Experimental and computational investigation of mechanical anchors for large-scale applications of reinforced concrete with a fiber-reinforced polymer blast retrofit

Abstract

While fiber-reinforced polymer (FRP) laminates have been shown to enhance the blast resistance of reinforced concrete (RC) structural elements, a knowledge gap exists when the RC components are large, and mechanical anchors must be installed throughout the RC component to avoid delamination and debonding. The objective of this study was to investigate two different mechanical anchorage systems installed throughout RC slabs with carbon fiber-reinforced polymer (CFRP) blast retrofits. Two RC slabs with CFRP retrofits were constructed, one with an epoxy anchor and steel strap anchorage system and the other with an epoxy anchor and steel plate anchorage system. The feasibility of each mechanical anchorage system for large-scale applications was assessed with considerations from the construction process. The two specimens were experimentally subjected to explosive loadings in full-scale live blast testing, and strain, acceleration, displacement, and damage were recorded during the experiments. Finite element analysis (FEA) models for the two specimens with different anchorage systems were developed and validated utilizing the experimental results. Because different loadings were utilized in the experiments, the validated FEA models were used to compare the performance of the two specimens. For both experiments, the epoxy anchors exhibited no visible movement and failure initiated in the concrete and not at the interface of the concrete and CFRP. The FEA comparison of the two specimens with different anchorage systems showed the inbound behavior of the two specimen to have nearly identical behavior. The steel plates required significantly less effort to install on the epoxy anchors compared to the steel straps making the plate anchorage system attractive for large-scale applications of FRP retrofits to RC structural elements.

Keywords

blast blast mitigation numerical analysis blast retrofit FRP retrofit

Introduction

The continued persistence and presence of terrorist groups highlight the ongoing need to decrease the vulnerabilities of military and civilian structures to blast loads (Bureau of Counterterrorism and Countering Violent Extremism, 2023). Terrorist attacks can lead to catastrophic damage of expensive infrastructure or loss of life. Fiber-reinforced polymer (FRP) laminates have been proven to increase the flexural strength as well as the blast resistance of reinforced concrete (RC) structural elements (Bonacci and Maalej, 2001; Buchan and Chen, 2007; Guo et al., 2017; Jackson et al., 2022; Wu et al., 2009). FRP laminates can be quickly installed post-construction and have high stiffness and tensile strengths (Orton et al., 2013; Triantafillou, 1998). These properties make FRP a desirable material for blast retrofits.

While there have been many studies on assessing FRP, few studies have been conducted that investigate the behavior of FRP retrofits with anchors installed throughout the specimen and not just at or near the edges of the FRP. For large structures, anchors must be installed throughout the component to prevent or delay delamination or debonding which are the most common failure modes of FRP retrofits (Al-Atta et al., 2022; Esmaeeli and Shadan, 2023; Teng et al., 2002). When debonding of the FRP and concrete substrate occurs, the retrofit is not as effective as when the FRP stays bonded to the concrete substrate. While anchors have been proven to delay or prevent debonding (Grelle and Sneed, 2011; Jackson et al., 2022; Orton et al., 2013; Zhao et al., 2021), the presence of anchors can create stress localizations that can result in FRP tearing, which can also initiate the delamination of the FRP (Alhelal, 2025; Bonacci and Maalej, 2001; Mutalib and Hao, 2010; Sadeghian et al., 2023). There is little data available on how RC components retrofitted with FRP respond to blast loads, and fewer reported tests on RC components retrofitted with FRP and varying mechanical anchoring techniques used throughout the RC component (Pezzola, 2018).

The objective of this paper was to investigate two different mechanical anchorage systems installed throughout RC slabs with carbon fiber-reinforced polymer (CFRP) blast retrofits. The study utilizes full-scale experiments and finite element analysis (FEA). The experiments were used to develop and validate the FEA model. The validated FEA models were used to compare the effects of the different mechanical anchorage systems on the performance of the RC slab retrofitted with CFRP.

This paper is organized such that it presents the experimental program first. The experimental program includes details about the mechanical anchorage systems, test setup, instrumentation, and experimental results. Following discussion of the experimental effort, details are provided on the FE models and associated numerical results. The numerical results are then used to make comparisons between the mechanical anchorage systems. Conclusions and design implications are discussed at the end of this paper.

