Concrete Damaged Plasticity Model Research Articles

Finite element analysis of RC moment-resisting frames to assess effective slab width; a parametric study

In reinforced concrete (RC) moment-resisting frames (MRFs) with cast-in-situ slabs, the slab action as tension flange during lateral loading enhances the flexural capacity of beams in negative moments. This enhancement may lead to strong beam-weak column unfavorable failure mode in these structures. Field observations of RC MRFs during strong ground motion indicated that the effective slab width values considered by the seismic provisions of the design codes are not adequate to guarantee the achievement of the design method of weak beam-strong column. An accurate estimation of effective slab width needs to assess factors such as geometrical characteristics of connection, continuity of models, and imposed story drift level. A 3D spatial two-story RC MRF was developed using finite element analysis (FEA) to explore the effect of mentioned factors on effective slab width. For finite element (FE) modeling of RC MRF, the concrete damaged plasticity (CDP) model is applied. The CDP model parameters are defined using a mesh-independent methodology introduced in the literature. Comparing the FEA results and results obtained from three half-scale RC MRFs, tested under reversed cyclic loading conditions showed an excellent correlation. The results predicted by the FE model in terms of lateral load–displacement response, reinforcement yielding sequence, crack patterns, and failure modes had a considerable agreement with test observations. The validated FE model was used to develop the other models to conduct a parametric study in the next step. Geometric parameters studied in this paper through numerical modeling were longitudinal and transverse beam length and height, and cross-sectional column dimension. Results of the parametric study showed that the effect of the ratio of transverse beam length to height is significantly more than the ratio of longitudinal beam length to height. The trend of effective slab width versus story drift depends on connection geometry, especially the ratio of transverse beam length to transverse beam height. Finally, an equation was driven to predict the effective slab width using linear regression analysis.

Numerical analysis on the mechanical response of grouted connection for pile-bucket foundation

As a new foundation type for offshore wind turbine (OWT), pile-bucket foundation, which consists of a monopile and a bucket foundation, has good prospect in engineering application and has received wide attention. However, most of the current research ignored the function of grouted connection (GC) and assumed that the pile and bucket were rigidly connected, which may lead to unrealistic estimation of the loading response of pile-bucket foundation. In this study, Finite Element Analysis (FEA) is conducted to study the influence of grout connection on the bearing characteristics of pile-bucket foundation, with a special focus on the mechanical response of the grout connection itself. The concrete damage plasticity (CDP) model is used to simulate the mechanical response of the grout material. After validation of the numerical model, twelve simulations are conducted by changing the grout thickness, grout length and stiffener arrangements. Though the variance of grout thickness and grout length has little impact on the load-displacement curves of the pile-bucket foundation, the optimal grout thickness and grout length could be determined according to the development of contact pressure, stress and damage of the grout connection. On the other hand, the employment of stiffener leads to notable stress concentration and fluctuation, however, it also improves the overall capacity of the pile-bucket foundation and effectively controls the damage of the grouted connection. The numerical result is expected to provide some reference value for the structural design of grouted connection for pile-bucket foundation.

Numerical seismic analysis of high-piled wharf strengthened with CFRP

High-piled wharves are widely employed in coastal areas, but their vulnerability to earthquake damage necessitates effective strengthening measures. This research focuses on investigating the effectiveness of carbon fiber reinforced polymer (CFRP) laminates in enhancing the seismic resistance of high-piled wharves. Full-scale 3D numerical high-piled wharves, divided into As-built groups and Retrofit groups, were established herein. During modeling, the concrete damage plasticity model (CDP) and the finite-infinite coupling element were contemplated. Two representative ground motions, i.e., the EI Centro wave and the Northridge wave, with peak accelerations of 0.2g and 0.4g, respectively, were utilized to simulate different earthquake scenarios. The responses of the resulting earthquake-induced deck displacement, pile distortion, and pile bending moment profile were explored. The computational analysis revealed significant improvements in the seismic performance of the retrofitted wharves compared to the as-built structures, proving that the externally bonded CFRP method was of great significance in improving overall structural seismic performance. Notably, the retrofitted wharf exhibited reduced deck displacement and remarkable decreases in pile deformation and bending moment. The modeling and analysis techniques can be applied to general wharves or other buildings strengthened with CFRP.

