The chapter investigates the crack propagation and failure of concrete columns reinforced with basalt fiber-reinforced polymer (BFRP) bars under eccentric loading. Eight columns of different heights and BFRP bar diameters were subjected to three cycles of loading-unloading with increasing eccentricity. Digital Image Correlation (DIC) method was employed to analyze crack propagation, revealing both expected vertical cracks and unexpected compression micro-damages. Numerical modeling using Concrete Damaged Plasticity (CDP) was conducted to validate experimental results. The study highlights the effectiveness of DIC in locating crack propagation and compression damages, and demonstrates a good resemblance between experimental and numerical failure modes. The research fills a significant gap in the literature by providing experimental data on BFRP-reinforced columns, which are relatively new in the field, and offers insights into their behavior under eccentric loading.
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Abstract
Available studies on concrete structural parts with FRP reinforcement bars concern mostly investigations on bent elements (beams, slabs) [1, 2]. There are also available a few theoretical analyses on columns [3‐5]. Though, there is still little experimental data concerning concrete columns with FRP bars [6‐8], especially subjected to eccentric load, as also underlined in the review article [9]. This research aims to fulfill this research gap. Also, basalt FRP bars were chosen as relatively new type of non-metallic bars with low ecological impact [1].
A total of eight columns with the height of either 750 mm or 1500 mm having 150 mm x 150 mm rectangular cross section were examined under axial or eccentric mechanical load up to 290 kN. Columns were reinforced with four BFRP main bars with the diameter of either 8 or 10 mm, and 8 mm steel stirrups in each case. The results on the thermal and mechanical properties’ investigations on BFRP bars were presented in [10]; the compressive strength values of the used BFRP bars were in the range of 441.2–466.8 MPa and elasticity modulus at compression values were equal to 31.0–38.4 GPa. Tested compressive strength of concrete, from which all columns were made (in one concrete pouring) were equal to 33.8 MPa. Each column was loaded in three cycles of loading-unloading, increasing the eccentricity, from 0 to 2 cm, and finally to 4 cm. DIC (Digital Image Correlation) method was used for the analysis of crack propagation (as in earlier research of bent elements [11]), but also unexpectedly there were visualised intensification areas of compression micro-damages. Failure was noted for two elements - B075_8_2 at the eccentricity of 4 cm (failure load – 290 kN after 60 s of sustained load) and B150_10_2 at the eccentricity of 4 cm (280 kN). Other specimens did not fail under load up to 290 kN. Maps from DIC method were also compared with results from numerical modelling (in Abaqus software) with good resemblance.
1 Introduction
Available studies on concrete structural parts with FRP reinforcement bars concern mostly investigations on bent elements (beams, slabs) [1, 2]. There are also available a few theoretical analyses on columns [3‐5]. Though, there is still little experimental data concerning concrete columns with FRP bars [6‐8], especially subjected to eccentric load, as also underlined in the review article [9]. This research aims to fulfill this research gap. Also, basalt FRP bars were chosen as relatively new type of non-metallic bars with low ecological impact [1].
In this study 8 concrete columns with BFRP main reinforcement and steel transverse reinforcement were investigated experimentally and numerically. Each column (150 mm x 150 mm x 750 mm or 1500 mm) was loaded in three cycles of loading-unloading, increasing the eccentricity, from 0 cm to 2 cm, and finally to 4 cm. DIC (Digital Image Correlation) method was used for the analysis of crack propagation (as in earlier research of bent elements [11]), but also unexpectedly there were visualised intensification areas of compression micro-damages.
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2 Specimens
A total of eight columns with the height of either 750 mm or 1500 mm having 150 mm x 150 mm rectangular cross section were examined. The scheme of the column is presented in Fig. 1, while types of analyzed columns in Table 1.
Fig. 1.
Scheme of the reinforcement.
Table 1.
Parameters of half-scale columns tested at room temperature.
Designation
Column height [mm]
Diameter of the main bar [mm]
B075_8_1
750
8
B075_8_2
750
8
B075_10_1
750
10
B075_10_2
750
10
B150_8_1
1500
8
B150_8_2
1500
8
B150_10_1
1500
10
B150_10_2
1500
10
×
Mechanical properties of the BFRP bars were subject of the earlier authors’ investigation [10] (Table 2). The concrete used for columns had w/c ratio equal to 0.57. Total water amount was 170 kg per 1 m3 of concrete. Type of used cement was CEM I 42.5N-NA. Consistency class was S1 according to [12]. The tested tensile strength of the steel stirrups was equal to 611.2 MPa, while the offset yield strength 0.2% was equal to 568.0 MPa (Table 3).
Stabilised secant elasticity modulus after 361 days
31.0 GPa
-
1in that day columns with height of 750 mm tested; 2in that day columns with the height of 1500 mm tested
3 Methods
3.1 Experiment
Each column was loaded in three cycles of loading-unloading, increasing the eccentricity, from 0 to 2 cm, and finally to 4 cm. DIC (Digital Image Correlation) method was used for the analysis of crack propagation. Each column was photographed from two perpendicular directions (Fig. 2).
Fig. 2.
Test stand - columns with the height of: a) 750 mm; b) 1500 mm.