Experimental program

Two experiments were conducted at Fort Polk, Louisiana to test mechanical anchor systems for a CFRP blast retrofit on large reinforced concrete slabs. A reaction structure designed and constructed by the U.S. Army Engineer Research and Development Center (ERDC) was used for the experiments, shown in Figure 1. The reaction structure consisted of multiple sections of large RC components post-tensioned together with a 3.98-m high × 1.69-m wide opening in the middle of the front slab of the structure. The front slab of the reaction structure, measured 6.7-m high, 6.1-m wide, and 0.3-m thick, with the opening’s centerline located 0.68-m off the ground. To elicit a one-way response, the specimens were constrained within the opening at their top and bottom by a combination of hollow structural sections (HSS), steel plates, and steel angles, as illustrated in Figure 2. The structure had large walls on both sides to prevent clearing effects from reducing the delivered impulse to the tested specimen. The reaction structure was designed to be non-responding for the impulses from the charge and standoffs utilized in the experiments.

A hemisphere of molded Composition C-4 was set on an 8.9-cm tall plywood platform and bottom detonated in a surface burst configuration for each experiment. The scaled distance for the first experiment was 1.32 m/kg^1/3, and the scaled distance for the second experiment was 1.03 m/kg^1/3. The scaled distance for the second experiment was different than the first experiment because the specimen in the first experiment experienced lower-than-intended damage. The explosive charge was moved closer for the second experiment to obtain more damage to better understand the behavior of the anchoring system being tested. Because the two specimens were not tested at the same scaled distance, direct comparison of the performance of the anchoring systems within the experiments was not possible. FEA, described later in this paper, was used for direct comparison of performance of the anchoring systems. Figure 1 shows the final test setup for the first experiment.

Test specimen

Two identical RC slabs were constructed for this test series using SAC-5 concrete, a locally available concrete mix that has pea gravel with a maximum aggregate size of 1 cm, described in Kipp et al., 1998, Reinhart et al., 1999. Each slab was 1.67 m wide, 3.9 m tall, and 15.2 cm thick. The slabs were symmetrically reinforced for flexure with five #5 rebar spaced at 36.8 cm with 2.54-cm clear cover. The slabs were also reinforced with 31 #5 rebar with 12.7-cm spacing to prevent shear failure. The design impulses for the reaction structure used in the experiments as well as the dimensions of the opening in the reaction structure informed the design of the RC slabs used in this experimental program.

Three weeks after the concrete was placed, Hilti HAS-R 304 stainless steel 15.88-mm anchor bolts were installed in the RC slabs using Hilti HIT-RE 500 epoxy adhesive. The guidelines provided by Hilti were followed during the installation of the anchor bolts.

The day after the anchor bolts were installed, CFRP made with BASF MasterBrace® FIB 600/50 CFS carbon fiber fabric and MasterBrace® SAT 4500 matrix was applied to the non-blast side of each specimen. Four layers of the fiber fabric were applied to the non-blast side with a layer of the saturant applied between each layer of fabric. Two layers of the fabric were applied parallel to the length of the slab, and two layers were applied parallel to the width of the slab following a 0◦-0◦- 90◦-90° layup per the guidelines from BASF. A series of coupon tests with the same layup used in the test series was conducted, which resulted in an average ultimate strength of 503 MPa and an ultimate rupture strain of 1.67% (Pezzola, 2018). While the CFRP was installed identically on each specimen, the mechanical anchorage systems varied. These systems differed in the number and location of the anchor bolts, and in the securing method used: straps versus discrete plates. The configuration for each specimen is described below.

Specimen S1, tested in the first experiment, featured a mechanical anchorage system consisting of three A36 steel straps herein referred to as the “strap anchorage system.” Each strap was 10.16-cm tall, 1.6-cm thick, and 1.67-m wide, spanning the full width of the specimen. The straps were placed at the mid-height and quarter points of the slab. The edges of the steel plates were rounded using a grinder to prevent tearing in the CFRP due to direct contact with sharp edges of the steel. This system was chosen for investigation due to its similarity to a previously-tested anchorage system employed in real-world construction (Pezzola et al., 2016).

Specimen S2, tested in the second experiment, utilized a mechanical anchorage system comprising 17 small A36 steel plates herein referred to as the “plate anchorage system”. Each plate measured 10.16-cm tall, 10.16-cm wide, and 1.6-cm thick. The plate anchors were positioned at the mid-height and quarter points, mirroring the strap system’s layout. Additional plate anchors were also placed at the eighth-points, between the mid-height and quarter points. The edges of the steel plates were rounded using a grinder to prevent tearing in the CFRP due to direct contact with sharp edges of the steel. The plate anchorage system was selected as an alternative to the strap anchorage system because it requires less steel and offers the potential for more balanced stress distribution across the specimen. The steel plate system required significantly less effort to install on the anchor bolts compared to the steel strap system. The plate anchorage system could be particularly attractive for large-scale applications where ease of installation is crucial. In such scenarios, the weight and bulk of the steel straps become increasingly problematic and aligning holes for strap installation would be cumbersome and time-consuming compared to the simplified plate installation.