Tensile Behavior of Anchored Stainless Steel T‐Head Blind Bolts within Concrete‐Filled Steel Square Tubes

AbstractBased on a recent review on blind bolted connections to concrete‐filled steel tubes, there is a need to improve the performance of anchored blind bolts in such composite connections. This paper presents a study on the pull‐out behavior of anchored blind bolts under applied tensile load in terms of stiffness, yield strength, ultimate strength and load‐displacement response. A finite element (FE) model with concrete damage plasticity model was developed for parametric study. Effects of key parameters, such as concrete strength, bolt grade, embedment length, tube thickness and tube grade, on the tensile behavior of the connection were studied to identify the key parameters influencing the behavior. Finally, a predictive model based on component method was proposed to estimate the structural behavior of the blind‐bolted connections.

Damage of CRTS III type ballastless track-32 m simply supported girder structural system under long-term deformation effects

Until now, the CRTS (China’s Railway Track System) III type ballastless track-girder system has been gradually used in high-speed railway engineering. However, the effect of long-term deformation of prestressed box girders on the upper track structure is often overlooked. Given the strict requirements for track smoothness in high-speed railways, an in-depth study of the long-term deformation of the CRTS III type ballastless track-32 m simply supported girder system (girder-track system) is particularly important. In this study, a refined finite element model was established for a three-span CRTS III type ballastless track- simply supported box girder system. Based on the aid of the CEB-FIP 90 creep model and the UMAT (User-Material) subroutine, the long-term deformation calculations were investigated. Furthermore, an in-depth analysis of stress and damage of the CRTS III type ballastless track under the long-term deformation of the box girder was conducted by combining concrete damaged plasticity (CDP) and cohesive zone model (CZM) constitutive models. The numerical simulated results indicated that after four years of operation, the creep camber of the box girder in the girder-track system would reach to 3.41 mm. The maximum tensile and compressive longitudinal stresses of the base plate would reach to 0.537 MPa and 11.983 MPa, respectively. Meanwhile, the maximum tensile and compressive longitudinal stresses of the self-compacting concrete layer would reach to 0.958 MPa and 2.701 MPa, respectively. In the box girder mid-span, significant damage could be observed in the edge of the two base plates near the mid-span, with a maximum compressive damage rate of 0.164 and the maximum tensile damage rate of 0.304. The research of this study has achieved the prediction of long-term deformation in the girder-track system, providing an important basis for the reliability assessment and life prediction of the girder-track system.

A quantitative investigation on the fragmentation performance of SCDA in cracking steel fiber reinforced concrete

A better application of Soundless Chemical Demolition Agents (SCDAs) in fragmentation is based on our knowledge on their expansive characteristics. In this study, an integration of experimental and modeling approaches was developed to investigate SCDA expansion and corresponding cracking processes of Steel Fiber Reinforced Concrete (SFRC). The expansive properties of the selected SCDA were first estimated by free volume expansion (FVE) tests and expansion pressure (EP) tests. Then, cracking experiments were performed on 150 mm cubic SFRC blocks with a predrilled hole, and the cracking process was monitored by using Acoustic Emission (AE) and Digital Image Correlation (DIC) techniques. Generally, the cracking process can be divided into three phases, termed micro-cracking phase, macro-cracking phase, and failure phase. It was observed the hole diameter and fiber content exert significant influences on the cracking process. The crack initiation time was shortened as the hole diameter increases, while it was prolonged with increasing fiber content. The cracked area ratio was further proposed and measured to assess the cracking performance of SCDA. The ratio increases from 2.73% to 8.293% as the hole diameter increases from 16 mm to 26 mm, while it decays from 9.75% to 1.823% as the fiber content increases from 0 to 2.4%. After verified with the experimental data, a modified Concrete Damaged Plasticity (CDP) model was adopted to extend the fragmentation of SFRC from the centimeter scale to the meter scale. The simulations were conducted on SFRC models with various hole diameters, spacings, and fiber contents. The simulated results show the fragmentation performance is related to both hole parameters (e.g., hole diameter, spacing, etc.) and SFRC properties (including elastic modulus, fiber content, etc.). In particular, the cracked area (DamageT > 0.9) varies directly with hole spacing, diameter, and fiber content. Built on the simulated results, an empirical equation was formulated to quantitatively evaluate the fragmentation ability of individual holes. In addition, extra simulations were conducted to assess the efficiency of SCDA in cracking PC/SFRC beams of various sizes. The obtained cracked area tends to decrease first and then approach a constant value with increasing beam sizes, indicating the existence of a size effect, which is primarily due to variations in concrete restraints provided by beams of different sizes. This work quantitatively evaluates expansive properties of SCDA and SCDA-induced cracks, and thus provides a reference for optimizing the field application parameters.

