Ultra-high Performance Concrete Materials Research Articles

Bond-slip behavior of steel reinforcing bars in ultra-high performance concrete for field-cast connection of precast bridge decks

In Accelerated Bridge Construction (ABC), Ultra-High Performance Concrete (UHPC) is often used for connecting precast concrete bridge components, including deck portions of the Deck Bulb-T girders. An alternative low-cost non-proprietary UHPC has been proposed for use in place of the proprietary UHPC for connecting the precast components. The pullout behavior of steel reinforcing bars in closure pour with typical range for embedment lengths is studied for both proprietary and non-proprietary UHPC materials.

Feasibility Study of UHPC Reinforced Masonry Structure

With the increase of service life of masonry structure and the damage of masonry structure caused by external environment, the structure will be difficult to meet the design requirements. It is necessary to repair and reinforce the existing structure or replace the original structure with a new type of composite structure. ultra-high performance concrete (UHPC) is a kind of high strength, high ductility, high durability material, which has the advantages of almost impermeability, almost no carbonization, and almost zero chloride ion penetration and sulfate penetration. UHPC has been widely used in the field of concrete structure reinforcement, whether the masonry structure can be better strengthened has become the research content of this paper. Basic mechanics of UHPC materials at home and abroad By systematically combing and summarizing the research progress of performance and reinforcement design, the feasibility of UHPC reinforced masonry structure is obtained.

Effect of Steel Fibers on Tensile Properties of Ultra-High-Performance Concrete: A Review.

Ultra-high-performance concrete (UHPC) is an advanced cement-based material with excellent mechanical properties and durability. However, with the improvement of UHPC's compressive properties, its insufficient tensile properties have gradually attracted attention. This paper reviews the tensile properties of steel fibers in UHPC. The purpose is to summarize the existing research and to provide guidance for future research. The relevant papers were retrieved through three commonly used experimental methods for UHPC tensile properties (the direct tensile test, flexural test, and splitting test), and classified according to the content, length, type, and combination of the steel fibers. The results show that the direct tensile test can better reflect the true tensile strength of UHPC materials. The tensile properties of UHPC are not only related to the content, shape, length, and hybrids of the steel fibers, but also to the composition of the UHPC matrix, the orientation of the fibers, and the geometric dimensions of the specimen. The improvement of the tensile properties of the steel fiber combinations depends on the effectiveness of the synergy between the fibers. Additionally, digital image correlation (DIC) technology is mainly used for crack propagation in UHPC. The analysis of the post-crack phase of UHPC is facilitated. Theoretical models and empirical formulas for tensile properties can further deepen the understanding of UHPC tensile properties and provide suggestions for future research.

The Properties of Ultra-High-Performance Concrete with Assembly Unit of Secondary Aluminum Dross and Waste Fly Ash

Waste fly ash (WFA) and secondary aluminum dross (SAD) are common solid wastes inducing environmental pollution. These materials contain certain active substances that can be used in cement-based materials. Therefore, cement concrete can be used to solidify these solid wastes. In this study, the influence of the assembly unit of secondary aluminum dross (SAD) and waste fly ash (WFA) on the properties of ultra-high-performance concrete (UHPC) is investigated. The slump flow, the plastic viscosity, the yield shear stress, and the initial setting time of fresh UHPC are measured. Moreover, the flexural and compressive strengths and the dry shrinkage rate (DSR) are determined. The electrical resistance and reactance are tested. The electron microscopy spectroscopy (EDS), thermogravimetric analysis (TG), and X-ray diffraction spectrum (XRD) curves are obtained for revealing the mechanism of macroscopic performances. Results show that due to the optimal specific surface area and the volcanic ash effect, the UHPC with the assembly unit of 50% SAD and 50% WFA provides the highest slump flow, DSR, and mechanical strengths, while the corresponding plastic viscosity, yield shear stress, and electrical resistance are the lowest. The SAD can delay the setting time of UHPC. The relationship between the electrical resistance or the electrical reactance and the mass ratio of SAD accords with the quadratic function. The corresponding electrical resistance is the lowest. The relationship between the mechanical strengths and the electrical resistance fits with the cubic function. The leaching amounts of Zn and Cr increase in the form of cubic function with the immersing time. Meanwhile, the SAD can decrease the Zn and Cr by 0%–46.3% and 0%–45.2% respectively. As obtained from the EDS results, the element of Al is increased by adding SAD. The XRD curves show that the crystals of Al2O3 are increased and the SiO2 crystals are decreased by the added SAD. UHPC with 50% SAD exhibits the highest compact microstructures and the least Ca(OH)2 and 3CaO·SiO2 hydration products. The TG results show that UHPC with 50% SAD shows the lowest TG values of all the groups. This research will provide new UHPC materials and techniques applied in solidifying the WFA and SAD in the future.

