_0}}$$

(5)

The compressive damage variable $d_c$, representing the rate of stiffness degradation under compression, is accurately determined using Equation (6).

$$d_c=1-{\displaystyle \frac{{\sigma }_c}{{\sigma }_{cu}}}$$

(6)

where

• ${\sigma }_{cu}$ is the peak compressive yield stress, which takes values between zero and one.
• ${\sigma }_{c }$ is the instantaneous compressive yield stress.

To accurately represent the deformation in all three directions, the FE model simulates concrete, ECC, and longitudinal reinforcement using a continuum 3-dimensional 8-node reduced integration element (C3D8R). Two-nodded linear 3D truss elements (T3D2) with three translational degrees of freedom per node along the x, y, and z axes are used to model the shear reinforcement, and a bilinear elastic–plastic technique is used to model the stress–strain response of steel reinforcement [38]. The interface between the ECC layer and concrete was modeled assuming a perfect bond using the tie constraint in ABAQUS, where no significant interface slips or debonding is observed experimentally [39]. The host region is designated as concrete, and the embedded constraint defines the interaction between concrete and steel reinforcement. In order to simplify interfacial behavior, tie constraints are used to assume a complete binding between ECC and concrete. Displacement constraints and support are used at the loading points to replicate the experimental conditions. The boundary conditions incorporate a combination of pinned and roller support. The concrete, ECC, longitudinal reinforcement, and shear reinforcement adopted a uniform mesh size of 20 mm to maintain node alignment throughout the model. The FE model includes meshing, boundary conditions, interaction properties, reinforcement representations, and loading patterns, which are illustrated in Figure 12.

3.2. Verification and FE Results

Verification against experimental results is essential for robust design applications to ensure the reliability of the FE analysis. The performed FE analysis successfully captured the overall response of the beam specimens, demonstrating a correlation with the experimental findings. The typical load–deflection responses of all RC deep beams are illustrated in Figure 13. In general, all the beam specimens exhibited a progressive increase in load with deflection up to their respective peak capacities. The CDB specimens failed abruptly upon reaching their peak load, with a major crack rapidly propagating from the loading point to the support. In contrast, the SDB beams demonstrated distinct load–deflection behaviors depending on the applied experimental parameters. Notably, all strengthened deep beams exhibited higher initial stiffness compared to the CDB specimens, indicating improved structural performance.

The numerical analysis demonstrated a strong ability to predict the load–deflection response, failure modes, and crack patterns observed in the experimental tests. The comparison between the FE analysis and experimental results showed close agreement, validating the accuracy of the simulation in capturing the structural response of RC deep beams. Furthermore, this study indicated that the longitudinal and shear reinforcement did not reach their yield limits, whereas the ECC material achieved yielding. This finding underscores the critical role of shear reinforcement in resisting shear forces within deep beams.

The stress in the shear reinforcement of both strengthened and control specimens at peak load, from the FE analysis, is shown in Figure 14. From Figure 14, it shall be observed that the stress value in the shear reinforcement for the strengthened specimen is higher than that of control specimen. This shows the effective confinement provided by ECC in the shear span.

Figure 15 depicts the stress distribution for concrete at peak load, obtained from the FE analysis, which illustrates the stress concentration patterns along the diagonal strut region between the loading and support points. The contours show that as the load increases, stress progressively accumulates within the strut zones, reaching values near the compressive strength of the concrete in some areas. This behavior aligns with typical deep beam mechanics, where a strut-and-tie action primarily resists shear. The presence of ECC appears to enhance stress dispersion and reduce the severity of localized crushing, promoting a more ductile failure mode.

4. Evaluation of Shear Capacity Using the Strut-and-Tie Method

The strut-and-tie (ST) method is a practical approach for understanding and predicting the shear load-carrying capacity of reinforced concrete deep beams. In contrast, traditional sectional methods based on linear strain distribution are inapplicable. The strut-and-tie shear equation were verified for both the concrete and shear reinforcement contributions, while the role of ECC was explicitly incorporated into the analysis. FE analysis revealed that the shear reinforcement and ECC worked together in resisting tensile stresses. As a result, the tensile stress in the steel reinforcement remained below its yield strength, indicating that the steel remained in the elastic range throughout peak loading. Similarly, the ECC did not reach its yield point, performing within its pre-cracking or proof stress range. This combined behavior highlights the effectiveness of ECC in delaying yielding and enhancing the overall shear load-carrying capacity. This approach ensures that the material behavior is realistically captured, especially in shear-critical zones where ECC plays a significant role.