Application of bridge information modelling using laser scanning for static and dynamic analysis with concrete damage plasticity

A new proposal has been applied using Bridge Information Modeling associated to Terrestrial Laser Scanning TLS and photogrammetry to obtain the digital model of an existing bridge. For the laser scanning process. Thus, it was also possible to identify the pathologies and damages in the concrete of the bridge. Furthermore, it was shown how geo-information with remote sensing using the station Trimble SX 10 can be applied in area of bridge projects with less time and lower cost, in relationship to a conventional survey Asbuilt with manual survey in field. One of the innovations of this paper was to obtain the digital model of the bridge by integration of TLS and photogrammetry to obtain the 3D digital model. The new methodology consisted of acquisition of the bridge scenes through points previously implanted, making the polygonal contour of the entire bridge. Furthermore, the execution of the field survey from georeferenced points to capture the scenes during the sweep with TLS facilitated the refinement and, consequently, it was possible to obtain the digital model with the concrete damage. It was also possible to perform a complex nonlinear analysis with Finite Element with the digital model of the bridge. Therefore, it was applied a reverse analysis of the strength of the structure using the Concrete Damage Plasticity Model using ABAQUS software. Two numerical analyses were performed on the bridge; one considering only the static behavior of the bridge and another considering the dynamic behavior. In the static analysis, the behavior of the dapped-end beam of the bridge, was investigated. On the other hand, in the dynamic evaluation, the natural frequency and damping ratio for bridges with Dapped-end beams was obtained in ABAQUS through Rayleigh damping and compared with the technical literature, which presented satisfactory results.

Failure prediction of syntactic foam core L-shaped sandwich structures

L-shaped laminates with a syntactic foam core were manufactured to investigate the bending behavior of the sandwich structures including sharp corners. The bending behavior, initial, and progressive failure modes of the sandwich structure were analyzed by four-point bending tests and the finite element method. The cohesive zone model and Hashin’s failure criteria were used for inter-laminar and intra-laminar failure of the laminates, respectively. The concrete damage plasticity model was proposed to model the foam material with considering different material properties in tension and compression. Mode-I and Mode-II fracture toughness of the foam was obtained to characterize the foam/laminate interface. Load-displacement curves predicted under bending simulation were quite well compliant with experimental results. The difference between numerical and experimental failure loads was 10.6 %, 1.2 %, and 1.9 % for the foam with facesheet stacking sequence of [0/90]2s, [0/90]3s, and [0/45/-45/90]2s, respectively. Predicted radial and hoop direction strain fields in the foam section were also compared to the measured one using a digital image correlation technique. Strain fields and failed regions and their mechanisms were captured well using the model. The initial failure mechanism was delamination at the interface between the foam and facesheet followed by foam tensile fracture.

Basalt fibre reinforced polymer bars as main reinforcement of axially compressed concrete column – experimental and numerical considerations of fire resistance

The study aimed to highlight the possibility of achieving satisfactory level of fire resistance in concrete column reinforced with Basalt Fibre Reinforced Polymer (BFRP) bars as a main reinforcement.The literature data [1] of steel reinforced columns was used for preliminary validation of the numerical model. Full scale BFRP-reinforced column was analyzed experimentally and numerically along with experimental evaluation of thermo-mechanical parameters of the BFRP bars and concrete.Fire resistance of the element was calculated by means of numerical simulation, as the time when further sustaining of the mechanical load was no longer possible. The Concrete Damaged Plasticity (CDP) model for concrete was used.The model appeared to be effective in predicting fire resistance of concrete columns with steel reinforcement with various spacings of stirrups (differences up to 12%). In terms of element reinforced with BFPR, the fire resistance of the column tested was about 30% higher than the numerically determined value. Also, the calculated temperatures were compared to values measured by means of thermocouples. Finally, the possibility of achieving over 3 h of fire resistance for columns with BFRP main reinforcement has been proven in both – numerical and experimental investigations.