Estimation of stress–strain constitutive model for ultra-high performance concrete after high temperature with an deep neural network based method

In order to better study and analyze the residual compressive behavior and stress–strain curve relationships of ultra-high performance concrete (UHPC) materials after high temperatures, high-temperature tests and uniaxial compression tests were carried out on 144 specimens in the temperature range of 20 °C-900 °C in this paper. The effects of different curing regimes and cooling regimes on the mechanical properties, apparent characteristic and stress–strain curves of UHPC after experiencing different temperatures were investigated respectively. As the target temperature increased, the stress–strain curves of all UHPC specimens gradually tended to be flatten, the peak point of the curve shifted to the right, the peak strain increased sharply, and the elastic modulus and proportional limits gradually decreased. The compressive strength and modulus of toughness of the UHPC specimens both increased and then decreased as the target temperature increased, with a critical temperature of 300 °C and 500 °C respectively. The Poisson's ratio of the UHPC specimens decreased and then increased as the target temperature increased, with a critical temperature of 500 °C. In addition, based on the experimental results, a Deep Neural Network (DNN) model with four hidden layers and 100 neurons in each layer was constructed to predict the complete residual stress–strain response of UHPC materials after high temperature. The training and validation of the DNN model was completed by pre-processing and segmenting the original dataset with the help of Pytorch deep learning libraries. The DNN model predicts stress–strain curves that are in excellent agreement with the UHPC test curves.

Utilizing Ultra-High Performance Concrete Overlay for Road Pavement Repair and Strengthening Applications

This study aims to develop a new thixotropic ultra-high-performance concrete (UHPC) overlay for the repair and strengthening of damaged hot mix asphalt (HMA) pavements. The overlay is purposely designed to accommodate the roadway slope of up to 10% due to presence of viscosifying agent materials. The original UHPC materials are comprised of granite aggregate, ultra-fine calcium carbonate, shrinkage-reducing admixture, viscosifying agent, and expansive agent. The study is conducted with three sets of samples provided and considers thixotropic and mitigated shrinkage properties through comparing control (non-thixotropic) overlay 1 (thixotropic), and overlay 2 (thixotropic) mixtures. Based on the obtained results, only overlay 1 corresponds to the minimum requirement for pavement rehabilitation, with 160-200 mm flowability and -545.3 µm/m free shrinkage. As a result, an average 50 mm thick overlay 1 is selected to repair a damaged HMA pavement (1800 m2), while the field implementation procedures and drawing details are also presented in this paper.

AI-powered shotcrete robot for enhancing structural integrity using ultra-high performance concrete and visual recognition

The integration of the shotcrete system with Ultra-High Performance Concrete (UHPC) to reinforce deficient concrete structures has been recognized as having significant potential. However, the execution of manual spraying operations within confined spaces or hazardous environments presents considerable risks, thereby highlighting the pressing necessity for implementing robotic solutions. This research focuses on developing an AI-powered shotcrete spraying robot prototype to address these challenges. Integrating ultra-high performance concrete (UHPC) and visual recognition techniques, the robot is designed to identify and repair concrete defects in real-time automatically. Defect detection is conducted using Google's MobileNetV1, a convolutional neural network (CNN)-based algorithm, which provides results comparable to standard CNNs with lower computational costs. The findings of this study indicate that the robot can precisely identify and reinforce defects using advanced UHPC materials, which offer superior mechanical properties and durability compared to conventional shotcrete. This performance is substantiated by F1-scores exceeding 90% for both training and testing datasets, with the Float32 model outperforming the Int8 model, yielding an impressive 98.0% accuracy compared to 94.2%. These results underline the feasibility and practicality of the proposed AI-powered shotcrete robot concept. This technological advancement could revolutionize concrete defect repair in challenging environments, such as large-span bridges, dams, and high-risk areas, enhancing safety and efficiency. Lastly, this prototype presents significant potential for future automatic concrete defect repair advancements.