Figure 3 shows the finished specimens S1 and S2, illustrating the two distinct configurations. The material properties for the components used to construct the finished specimens S1 and S2 are shown in Table 1.

Table 1.

Material properties.

Material	Material properties
SAC-5 concrete	28-day strength: 31.1 MPa S1 compressive strength on day of experiment: 32.36 MPa S2 compressive strength on day of experiment: 32.86 MPa
Steel reinforcement	Minimum tensile yield strength: 413 MPa
CFRP (MasterBrace® FIB 600/50 CFS)	Ultimate tensile strength: 3800 MPa Tensile modulus of elasticity: 227 GPa Rupture strain: 1.67%
Matrix (MasterBrace® SAT 4500)	Ultimate tensile strength: 55.2 MPa Tensile modulus of elasticity: 3034 MPa Rupture strain: 3.5%
Steel straps and plates	Minimum tensile yield strength: 348 MPa

Instrumentation

Each specimen was instrumented with the same configuration. Ten precision linear pattern constantan foil strain gauges with a gauge length of 5.1 cm, 350 ± 0.02% resistance (Ω), and a strain limit of ±3% strain from Micro-Measurements were installed on each specimen. Two ENDEVCO® Model 2262A piezoresistive accelerometers with a 2,000 g full range were placed in a low-frequency foam insulator (LOFFI) mount were used for each test. The series of aluminum rings and elastomeric damping material that form the LOFFI mount prevent high-frequency noise in the accelerometer data. To measure the displacement-time histories, ERDC-manufactured rack-and-pinion displacement gauges were used. These gauges use a Vishay 534 potentiometer mounted with a pinion housing secured to a stand, allowing for rotation in two-axes.

To obtain the reflected pressures delivered to the specimen, four HKS-11-375 pressure gauges were installed surrounding the specimen (directly below the centerline of the specimen, on either side at the mid-height of the specimen, and directly above the specimen. These are later referred to as “RPB,” “RPL,” “RPR,” and “RPT,” respectively). These piezo-resistive sensors were manufactured by Kulite and use a silicone shielding layer over a ruggedized sensor. Three high-speed Phantom cameras were used for each test, which allowed for qualitative observations on the retrofit behavior. Figure 4 shows the pressure gauge layout, where the pressure gauge locations are circled in yellow, and the instrumentation on the non-blast side of the specimen, where a strain gauge, a rack-and-pinion displacement gauge, an accelerometer, and a high-speed camera are pointed out.

Experimental results

The peak reflected pressures and impulses for both S1 and S2 are shown in Table 2. The pressure-time history for RPB on S2 is unreliable after the positive phase. The signal was compromised and never returned to zero, most likely due to cable damage. Therefore, the signal was truncated at the end of the positive phase. The signal for RPT on S2 exhibited a brief, small positive pulse from 10 to 11 ms, resulting in an increase in impulse. However, this pulse is likely an artifact of cable movement and not indicative of the shock wave behavior. Therefore, the maximum impulse reported in Table 2 was determined at 10 ms, prior to the occurrence of this pulse. The pressure and impulse time histories for S1 and S2 are shown in Figures 5 and 6, respectively. The results for the peak accelerations from each accelerometer, maximum displacement, and maximum strain for each test are shown in Table 3.

Table 2.

Peak reflected pressures and impulses.

Test	Location	Peak pressure (MPa)	Impulse (MPa-ms)
S1	RPB	2.74	2.41
	RPL	2.51	2.36
	RPR	1.57	1.89
	RPT	1.54	1.54
S2	RPB	6.38	4.86
	RPL	4.69	2.92
	RPR	3.84	2.72
	RPT	1.92	1.39

Table 3.

Experimental Results for both S1 and S2.

Test	Top accel.	Bot accel.	Max disp.	Max strain
S1	561.1 g	666.2 g	11.4 cm	0.8%
S2	948.4 g	1198.3 g	16.3 cm	0.804%

Concrete damage and CFRP damage were observed in both the specimens S1 and S2, as can be seen in Figures 7 and 8, respectively, with higher damage exhibited in specimen S2 as expected due to the higher loading from the scaled standoff of 1.03 m/kg^1/3 used in the second experiment. Notably, neither slab exhibited any adhesive failures, as all debonding initiated within the concrete substrate. Under these specific loading conditions, the epoxy anchors exhibited no visible movement and performed well for this test.