Influence of surface cracking, anchor head profile, and anchor head size on cast-in headed anchors in geopolymer concrete

In this study, the concrete cone capacity, concrete cone angle, and load–displacement response of cast-in headed anchors in geopolymer concrete are explored using numerical analyses. The concrete damaged plasticity (CDP) model in ABAQUS is used to simulate the behavior of concrete substrates. The tensile behavior of anchors in geopolymer concrete is compared with that in normal concrete as well as that predicted by the linear fracture mechanics (LFM) and concrete capacity design (CCD) models. The results show that the capacity of the anchors in geopolymer concrete is 30%–40% lower than that in normal concrete. The results also indicate that the CCD model overestimates the capacity of the anchors in geopolymer concrete, whereas the LFM model provides a much more conservative prediction. The extent of the difference between the predictions by the numerical analysis and those of the above prediction models depends on the effective embedment depth of the anchor and the anchor head size. The influence of concrete surface cracking on the capacity of the anchor is shown to depend on the location of the crack and the effective embedment depth. The influence of the anchor head profile on the tensile capacity of the anchors is found to be insignificant.

Investigation of the shear behavior of ultra-high performance concrete girder by simulation approach

The present study investigates the shear behavior of the Ultra High Performance Concrete girder strengthened by steel bars and stirrups by simulation approach. Utilizing the Concrete Damage Plasticity model that involves strength reduction and nonlinear behavior of the material, 3D simulation models are established and analyzed by the commercial software Abaqus. The numerical simulation model is verified by comparing the test data to ensure reliability. Numerical simulation models were then developed to investigate the relationship of shear force with parametric studies of shear span to depth ratio, steel bar ratio and stirrups spacing. Based on the obtained results, the simulation model and test results show a good agreement. The relation between the shear capacity of UHPC girder and parametric studies was also enlightened.

NLFEA of Reinforced Concrete Corbels: Proposed Framework, Sensibility Study, and Precision Level

Non-linear finite element analysis (NLFEA) has been frequently used to assess the ultimate capacity of reinforced concrete (RC) structures under the most complex conditions. Nevertheless, the guidelines using such methods to evaluate RC corbels are limited. In addition, the influence of material modeling options regarding the behavior of such members was not investigated until now. This paper proposes to present a framework for the NLFEAs of RC corbels using the Concrete Damaged Plasticity (CDP) model. the influence of several modeling choices related to this constitutive model also is discussed in detail, including the assumed stress–strain behavior in compression and tension and the parameters related to the yield criterion and flow rule. For this, a first set of test results was used to validate the proposed approach to the NLFEA. Afterwards, the sensibility of the numerical results for several modeling choices was investigated. In the end, the proposed framework for the NLFEA was checked against a database of 36 test results from the literature. The mean ratio between the predicted and experimental test results was 1.015 with a coefficient of variation of only 8.57%. The governing failure mechanism of the tests was predicted correctly in approximately 88% of the simulations. In summary, the proposed approach allows for predicting the ultimate capacity and failure mechanism of RC corbels accurately.

3D simulation of non-uniform corrosion induced damage in reinforced concrete exposed to real climate

A three-dimensional (3D) numerical model to simulate damage in reinforced concrete (RC) under non-uniform corrosion as a function of the real climate, is presented in this study. The concrete damage plasticity model is implemented to investigate the damage behavior of reinforced concrete. Numerical predictions in terms of damage patterns are obtained and verified with the experimental results to demonstrate the applicability of the model. The validated model is extended to ascertain the role of variations in real temperature (T) and relative humidity (RH) on non-uniform corrosion-induced concrete damage, for a multi-rebar RC system. Representative tropical and temperate marine climates have been chosen in the investigations. Considerably different damage patterns and crack widths are obtained in the reinforced concrete under both climates. Effect of different anode–cathode configurations of steel bars on concrete damage under non-uniform corrosion in 3D is also investigated. 3D modelling techniques used in the study provide a true insight into the deterioration of RC under non-uniform corrosion, considering the role of T and RH variations in the external environment.