Influence of Random Vehicle–Bridge Coupling Vibration on the Anti-Disturbance Performance of Concrete Materials

Without interrupting the traffic on the old bridge, the connection of the widening bridge will cause disturbance to the concrete in the splicing position. In order to study the anti-disturbance performance of concrete material, the Normal Concrete (NC) material and the Ultra-High-Performance Concrete (UHPC) material were experimentally investigated by the vertical shaking table and X-ray computed tomography scanning. It can be learnt from tests that the compressive strength of NC and UHPC can be increased by about 10% to 20% after disturbance, while the flexural tensile strength and splitting tensile strength of both NC and UHPC can be reduced by about 20% to 25% and 10% to 20%, respectively. The elastic modulus of UHPC is not significantly affected by the vibration disturbance, and that of NC can be increased by about 20%. The setting time difference of the proposed NC material can be controlled within 100 min, and it can improve its anti-disturbance performance. Excessive vibration disturbance affects the internal structure of NC, while it has little effect on the distribution of steel fiber in UHPC. Due to the high cost of UHPC materials, it is recommended to analyze the joint performance requirements before the selection of splicing materials. If the stress requirement is not particularly high, it is still recommended to apply the proposed NC material for the splicing of widening bridge.

Theoretical analysis of bond characteristics between steel bars and ultra-high-performance concrete

In order to investigate the bond and anchorage characteristics of steel bars embedded in ultra-high-performance concrete (UHPC), Tepfers’ (1979) thick-walled cylinder theory and elastic mechanics theory were used to establish a theoretical calculation model of bond strength between deformed steel bars and UHPC under the conditions of splitting failure and pullout failure, respectively. The proposed calculation model was verified with a large number of test data from the literature and experiments conducted by the authors. Finally, the anchorage length of deformed steel bars in UHPC was calculated by the centre point method, the check point method and the design specification of normal concrete structure; recommended values of anchorage length are given based on anchorage reliability theory. The research results can provide design basis for design engineers, and are also a useful guideline for the popularisation and application of UHPC materials.

Bond slip detection of shear interfaces for GFRP and UHPC composite members using piezoceramic smart aggregates

Ultra-high performance concrete (UHPC) and fiber-reinforced polymer (FRP) have been more and more widely used in large-scale constructions. Using FRP at the shear and bending section of concrete can increase the strength and fatigue resistance of the concrete members. However, the performance of FRP-UHPC composite structure depends mainly on the interface connection between FRP and UHPC. Therefore, to prevent the bond-slip of FRP-UHPC composite structure from causing destructive structural damage, it is essential to detect the bond-slip of interfaces for providing early warning of composite structures. Glass fiber reinforced polymer (GFRP) and concrete can be combined through several interface bond methods to form innovative composite structures. This study experimentally investigated the bond-slip detection of the shear interface of GFRP-concrete composite members using piezoceramic smart aggregates (SAs). Two groups of eight GFRP-concrete composite members with different bond methods were fabricated and tested. Both UHPC and regular concrete materials were considered. Six kinds of bond types were employed, including bolted, epoxy bonded, bonded by GFRP stay-in-plane form and their combinations. The push-out experimental results were analyzed in detail, involving the load versus slip displacement curves and failure modes. Meanwhile, the bond-slip between GFRP and UHPC interfaces was detected by the SA-based active sensing approach. A pair of SAs attached at both sides of each composite member was employed as an actuator and a sensor, respectively. The wavelet packet-based analyses, including the energy indices and damage index, were applied. Using an SA-based active sensing approach, the initiation and development of bond-slip for GFRP and UHPC composite members with different bond methods were successfully captured and quantitatively evaluated.