In this section, the ST method is utilized to evaluate the contribution of different materials in transferring loads within deep beams strengthened with ECC and shear reinforcement. Considering the equilibrium of forces within the truss mechanism, the load-carrying mechanism is represented by an idealized truss system, where concrete struts resist compressive forces. At the same time, steel reinforcement and ECC ties act as tensile load-carrying elements, as shown in Figure 16. Including ECC as a tensile tie member enhances the structural integrity by providing additional resistance to diagonal tension stresses, thereby improving shear performance. The failure of the diagonal strut may occur due to concrete crushing under compressive stress or splitting due to diagonal tensile stress. The latter is effectively countered by the combined action of shear reinforcement and ECC ties, ensuring the enhanced shear strength of the beam [40,41]. This study employs the ST method to estimate the load-carrying capacity of deep beams strengthened with ECC [42].

The shear capacity $\left(V_{ST}\right)$ of the strengthened deep beam, based on the equilibrium of forces operating on the concrete strut, is illustrated in Figure 16. The shear capacity based on the ST method can be obtained using Equation (7).

$$V_{ST Method}=V_{Con} sin\theta +V_{T}cos\theta$$

(7)

where

• $V_{Con}$ is the effective compressive force;
• $V_T$ is the total tie force;
• $\theta$ is the angle between the concrete strut and longitudinal reinforcement.

Within the shear span, the load is transferred from the loading plate to the support plate through a concrete strut under the action of compression. Here, the concrete strut is assumed to have a prismatic shape with a constant width. The effective compressive force, $V_{Con}$, is calculated using the following Equation (8), based on FE analysis results, which indicate that the concrete effectively reached its compressive strength at peak load, justifying the adoption of the full compressive strength value in the numerical simulation.

$$V_{Con}=f_c^{\prime }\times A_{st }$$

(8)

where $f_c^{\prime }$ is the actual compressive stress in concrete at the peak load, $A_{st}$ is the cross-sectional area of the strut, $b_w$ is the width of the beam, $w_{st}$ is the width of a strut based on the dimensions of the loading plate, and the position of longitudinal bars is expressed by Equation (10).

$$A_{st}=w_{st}\times b_w$$

(9)

$$w_{st}=min\left[\right({LP}_b\mathit{sin}\theta +w_{th}\mathit{cos}\theta ),({LP}_T\mathit{sin}\theta +x\mathit{cos}\theta \left)\right],$$

(10)

where θ can be calculated using Equation (11):

$$\theta ={\mathit{tan}}^{-1}\left({\displaystyle \frac{z}{a}}\right)$$

(11)

$$z=y-{\displaystyle \frac{ky}{3}}$$

(12)

$$k=\sqrt{{\left(n\rho \right)}^2+2n\rho }-n\rho$$

(13)

$$x={\displaystyle \frac{2ky}{3}}$$

(14)

where a is the length of the shear span; $\rho$ is the ratio of longitudinal reinforcement; $n$ is the modular ratio; ${LP}_b$ and ${LP}_T$ are the width of the loading and support plate, respectively; $w_{th}$ is the thickness of the bottom node, which is equal to twice the clear cover; and $y$ is the effective depth of the beam. Further, the compressive strut is always accompanied by tie forces given by steel and ECC, which are carried by shear reinforcements and ECC. Based on this observation, the load-carrying capacity of shear reinforcements and ECC, the actual yield strength values obtained from the FE analysis are observed at peak load. The stress values for both the shear reinforcement and the ECC layer were considered, and these were included in the shear capacity equations to accurately estimate the overall shear resistance of the beam.

The total tie force $V_T$ is comprised of contributions from steel reinforcement ${(V}_{SR})$ and ECC ${(V}_{ECC})$, and they are expressed by Equations (16) and (17),

$$V_T=V_{SR}+V_{ECC}$$

(15)

$$V_{SR}=A_s\times f_y$$

(16)

$$V_{ECC}=t_{ECC}\times w_{ECC}\times f_{ECC}$$

(17)

The overall shear capacity of the beam is given by Equation (7), where $A_S$ is the area of steel shear reinforcements; $f_y$ is the actual yield stress of the shear reinforcement; $t_{ECC}$ is the thickness of the ECC layer; $w_{ECC}$ length of the ECC in the shear span; and $f_{ECC}$ is the actual yield stress of ECC.