Parameter Selection for Concrete Constitutive Models in Finite Element Analysis of Composite Columns

Concrete, as a complex and anisotropic material, poses challenges in accurately simulating its behavior in numerical simulations. This paper focuses on selecting an appropriate constitutive model for simulating the behavior of a steel–concrete composite column using finite element analysis under compression and push-out tests. Two models are analyzed and compared, namely, Drucker–Prager and concrete damage plasticity. The results demonstrate that the concrete damage plasticity model outperforms the Drucker–Prager model in all six test cases, indicating its superior accuracy in capturing the composite column’s behavior. This study enhances the reliability of numerical simulations for steel–concrete composite structures by choosing the most suitable constitutive model, parallel with extensive sensitivity analysis and model calibration. The findings emphasize the significance of meticulous model selection and precise parameter definition for achieving accurate predictions of concrete behavior. This research contributes to advancing the understanding and modeling of concrete’s intricate behavior in structural analyses.

Meso-concrete Uniaxial Compression Experiment Based on ABAQUS

Plain concrete is made of cement matrix and aggregates. The current numerical model researches mostly consider the cement matrix and ignore the existence of coarse aggregates, which is not consistent with the reality. In view of that, this article uses ABAQUS as the platform to establish a meso-concrete damage model based on the concrete coarse aggregates and CDP (Concrete Damaged Plasticity) model constructed in Python language. The results show that: (1) The main failure mode of concrete model is shear failure, and the crack is about 45° to the vertical plane. (2) Under the action of the load, multiple micro-cracks are formed at the end of the concrete, which are gradually extended to each other, and finally a macroscopic large crack is formed. (3) The damage model proposed in this article is in line with reality and provides guidance for concrete damage research.

Seismic damage characteristics of high arch dams under oblique incidence of SV waves

This study investigates the seismic damage characteristics of high arch dams considering the oblique incidence of seismic waves. Based on the dynamic implicit finite element method, a viscous-spring artificial boundary is applied to consider radiation damping of the infinite foundation, the seismic wave input is converted into an equivalent nodal force of the artificial boundary, and the equivalent nodal loads of the wave input under oblique incidence of the SV wave is deduced. Taking JP Ⅰ arch dam as an example, combined with the concrete damaged plasticity (CDP) model, the nonlinear dynamic response of the dam under 25° oblique incidence of the SV wave is conducted considering the geometrical nonlinearity of contraction joints and the dynamic mechanical properties of concrete materials. Based on the incremental dynamic analysis (IDA) method, the relative displacement and transverse joint opening are selected as the damage measures for fragility analysis of the arch dam. According to the damage distribution from the analysis of a large number of seismic time-history responses, the damage levels of the arch dam are classified. Three limit states of slight damage, moderate damage and severe damage are proposed for the arch dam. The average responses of the 10 earthquakes are considered as the limit values to quantitatively describe the damage of the arch dam. By fitting the results of incremental dynamic analysis, the seismic probabilistic demand model and seismic fragility curves for the two damage measures to predict the probability of the arch dam reaching damage levels under different seismic actions have been established. The fragility curve shows that the probability of severe damage is almost zero under the maximum design earthquake (PGA = 0.1971 g) and less than 5% under the maximum credible earthquake (PGA = 0.2299 g). It is concluded that JP Ⅰ arch dam has a high degree of safety redundancy and fully satisfies the “two levels” design requirements.

Experimental and Numerical Research of Post-Tensioned Concrete Beams.

The purpose of this paper is to present a new approach for the modelling of post-tensioned beams with calibration of the FE model to experimental results until the load capacity and post-critical state are reached. Two post-tensioned beams with different nonlinear tendon layouts were analysed. Material testing for concrete, reinforcing steel and prestressing steel was performed prior to the experimental testing of the beams. The Hypermesh program was used to define the geometry of the spatial arrangement of the finite elements of the beams. The Abaqus/Explicit solver was used for numerical analysis. The concrete damage plasticity model was used to describe the behaviour of concrete with different laws of elastic-plastic stress-strain evolution for compression and tension. Elastic-hardening plastic constitutive models were used to describe the behaviour of steel components. An effective approach to modelling the load was developed, supported by the use of Rayleigh mass damping in an explicit procedure. The presented model approach ensures good agreement between numerical and experimental results. The crack patterns obtained in concrete reflect the actual behaviour of structural elements at every loading stage. Random imperfections found during experimental studies on the results of numerical analyses were also discussed.