Effect of grouped L-shape rebar connectors on the shrinkage behavior of UHPC overlay cast on hardened NSC substrate

Ultra-high performance concrete (UHPC) overlay deployed in concrete bridge deck pavement exhibits a high amount of shrinkage that can lead to warping and debonding from the substrate of normal-strength concrete (NSC). This paper is to use grouped L-shape rebar connectors as a solution to alleviate the warping and debonding of the UHPC overlay which is cast on the NSC substrate. The rebar connectors are designed to be post-installed vertically in the hardened NSC substrate, and the rest part of the connectors are anchored in the UHPC overlay after the UHPC casting. In this study, an outdoor UHPC-NSC composite slab test was carried out, and two types of UHPC materials with distinct autogenous shrinkage were produced to cast the overlay. Different schemes of the rebar connector layout with various installing rates were performed. The restrained shrinkage of the UHPC overlay was monitored by the embedded strain sensors, and the UHPC overlay's long-term warping behavior was evaluated. In addition, a numerical model was established considering the shrinkage and creep of UHPC, the contact between the UHPC and the NSC substrate, and the concrete-to-rebar interaction. The results show that the grouped L-shape steel rebar connectors significantly affect the restrained shrinkage of the UHPC overlay by increasing the degree of restraint to the UHPC overlay by 13%-38%. The grouped L-shape steel rebar connectors are proven effective in alleviating warping and delamination in the UHPC-NSC composite slabs. Therefore, the use of grouped rebar connections is feasible in bridge deck pavement engineering.

Experiments and Stress-Strain Model of Concrete Confined by UHPC Materials

Compressive behaviors of 12 stub normal-strength concrete (NC) columns were experimentally investigated, which were confined by ultra-high performance concrete (UHPC) jackets. The governing influencing factors consisted of the thickness of the UHPC jacket, shape of specimens, and compressive strength of the core concrete. Generally, the UHPC jacket greatly improved the ductility of the stub columns. The final failure pattern transferred from crushing for concrete stub columns to the expansive crack of the UHPC jacket for UHPC-confined stub concrete columns. Moreover, the thickness of the UHPC jacket was found to greatly affect the compressive strength of specimens. In particular, the circular UHPC-confined stub columns, of lower-strength core concrete, were prone to gain more increments in compressive strengths. Debonding of the UHPC-NC interface was observed in the rectangular and square UHPC-confined stub columns. Enlightened from experimental observations, an analytical model is proposed to predict the axial stress-strain behavior of UHPC-confined concrete columns. It is noteworthy that the UHPC-NC interfacial behavior is identified and accounted for. The accuracy of the analytical model is validated by the reported experimental results. The model provides a useful tool to predict the axial strain-stress relation of UHPC-confined concrete columns in closed-form expressions for design-oriented purposes.

Behavior of Reinforced Ultra-High Performance Concrete Slabs Under Impact Loading After Exposure to Elevated Temperatures

Steel fiber-reinforced ultra-high performance concrete (UHPC) material is prone to explosive spalling under elevated temperatures. With the addition of polypropylene (PP) fiber, thermal spalling of UHPC can be mitigated and its fire resistance can be improved. This research investigates the impact resistance of steel and PP fiber-reinforced UHPC slabs after exposure to elevated temperatures, and the structural behavior and damage were compared against normal strength concrete (NSC) slabs. Karagozian & Case concrete (KCC) model was adopted to simulate both NSC and UHPC materials. With consideration of thermal hazards, the material damage, equation of state and strain rate sensitivity were adapted. The validity of this numerical model was evaluated against available experimental results. The numerical model was used to investigate the impact resistance of the reinforced UHPC slabs after exposure to fire hazards. The effect of fire exposure time, impact velocity and impact mass on the resistance of the reinforced NSC and UHPC slabs were analyzed. The simulation results revealed that punching shear failure areas in the NSC slabs were 2.5 times, 3.4 times, 3.0 times and 1.2 times larger than the UHPC slabs after exposure to international standardization ISO-834 standard fire for 1[Formula: see text]h, 2[Formula: see text]h, 3[Formula: see text]h and 4[Formula: see text]h, respectively. After exposure to the standard fire ISO-834 for 2 h, the punching shear failure on the bottom side of NSC increased 90.9% with the increase in falling height from 1[Formula: see text]m to 7[Formula: see text]m, while for the UHPC slabs, the increment was around 67.9%. After exposure to the standard fire ISO-834 for 2[Formula: see text]h, the punching shear damage of the NSC slabs increased by 72.9% with the punch weight increased from 100[Formula: see text]kg to 700[Formula: see text]kg, whereas the damage in the UHPC slabs increased by 53.8%.