The S1 specimen exhibited most of its concrete damage on the non-blast side, concentrated at the steel straps. CFRP tearing along the straps also occurred in this specimen. Debonding of the CFRP from the concrete substrate occurred throughout the specimen and was concentrated at the location of the straps. The observed failure mode shared similarities with, “plate-end debonding” (Teng et al., 2002), but with noticeable differences. Unlike plate-end debonding, which initiates at the end of the CFRP application, the observed failure mode initiated at the location of the straps in the anchorage system. This distinct failure mode had not been reported in the literature before this test series (Pezzola, 2018).

The S2 specimen exhibited flexural and flexural-shear cracks, as well as concrete crushing on the inbound compressive side of the specimen. The debonding initiated due to the widening of the major flexural and flexural-shear cracks at the interface of the concrete and the CFRP. This failure mode is classified as “intermediate flexural and flexural shear crack-induced debonding” (Teng et al., 2002). The anchorage system enabled containment of the debonding.

After the S1 test, there was noticeable residual displacement, on the order of several centimeters, of the reaction structure’s front wall and culverts. The movement of the reaction structure was attributed to pre-existing damage from prior use. The timing of the movement of the structure is likely after the initial movement of the specimen because of the larger mass of the structure, making it difficult to understand the effects of the movement of the structure on the results. However, it is likely that the movement of the structure dissipated some of the energy imparted into the specimen especially on the rebound of the specimen. The movement of the reaction structure and the effects on the assessment of specimen performance was further examined with the FEA and is discussed further in the next section.

To mitigate this issue during the S2 test, modifications were made to the reaction structure. Measurements taken after the S2 test showed that the modifications reduced the movement of the reaction structure components compared to S1 even with higher loading from the scaled standoff of 1.03 m/kg^1/3.

Finite element analysis

FEA with LS-DYNA software was utilized to enable direct comparisons between the mechanical anchorage systems, which was not possible with the limited experimental data. The experimental results were used to calibrate and validate the models for each anchorage system, and then the validated models were utilized for a more comprehensive understanding of the systems’ performance.

Finite element analysis setup

Half symmetry along the centerline of the slab was used due to the symmetric nature of the experiments. Due to the observed movement of the reaction structure during the experiments, portions of the reaction structure were included with the specimen in the model to account for the effects the reaction structure’s movement had on the specimens’ response behavior. Pictures taken before the first experiment showed an approximate 4-cm gap between the front slab of the reaction structure and the next section of the reaction structure. The model included a portion of the front slab of the reaction wall, the observed gap, a portion of the structure behind the front slab, and the ground surface, in addition to the physical boundary conditions. The front slab of the reaction structure was modeled with its full thickness of 30.48 cm, while only 12.7 cm of the thickness of the structure behind the front slab was modeled. In reality, the structure behind the front slab was three 1.22-m-thick RC sections post-tensioned together.

Only portions of the reaction structure were modeled to improve computational efficiency. To allow for more realistic simulations, the density of the portions of the reaction structure that were modeled was increased to account for the mass of the portions of the reaction structure that were not included in the model. Increased friction coefficients were applied between the simulated portions of the reaction structure and the ground surface to compensate for the limited surface area modeled. Throughout the analysis, the displacement of the reaction structure was monitored, and adjustments were made as necessary to ensure that the simulated displacement of the reaction structure was consistent with the measurements from the experiment.

The FE simulation for S2 was adapted from the S1 simulation to account for the distinct conditions of the S2 experiment. Specifically, the model was updated to include the 17 small steel plates that comprised the mechanical anchorage system used in S2, as well as the modifications made to the reaction structure during the experimental program. Additionally, the loading conditions were adjusted to account for the smaller standoff distance used in the S2 test. The changes allowed for a more accurate representation of the S2 test conditions, without changing other aspects of the FEA setup.