×
3.2 Numerical Model
The numerical model consisted of:
two rigid bodies – upper and lower (r3d4 mesh elements), at which boundary conditions for the displacement were defined (lower: no rotation and movement, upper: enabled movement at Y axis and rotation against
Z axis);
one concrete part (modelled with the use of 10 mm c3d8r finite elements);
reinforcement modelled by truss (t3d2) elements with the length of 10 mm;
two steel elements (by which the force was transferred from the hydraulic press to the element), modelled with the use of c3d8r 10 mm elements.
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The embedded region function was used for modelling the interaction between concrete and reinforcement. Calculations were performed in one step (static general), in which vertical displacement of upper rigid body was forced and reaction in the reference point in lower rigid body was measured in order to register a maximum value, after which decrease of reaction was noted (as a failure force value). Similar method was used with satisfactory agreement to experimental results in [6]. The representation of numerical model meshes are shown in Fig. 3.
Fig. 3.
Numerical model - columns with the height of: a) 750 mm; b) 1500 mm.
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Concrete was modelled with the use of Concrete Damaged Plasticity. The general assumptions for CDP (which is modification of Drucker-Prager model) model are described in [15‐17].
Parameters for Concrete Damaged Plasticity was following: dilatation angle - \(\Psi\): 36, eccentricity - \(\in\): 0.1, fb0/fc0: 1.16, κ: 0.667 and viscosity parameter: 5E-05 [4]. Poisson’s ratio is assumed as 0.2. Damage parameters dc and dt were calibrated followingly:
The relation between stress and stress-related strains for concrete and steel was based on the European standard [19] for steel-reinforced concrete elements at high temperatures (as the further aims of these calculations were related with the analysis of such structures at high temperatures).
The material parameters were assumed as follows: concrete compressive strength = 35.0 MPa; steel yield strength = 550 MPa, elasticity modulus = 210 GPa for steel, and 35 GPa for BFRP.
4 Results and Discussion
DIC method have been proved useful in determination of crack propagation (as in earlier research of bent elements [11]), but also enabled analysis of compression micro-damages. Observation of compression zones of damages in the experimental part was especially interesting (example shown in Fig. 4b). Vertical cracks at the top of the columns were visible in both – DIC maps (Fig. 4a) and numerical considerations (Fig. 5a,b). At failure, these cracks resulted in detachment of part of the concrete. Also, good resemblance of the damaged areas of the specimen at failure (Fig. 5b) to maps of damages from numerical part of the study (dc and dt values) was noted (Fig. 5a).
Fig. 4.
Observed damaged zones (B075_8_2 column, 4 cm eccentricity): a) major strains (visible cracks); b) minor strains (visible damages in compression).
Fig. 5.
a) Damages of the column (dt) noted in numerical considerations (cross section view of 1500 mm column with 10 mm BFRP reinforcement at 4 cm eccentricity) 100 kN; b) at failure; c) column after failure – B075_8_2; d) column after failure - B150_10_2.
×
×
Failure was noted for two elements in the experiment- B075_8_2 at the eccentricity of 4 cm (failure load – 290 kN after 60 s of sustained load) and B150_10_2 at the eccentricity of 4 cm (280 kN). Other specimens did not fail under the mechanic load up to 290 kN with eccentricity varying from 0 cm to 4 cm.
The predictions on failure force from numerical part of the study were higher than loads applied during the experimental part and are given in Table 4. The values of maximum forced were in the range from 303.1 kN to 355.9 kN. In most cases the numerically predicted failure force was lower with the eccentricity increase. Better utilisation of the BFRP bars (higher stresses) at failure of the column was noted for higher eccentricity (97.8–120.7 MPa for 0 cm; 126.1–133.6 MPa for 2 cm and 221.3–249.7 MPa for 4 cm), but in each case they were much lower than the experimentally determined compressive strength. Lower values of failure force (by 3.5–9.1%) was noted for higher columns.
Table 4.
Maximum force values observed in numerical model along (values in brackets – stresses in the BFRP bars).
Type of column
Eccentricity [cm]
0
2
4
Column height: 75 cm,
main reinforcement: 8 mm
355.9 kN
(118.1 MPa)
327.5 kN
(126.1 MPa)
330.8 kN
(246.2 MPa)
Column height: 75 cm,
main reinforcement: 10 mm
354.2 kN
(97.8 MPa)
326.6 kN
(128.2 MPa)
341.0 kN
(221.3 MPa)
Column height: 150 cm,
main reinforcement: 8 mm
340.6 kN
(120.7 MPa)
311.7 kN
(124.6 MPa)
303.1 kN
(249.7 MPa)
Column height: 150 cm,
main reinforcement: 10 mm
340.0 kN
(110.7 MPa)
315.3 kN
(133.6 MPa)
314.6 kN
(245.6 MPa)
5 Conclusions
The following conclusions can be drawn from this study:
1.
Most of the columns (6 out of 8) did not fail under the applied load (290 kN), which is in line with prediction on the values of failure forces in numerical model (303.1–355.9 kN).
2.
In the case of two columns that failed at mechanical load at the level of 280 kN (B150_10_2) and 290 kN (B075_8_2), both at the eccentricity of 4 cm, the experimentally determined failure load was lower than numerical by 11% and 12%, respectively. Also, the column B075_8_2 did not fail immediately, but after 60 s of sustained load.
3.
The usefulness of DIC method in location of crack propagation in concrete columns has been confirmed. Also, compressive damaged zones were registered with the use of that method.
4.
Failure mode had a good resemblance in damage (dc and dt) parameters location in numerical model.
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