Effects of Internal Curing on Inclusion in Prepackaged Cementitious Grout and Ultra-High Performance Concrete Materials

Proprietary, prepackaged materials such as some cementitious grouts and ultra-high performance concretes (UHPC) are commonly used in the bridge construction industry due to their convenience and desirable properties. However, due to particularities of their mixture designs, grouts and UHPC are prone to exhibit shrinkage, thus resulting in potential durability issues. This paper describes a step-by-step methodology for including internal curing (IC) in these types of materials, with the main goal of addressing some of their shrinkage and durability issues. A brief analysis of the relative cost implications is also provided, along with a compilation of experimental results to show the effect that IC has on important material properties. The results from this study indicate that the inclusion of IC in cementitious grouts and UHPC has the potential to increase durability, leading to more sustainable bridge structures with longer service lives.

Experimental, analytical, and numerical investigation on flexural behavior of hybrid beams consisting of ultra-high performance and normal-strength concrete

In this study, the flexural behavior of hybrid beams consisting of an ultra-high-performance concrete (UHPC) substrate and normal-strength concrete (NSC) overlay is investigated. From the experimental perspective, five UHPC-NSC hybrid beams were loaded to failure, and their failure patterns, load–deflection curves, ductility, strain distributions, and crack evolutions were compared. The UHPC substrate was found to significantly enhance the load-carrying capacity and suppress massive cracking of the hybrid beams. Interestingly, the increasing thickness of the UHPC substrate was observed to impair the beams’ overall ductility, leading to the apparent descending post-peak branch of the load–deflection curve. In other words, the agreed ductility of UHPC at the material level did not always benefit the deformation capacity of the beams at the structural level. Furthermore, an analytical derivation is proposed to capture the load–deflection curve of the hybrid beams. Specifically, sectional analysis in OpenSees was adopted to obtain the moment–curvature relation. This numerical strategy significantly alleviates the complicated derivation of the moment–curvature relation from conventional analytical formulas, owing to the significant tensile contribution of the UHPC material. Finally, finite element (FE) modeling of the hybrid beam specimens was performed. A nonlocal phase-field approach was implemented for UHPC and NSC materials. The numerical simulations are in good agreement with the experimental observations in terms of stiffness, load–deflection relation, and crack evolution.

Flexural behavior of UHPC-filled longitudinal connections with non-contacting lap-spliced reinforcements for narrow joint width

In this study, the longitudinal connections between precast concrete box girders were closure-poured by ultra-high performance concrete (UHPC), where were reinforced by three anchorage details of non-contacting lap-spliced reinforcements including straight bars, U-bars, and headed bars. UHPC made it possible to narrow the joint width because of its high mechanical properties. A testing procedure of four-point loading scheme was adopted to evaluate the flexural behavior of the UHPC-filled longitudinal connections. For comparison, the connections filled with fast-setting concrete (FSC) and self-compacting concrete (SCC) were also investigated. Experimental results indicated that 300-mm-width connections filled by UHPC materials efficiently accommodated the development length of lap-spliced reinforcements, performed a more deformable behavior, and obtained a higher flexural capacity. When a narrower joint width less than 200 mm was adopted, however, headed bars were not fully developed in UHPC-filled joint panels. UHPC-filled joint panels controlled interfacial cracks better and showed a 50% increase of cracking load than FSC-filled and SCC-filled joint panels. In terms of flexural capacity, the panels with U-bars exhibited the highest value, followed by those with headed bars and straight bars, regardless of different filling materials. A strut-and-tie model, considering the effective compressive strength and the effective height of concrete strut, was proposed to evaluate the flexural capacity of joint panels. The average ratio of experimental values to the calculated ones of all joint panels was 1.10.

Triaxial strength and failure criterion of ultra-high performance concrete

Over the past few decades, ultra-high performance concrete (UHPC) has been widely studied and applied because of its outstanding mechanical properties. A large number of studies have been conducted on the uniaxial static and dynamic performance of UHPC materials, however, limited investigations exist on the triaxial compression properties of UHPC. In this study, 98 cylindrical samples of UHPC with different steel fiber volumetric ratios (0.0%–1.5%) were tested to investigate the triaxial behavior of UHPC under different confining pressures (0 MPa–40 MPa). The confining pressure and steel fiber contents have clear impact on the triaxial strength, failure mode, crack width, and the angle between the oblique crack and the axial direction. The triaxial compressive strength and compressive toughness of UHPC subjected to various confining pressures are obtained from the tests and discussed in the study. Based on the testing data, the triaxial compression failure criterion of UHPC is established according to the unified strength theory. Finally, the simplified empirical equations for the full stress-strain curves of UHPC specimens subjected to uniaxial and multiaxial loads are derived, and good agreement with the experimental results is achieved.