Failure modes and dynamic responses of roller compacted concrete gravity dams subjected to underwater contact explosion based on the cohesive model

Considering the construction technology of roller compacted concrete (RCC) gravity dams, there are layers in dams inevitably, which may affect the blast responses of dams. This paper is aimed to investigate the effects of RCC layers on the failure modes and dynamic responses of RCC gravity dams bearing underwater contact explosion loading. Initially, the zero-thickness cohesive element model is presented to simulate the crack behavior of the RCC layers. An impact test of a concrete beam is selected to verify its reliability. The concrete damage plasticity model considering strain rate effects is utilized to simulate the various responses of concrete under blast load. The dam–reservoir–foundation interactions are described using the coupled Eulerian-Lagrangian method. The numerical methods are validated by a field blast test of a concrete structure. Subsequently, numerical models were established for gravity dam-reservoir-foundation systems, with and without considering RCC layers respectively. Based on validated algorithms, these models were utilized to explore the effects of RCC layers on the blast performance of the dam. Finally, the influence of the parameters of RCC layers on the nonlinear responses and failure modes of the dam is further investigated, including the maximum traction, the fracture energy, and the layer thickness. The results reveal that the layers significantly change the failure modes. The RCC layers are the weak link of the dam and they will lower the anti-explosion performance of the dam. Therefore, it is crucial to take the layers into account when conducting anti-explosion research, and RCC dams cannot be simply simplified as normal concrete dams. To guarantee the safety of the dam, it is important to ensure the layers with sufficient strength and fracture energy, as well as an appropriate thickness.

Mesoscale modelling of concrete damage in FRP-concrete debonding failure

It is challenging to simulate fibre-reinforced polymer (FRP)-concrete debonding failure in detail because concrete damage usually occurs with a thin layer of mortar debonding attached to the FRP. This study applied a single-lap shear test with a digital image correlation technique to externally bonded FRP–strengthened concrete elements. An improved random walk algorithm method generated a realistic mesostructure of concrete. The two-dimensional mesoscale finite element model for FRP–strengthened concrete was established. The cohesive interface elements were inserted along all mortar–aggregate interfaces. Concrete damaged plasticity and cohesive zone model were applied to simulate the nonlinear properties of mortar and mortar–aggerate interface, respectively. The experimental and numerical load–displacement curves, strain/stress distribution, and local bond–slip curves were obtained and compared. A numerical parametric study investigated the effects of the aggregate, mortar, and adhesive on debonding failure. The main conclusions are: (1) the initiation and propagation of mortar damage and mortar–aggregate interface cracking in the FRP debonding process were directly conducted by the mesoscale model; (2) the numerical curves showed considerable oscillation, possibly due to the stress concentration near the aggregate boundary when the crack transmitted the aggregate, and the stiffness decreased after cracking was initiated at the mortar–aggregate interface; (3) concrete damage may extend to a depth of 25 mm, indicating that the concrete damage is greater than a thin layer of mortar debonding observed in the test; (4) applying polygonal aggregates, increasing aggregate size and surface mortar thickness, and reducing the adhesive layer thickness improves bond performance.

Experimental and Numerical Analysis of Steel-Polypropylene Hybrid Fibre Reinforced Concrete Deep Beams.

This work experimentally and numerically explored how varied steel-polypropylene fibre mixtures affected simply supported reinforced concrete deep beams. Due to their better mechanical qualities and durability, fibre-reinforced polymer composites are becoming more popular in construction, with hybrid polymer-reinforced concrete (HPRC) promising to increase the strength and ductility of reinforced concrete structures. The study evaluated how different combinations of steel fibres (SF) and polypropylene fibres (PPF) affected beam behaviour experimentally and numerically. The study's focus on deep beams, research of fibre combinations and percentages, and integration of experimental and numerical analysis provide unique insights. The two experimental deep beams were the same size and were composed of hybrid polymer concrete or normal concrete without fibres. Fibres increased deep beam strength and ductility in experiments. The calibrated concrete damage plasticity model in ABAQUS was used to numerically calibrate HPRC deep beams with different fibre combinations at varied percentages. Based on six experimental concrete mixtures, calibrated numerical models of deep beams with different material combinations were investigated. The numerical analysis confirmed that fibres increased deep beam strength and ductility. HPRC deep beams with fibre performed better than those without fibres in numerical analysis. The study also determined the best fibre percentage to improve deep beam behaviour where a combination of 0.75% SF and 0.25% PPF was recommended to enhance load-bearing capacity and crack distribution, while a higher content of PPF was suggested for reducing deflection.