From the above-described theoretical procedure, the overall shear load-carrying capacity is evaluated for all the beams.

Table 8. Load-carrying capacity and effectiveness of each material using ST method.

Experimental Set	Specimen ID	Peak Load (kN)		Effective Contribution (%)
		Experimental	Theoretical	VCon	VSR	VECC
Set-I	CDB-100-0	176	185	100	0	0
	CDB-100-1	194	204	97	3	0
	CDB-100-2	229	232	93	7	0
	SDB-100-0	272	281	80	0	20
	SDB-100-1	298	301	77	3	20
	SDB-100-2	339	342	71	6	23
Set-II	CDB-200-0	184	200	100	0	0
	CDB-200-1	196	216	97	3	0
	CDB-200-2	236	238	93	7	0
	SDB-200-0	276	289	82	0	18
	SDB-200-1	304	310	78	3	20
	SDB-200-2	343	347	72	7	21

presents the shear load-carrying capacity of all the beams and the effectiveness of each material in terms of percentage.

From the table, it is evident that the ST method predicts the peak load-carrying capacity of the deep beams with less than a 10% error. The ST method analysis provides valuable insight into the individual contributions of concrete, shear reinforcement, and ECC in resisting shear forces across two experimental sets, as shown in Table 8. In the CDB series, the entire shear capacity was initially carried by concrete, especially in the absence of ECC and steel, with up to 100% contribution from concrete. As the steel reinforcement was introduced, the contribution from concrete gradually decreased, while that from shear reinforcement increased, indicating an effective load-carrying mechanism. In the SDB series, where ECC was incorporated, a significant portion of the shear resistance shifted from concrete to ECC. The ECC contribution ranged from 18% to 23%, while the concrete contribution decreased to as low as 71%. This demonstrates the beneficial role of ECC in enhancing the shear capacity through its strain-hardening and crack-bridging characteristics. The shear reinforcement, though contributing modestly up to 7%, played a supplementary role in load resistance, especially as the concrete share declined. Overall, the findings emphasize the importance of a balanced design strategy where the ECC and shear reinforcement collectively enhance the performance of concrete in shear-critical regions. The ST-based evaluation provides a reliable approach to quantify these contributions and can serve as a useful tool to understand the effectiveness of ECC and placement shear reinforcement.

5. Conclusions

This study investigated ECC-strengthened RC deep beams’ shear behavior and peak load-carrying capacity using experimental investigation, non-linear analysis, and the ST method. The results demonstrated the effectiveness of incorporating shear reinforcement and ECC in enhancing shear performance. Based on the findings, the following conclusions can be drawn:

• The inclusion of a 20 mm ECC layer along the shear zone of RC deep beams increased the peak load-carrying capacity by up to 54.7% compared to unstrengthened control beams. This improvement was accompanied by enhanced ductility and a shift in failure mode from brittle diagonal splitting to ductile, distributed cracking.
• Increasing the number of vertical shear reinforcements further improved the shear capacity of the ECC-strengthened beams, confirming the combined effect of ECC and transverse reinforcement in enhancing structural performance.
• Finite element analysis using the Concrete Damaged Plasticity (CDP) model accurately predicted the load–deflection response, with an average error of 6.32% relative to experimental results. Stress analysis showed that ECC contributed to reducing stress concentrations, with longitudinal and shear reinforcements remaining below yield at peak load.
• The strut-and-tie method offered a simplified approach for shear capacity estimation but exhibited minor deviations in predicting peak load in ECC-strengthened specimens due to its limitations in modelling tensile and non-linear material behaviors.
• This multi-level approach combining experimental, numerical, and analytical methods confirmed the effectiveness of ECC layers in enhancing shear performance, providing valuable data for developing reliable strengthening strategies, particularly in structures built with low-strength concrete.
• Although direct cost–benefit analysis was not conducted, based on the literature, ECC offers long-term advantages in terms of durability, crack control, and reduced maintenance. Future research should incorporate life-cycle cost analysis and long-term durability assessments to support practical implementation of ECC strengthening systems.