A coupled adhesive-frictional model tailored for interfacial behaviors between UHPC and NC materials

In this paper, a coupled adhesive-frictional is proposed and implemented within an implicit finite element (FE) solver, targeting interfacial behaviors between ultrahigh-performance concrete (UHPC) and normal concrete (NC) materials. The model couples the adhesive force and frictional force, which is consistent with the mainstream shear-friction theory. The proposed model is realized by the zero-thickness cohesive element, thorough user-defined element (UEL) subroutine provided by the general FE software Abaqus/Standard. The model satisfactorily predicts the bond strength between UHPC and NC materials subject to various statuses, i.e., the tensile force (direct-tensile test), and combined compressive and shear forces (slant shear test). In addition, the interfacial model works fully compatible with the concrete damaged plasticity model, which is adopted for the UHPC and NC materials. The combination of these two models yields agreed with simulation results, which effectively predicts various cracking propagation and failure patterns of UHPC-NC composite specimens. The specimens in literatures are selected for comparisons and the numerical simulations clearly illustrate the complex interactions between the matrix cracking and interfacial debonding.

Ultra-high-strength engineered/strain-hardening cementitious composites (ECC/SHCC): Material design and effect of fiber hybridization

It is well known that an increase in the compressive strength of cementitious composites is usually accompanied by a loss of tensile ductility. Designing and developing ultra-high-strength cementitious composites (e.g., ≥200 MPa) with high tensile strain capacity (e.g., ≥3%) and excellent crack resistance (e.g., crack width ≤100 μm) remain challenging. In this study, a series of ultra-high-strength Engineered Cementitious Composites (UHS-ECC) with a compressive strength over 210 MPa, a tensile strain capacity of 3–6% (i.e., 300–600 times that of ordinary concrete), and a fine crack width of 67–81 μm (at the ultimate tensile strain) were achieved. Hybrid design of fiber reinforcement and matrix for UHS-ECC was adopted by combining the ECC and ultra-high-performance concrete (UHPC) design concepts, and the effect of fiber hybridization and aspect ratio on the mechanical behavior of UHS-ECC was comprehensively investigated. The overall performance of UHS-ECC was assessed and compared with the existing high-strength ECC and strain-hardening UHPC, and it was found that the currently designed UHS-ECC recorded the best overall performance among the existing materials. Finally, the multiple cracking behavior of UHS-ECC was analyzed and modeled based on a probabilistic approach to evaluate its critical tensile strain for durability control in practical applications. The results of this study have pushed the performance envelope of both ECC and UHPC materials and provided a basis for developing cementitious composites with simultaneously ultra-high compressive strength, ultra-high tensile ductility, and excellent crack resistance.

A mesomechanics-based analysis on the flexural behavior of ultra-high-performance concrete (UHPC) with different steel fiber lengths

This study investigates the flexural behavior of UHPC materials containing steel fibers of varying lengths. Mesomechanical analysis is performed according to the analytical pullout model, using actual measured fiber distributions. The flexural behavior of UHPC after cracking is simulated by superposing the fiber bridging and matrix softening curves. Subsequently, the evolution of stress–strain along the axial crack of UHPC is evaluated under different loading conditions. The obtained results indicate that longer steel fibers can efficiently improve the flexural behavior of UHPC. Moreover, the actual fiber orientation and pullout length distributions can be well fitted by two-parameter probability distribution (PDF) and Gaussian functions, respectively. Based on the micromechanical analysis, the fiber bridging behavior is overestimated under the assumption of 2D random fiber distribution, and it is underestimated under the assumption of 3D random fiber distribution. Interestingly, the length of the shear lag zone is independent of the fiber length, which is about 20.16 mm. The obtained results demonstrate that the compressive stress and strain at the top of the tested specimen gradually transform into tensile stress and strain at the opposite side. Interestingly, the stress of the specimens with fiber length of 20 mm are slightly higher than the specimens with fiber lengths of 6 and 13 mm, and the strain just lower than the specimens with fiber lengths of 6 and 13 mm in all crack propagation stages, respectively. This indicates that, in addition to the number of steel fibers, the stress/strain dispersion depends on fiber length.