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Experimental and Numerical analysis for ultra-high performance concrete beams strengthened with CFRP sheet Cover

Experimental and Numerical analysis for ultra-high performance concrete beams strengthened with CFRP sheet

Civil and Environmental Engineering
Volume 22 (2026): Issue 2 (June 2026)
By:  and    
Open Access
|Jun 2026
Figures & tables

Figures & Tables

Table 1:

Concrete mixes

Mixes all in [kg/m3]Fine sandcementWaterSuperplastizerSilica FumeFly AshCompressive strength [MPa] 28 days
107097018433.4107192.6126.97
Figure 1:

Dimension and reinforcement details of specimens (all dimensions in mm)

Table 2:

CFRP-Reinforcement Configurations and Strengthening

SampleCFRP strengthening type at each sideCfrp orientation [degrees]
RC-CWithout/
RC-U-90-100U- shape,100 mm width,150mm spacing c/c90°
RC-U-45-100U- shape,100 mm width,150mm spacing c/c45°
RC-2side-90-6002-sided-shape,600 mm width90°
RC-U-90-600U- shape,600 mm width90°
RC-Full-FaceFull Face90°
Figure 2:

(RC-C) control specimen (all dimensions in mm)

Figure 3:

(RC-CFRP-U-90-100) (all dimensions in mm)

Figure 4:

(RC-CFRP-U-45-100) (all dimensions in mm)

Figure 5:

(RC-CFRP-2side-90-600) (all dimensions in mm)

Figure 6:

(RC-CFRP-U-90-600) (all dimensions in mm)

Figure 7:

(RC-CFRP-Full Face) (all dimensions in mm)

Figure 8:

Uniaxial load cycle (tension-compression-tension) ABAQUS 6.14

Figure 9:

Flow potentials in the p-q plane CAE (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011)

Figure 10:

Yield surface in plane stress (Yu, J., Chen, S., Li, L., & Wang, H. 2011)

Figure 11:

(a) Drucker-Prager Yield Criteria in the Deviatoric Plane for Different Kc (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011) and (b) Yield Surface in 3D for Kc =1 (Pankaj, P. & Donaldson, C. 2013)

Figure 12:

(a) post-failure tensile behaviour:(a) stress-strain approach;(b) fracture (Hillerborg, A., Modéer, M., & Petersson, P.-E. 1976)

Figure 13:

Uniaxial tensile stress-strain behavior of concrete (Hsu, H.-M., & Wang, W.-P. 2001)

Table 3:

Strength and deformation characteristics of concrete (British Standards Institution, 2004)

Strength classes for concreteAnalytical relations / Explanation
fck (MPa)1216202530354045505560708090
fck,cube (MPa)15202530374550556067758595105
fcm (MPa)2024283338434853586368788898fcm ​ = fck ​+ 8 (MPa)
fctm (MPa)1,61,92,22,62,93,23,53,84,14,24,44,64,85,0 fctm=0,3×fck23≤C5060fctm=2,12.ln1+fcm10>C5060
fctk,0,05 (MPa)1,11,31,51,82,02,22,52,72,93,03,13,23,43,5fctk,0,05​ = 0,7 × fctm​ 5% fractile
fctk,0,95 (MPa)2,02,52,93,33,84,24,64,95,35,55,76,06,36,6fctk,0,95 ​ = 1,3 × fctm​ 95% fractile
Ecm (GPa)2729303133343536373839414244 Ecm=22fcm100.3
εc1 (%0)1,81,92,02,12,22,252,32,42,452,52,62,72,82,8 εc1%0=0,7fcm0,31<2,8
εcu1 (%0)3,53,23,02,82,82,8 f or fck≥50MPaεc1%0=2,8+2798−fcm1004
Table 4:

Mechanical properties of CFRP sheet (Sika Wrap®-300C) used in Abaqus modelling

PropertyValue [MPa]Notes
E1230,000Longitudinal modulus (fiber direction)
E216,000Transverse modulus (in-plane, epoxy dominated)
E316,000Transverse modulus (through-thickness)
G126,894In-plane shear modulus
G136,894Shear modulus (fiber–thickness plane)
G234,137Shear modulus (transverse plane)
ν120.30Poisson’s ratio (longitudinal transverse)
ν130.25Poisson’s ratio (longitudinal–through-thickness)
ν230.25Poisson’s ratio (transverse–through-thickness)
Figure 14:

Mesh for Abaqus model

Figure 15:

Linear brick elements undergo pure bending (reduced integration) (Daud, R., Cunningham, L., & Wang, Y. 2015)

Figure 16:

Element AB is Embedded in (3-D) Continuum Element; Node A is Constrained to edge (1-4), and Node B is constrained to face (2-6-7-3) (Daud, R., Cunningham, L., & Wang, Y. 2015)

Figure 17:

Boundary Conditions for Beam Model in ABAQUS

Figure 18:

Specification of Loading Line as Pressure on Beams in ABAQUS

Table 5:

Concrete Compressive Strength Data Used in Numerical Model (Yield stress versus inelastic strain values for concrete under compression)

Yield Stress [MPa]Inelastic strain [με]
72.630.000604
88.930.000768
92.690.000809
98.350.000878
108.140.001015
124.940.001425
127.000.001642
125.240.001806
121.360.001970
116.040.002135
108.740.002299
95.000.0026001
80.000.002910
65.000.003200
50.000.003500
35.000.003790
20.000.004200
10.000.004580
0.000.005000
Table 6:

Concrete Tensile Strength Data Used in Numerical Model (Yield stress versus tensile strain values for concrete)

Yield Stress [MPa]Inelastic Strain [με]
8.000.00005
6.000.00012
4.000.00022
2.000.00040
1.000.00060
0.500.00080
0.200.00100
Table 7:

Input Parameters for Concrete Plasticity Model in ABAQUS (Material properties and plasticity parameters for concrete)

DataValue
Poisson ratio0.2
Dilation angle (degree)36
Eccentricity0.1
ϵbo/ϵc3.0
kc0.667
Viscosity parameter0.0001
Table 8:

Mechanical Properties of CFRP Sheet Used in Numerical Analysis (Elastic constants and stiffness matrix components of CFRP)

DataValue
D1111233,289.0
D11224,111.30
D222217,235.46
D11333,029.38
D22334,237.36
D333317,202.34
D12126,894.00
D13136,894.00
D23234,137.00
Figure 19:

Validation of (RC) sample

Figure 20:

Validation of (RC-CFRP-U-90-100) sample

Figure 21:

Validation of (RC-CFRP-U-45-100) sample

Figure 22:

Validation of (RC-CFRP-2SIDE-90-600) sample

Figure 23:

Validation of (RC-CFRP-U-90-600) sample

Figure 24:

Validation of (RC-CFRP-FULL-FACE) sample

Figure 25:

Von Mises stress distribution and failure pattern of RC-CFRP-FULL-FACE beam model

Table 9:

Summary for the thickness of the beam parameter

Name of beamThickness 0.167mmThickness 0.334mmLoad increase [%] rate
Load [kN]Deflection [mm]Load [kN]Deflection [mm]
RC-CFRP-U-90-100459.9016.54512.2418.3411.38
RC-CFRP-U-45-100481.2416.98541.2318.9312.46
RC-CFRP-2SIDE-90-600483.2416.92543.6518.8512.50
RC-CFRP-U-90-600502.5717.32565.4019.3212.50
RC-CFRP-FULL FACE519.4612.73621.7515.2719.69
Figure 26:

Thickness of CFRP compares for the (RC-CFRP-U-90-100) sample

Figure 27:

The thickness of CFRP compared for the (CFRP-U-45-100) sample

Figure 28:

The thickness of CFRP compared for the (RC-CFRP-2SIDE-90-600) sample

Figure 29:

The thickness of CFRP compared for the (CFRP-U-90-600) sample

Figure 30:

The thickness of CFRP compared for the (RC-CFRP-FULL-FACE) sample

Figure 31:

Load deflection charts for the samples with CFRP spacing parameter

Table 10:

Summary for the thickness of the beam parameter

Name of beamThickness 0.167mmThickness 0.334mmLoad increase rate [%]
Load [kN]Deflection [mm]Load [kN]Deflection [mm]
RC-CFRP-U-90-100298.9410.17352.7412.5118
RC-CFRP-U-45-100361.7012.63410.4513.7813.48
Figure 32:

Load deflection charts for the (RC-U-90-100) specimen with CFRP spacing (200 mm)

Figure 33:

Load deflection charts for the (RC-U-45-100) specimen with CFRP spacing (200 mm)

Table 11:

Summary for the thickness of the beam parameter

Name of beamThickness 0.167mmThickness 0.334mmLoad increase rate [%]
Load [kN]Deflection [mm]Load [kN]Deflection [mm]
RC-CFRP-U-90-100459.9016.54512.2418.3411.38
RC-CFRP-U-45-100483.2417.05543.6519.0112.46
Figure 34:

Load deflection charts for the (RC-U-90-100) specimen with CFRP spacing (150 mm)

Figure 35:

Load deflection charts for the (RC-U-45-100) specimen with CFRP spacing (150 mm)

Table 12:

Observed versus estimated shear contributions of CFRP in the strengthened specimens

SpecimensCFRP Contribution Determined by the Subtraction approach: [kN]CFRP Contribution According to ACI 440.2R-17: [kN]CFRP Contribution According to CNR-DT-215-2018: [kN]CFRP Contribution According to TR-55 (CS, 2013): [kN]
RC-U-90-10070.11073.13257.23463.593
RC-U-45-10080.615103.69857.23489.934
RC-2side-90-60080.900109.69885.85195.390
RC-U-90-60095.090109.69885.85195.390
RC-Full-Face99.120109.69885.85195.390
DOI: https://doi.org/10.2478/cee-2026-0024 | Journal eISSN: 2199-6512 (formerly 1336-5835) | Journal ISSN: 1336-5835
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Language: English
Page range: 558 - 584
Submitted on: Jul 2, 2025
Accepted on: Aug 14, 2025
Published on: Jun 19, 2026
Published by: University of Žilina
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Strengthening by CFRP Sheet,
Shear strengthening of ultra-high-performance concrete,
Finite element methodology of Ultra ultra-high-performance concrete
Related subjects:
Business and economics,
Business management,
Industries,
Environmental management

© 2026 Ali Khalid Ahmed, Mustafa Hameed Al-Allaf, published by University of Žilina
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 22 (2026): Issue 2 (June 2026)
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