Contact surfaces were specified in the model between different materials and parts. The contact surfaces between the specimen and the explicitly modeled reaction structure were defined using the Automatic Surface-to-Surface contact in LS-DYNA, which allows for penetration on either side of the surface’s elements to be checked in each time step. For simulations completed prior to the experimentation, a tiebreak contact surface was included to simulate the failure mode as an adhesive failure. However, the experimental program showed that debonding was initiated by a failure in the concrete, not the adhesive interface, as a thin layer of concrete separated from the slab and adhered to the CFRP. As a result, the tiebreak condition was removed, as it did not accurately represent the observed failure behavior, and the CFRP elements were merged to the non-blast side surface of the concrete. This approach ensures that debonding can only occur if the adjacent concrete elements fail, which is consistent with the experimental observations.

Finite element analysis material models

The Karagozian & Case Concrete Model - Release III (K&C, or material number 72R3 in LS-DYNA) material model was used to model all concrete elements in the FEA. The K&C concrete model is a three-invariant formulation that includes damage, plasticity, and strain-rate effects and uses three independent failure surfaces. To accurately capture the behavior of concrete, the K&C model allows the plastic flow to adapt to be either partially associative, fully associative, or non-associative. This model has been validated for use in modeling concrete subjected to blast loads (Malvar et al., 1997). More details on the K&C model can be found in (Livermore Software Technology Corporation, 2006; Malvar et al., 1997).

The K&C model includes an automated parameter generation feature, which was used for this analysis. A Poisson’s ratio of 0.19 was used for every concrete part in the model, and the corresponding compressive strength and density were used to generate the rest of the parameters in the K&C model. To improve the concrete model performance for the tests described in this paper, it was determined that adjustment of the default parameters that affect fracture energy was necessary. This was likely necessary due to the localized confining stresses at the strap and plate locations throughout the slab that influence localized fracture formations. The compressive damage scaling parameter, b1, damage localization parameter, locwid, and tensile damage scaling exponent, b2, were varied in an iterative manner to determine which set of values resulted in the most accurate FEA results for both experiments. Many combinations of b1, b2, and locwid resulted in very good agreement both in terms of qualitative behavior and displacement time-histories between the S1 experiment and simulation. Many of those same combinations also resulted in very good agreement between the S2 experiment and simulation, but only for the inbound behavior. There were only several combinations of the fracture energy parameters that resulted in good agreement for both the inbound and rebound behavior for the S2 experiment. The parameters used in this analysis for both the S1 and S2 simulations are shown in Table 4. These parameters were calibrated specifically for the geometric and material configurations in this study. Applying them to RC slabs with different dimensions or to alternative retrofit systems would require further investigation to validate their accuracy. Erosion was permitted in the model solely for the specimen and at strain levels high enough that erosion occurred only after elements had first lost all ability to sustain deviatoric stress. The concrete elements in the specimen were prescribed to erode if the maximum effective strain reached 6.0% or if the maximum principal strain reached 6.0%.

Table 4.

Karagozian and case concrete parameters.

Property	Value
Compressive damage scaling parameter, b1	0.3
Damage localization parameter, locwidth	5.0
Tensile damage scaling exponent, b2	1.5

The 414 MPa rebar in the specimen as well as the steel angles and HSS sections that were used as boundary conditions in the experiments were modeled explicitly, using the plastic kinematic material model in LS-DYNA (Livermore Software Technology Corporation, 2006).

The material properties for the composite layers were obtained from the manufacturer’s specifications (BASF, 2014). Using the theory provided by Jones (Jones, 1975), appropriate properties for the layup used in this test series were calculated, listed in Table 5. The Enhanced Composite Damage material model in LS-DYNA (material number 54 – 55) was used to simulate the CFRP behavior. This material model was validated using data from a series of coupon tests conducted in accordance with ASTM D3039 and a corresponding simulation, where the physical setup of the coupon tests was modeled explicitly (ASTM International, 2007). The stress-strain curves of the coupon data are plotted with the simulation of the coupon tests in Figure 9. More details on the composite material model can be found in (Chang, 1987).

Table 5.

CFRP properties.

Property	Value
Density $ρ, \frac{g}{{c m}^{3}}$	1.20
Tensile modulus $E_{A}, E_{B}, E_{C}, M P a$	2.86 × 10³, 2.86 × 10³, 7.22 × 10³
Poisson’s ratio $ν_{B A}, ν_{C A}, ν_{C B}$	0.0543, 0.132, 0.132
Shear modulus $G_{A B}, G_{B C}, G_{C A}, M P a$	1.54 × 10³, 1.54 × 10³, 1.54 × 10³
Longitudinal tensile strength $X_{T}, M P a$	503
Transverse tensile strength $Y_{T}, M P a$	503
Compressive strength $X_{C} a n d Y_{C}, M P a$	290
Shear strength $S_{C}, M P a$	48.3
Effective failure strain, $D F A I L T$	1.67%

Finite element analysis loading

The Load Blast Enhanced loading card in LS-DYNA allows for a subset of ideal charge scenarios to be simulated accurately, using the predictive curves in the UFC 3-340-02, “Structures to Resist the Effects of Accidental Explosions” Manual (Department of Defense, 2008). The hemispherical surface burst option was selected, and the appropriate charge weight, standoff, and height of detonation point were used for each experiment to produce air-blast loading on the specimen. As the charge was not an ideal hemispherical surface burst (the charge was raised 8.9-cm off the ground), and was not set on a rigid surface, it was expected that the loading generated from LS-DYNA would not perfectly match the loading conditions captured by the pressure gauges in the experiments. A scaling factor, derived by comparing predictive curves from UFC 3-340-02 to the measured experimental data, was applied to the LS-DYNA calculated pressure to match the average maximum impulse recorded by the mid-height reflective pressure gauges. A factor of 0.8575 was applied to the loading for the S1 simulation, which resulted in a 0.038% difference in the average experimental maximum impulse. A factor of 0.8975 was applied to the loading for the S2 simulation, which resulted in a 0.0011% difference in the average experimental maximum impulse. Figure 10 shows the LS-DYNA idealized blast loads, plotted along with the factored loads and pressure-time histories for the gauges at mid-height for the two experiments. Load Blast Enhanced was only used for the positive phase of the air-blast loads. To accurately capture the negative phase loading, a simplified loading profile with an impulse equivalent to that calculated from the experimental pressure-time histories was applied to the front face of the specimen as a segment set load. This approach effectively simulated the 'pulling' effect of the negative phase, drawing the specimen back towards the charge. This approach was able to better represent the average negative phase compared to the Load Blast Enhanced negative phase option, which was disabled. The simplified negative phase loading profiles for both S1 and S2 specimens are compared to the experimental data in Figure 11.

Finite element analysis results

Figure 12 presents a comparison of the displacement time histories for the middle anchor location, obtained from both the FEA and the experimental data. The FE results are plotted alongside the displacement-time histories recorded by the two displacement gauges from equivalent locations within the experiments allowing for a direct comparison between the numerical analysis and the experimental measurements. It should be noted that during the S1 experiment, the mount for one of the displacement gauges fell over after the initial peak displacement. In Figure 12, the displacement-time history for the displacement gauge for which the mount fell over is only shown through the peak displacement. Table 6 and Table 7 summarize the key displacement metrics obtained from the FEA for S1 and S2, including the maximum inbound and rebound displacements and corresponding timing. These values are compared to the average experimental measurements from the two displacement gauges, with the resulting percent errors also reported. This comparison enables a quantitative evaluation of the accuracy of the FE model in capturing the dynamic response of the system.

Table 6.

Comparison of inbound behavior.

Test	Max disp.	Max disp. Error	Timing of peak displacement	Timing of peak displacement error
S1	8.76 cm	9%	27.27 ms	5%
S2	14.00 cm	7%	31.84 ms	6%

Table 7.

Comparison of rebound behavior.

Test	Peak rebound	Peak rebound error	Timing of peak rebound	Timing of peak rebound error
S1	10.09 cm	24%	99.27 ms	11%
S2	2.90 cm	66%	127.37 ms	0%

Figure 13 shows images of the specimen at the end of each simulation. The S1 simulation shows slight concrete damage and CFRP delamination near the center anchor as well as slight concrete cracking on the front face of the specimen. The S2 simulation, with the higher blast loading, shows more widespread and more overall concrete damage and CFRP delamination near the center anchors, as well as more concrete damage on the front face of the specimen.

Discussion of analysis results

For both FE simulations, the slopes of the displacement-time histories, peak inbound displacements, and timing of the peak displacements match very well between the FEA and the experimental data. The FE simulations captured the inbound behavior of both slabs, accurately matching the experimental results during the loading phase and up to the maximum displacement. Additionally, both simulations successfully replicated the types and magnitudes of damage observed in the experiments. The timing of the peak rebound displacement was also well-captured, but the simulations were not able to accurately capture the magnitude of the peak rebound displacement. This discrepancy indicates an overestimation of the system’s stored strain energy at the point of maximum displacement, suggesting that the FE models did not dissipate enough energy during the loading phase. The primary sources of this discrepancy are likely the idealized modeling of the reaction structure, and the modeling of the concrete-CFRP interface.

It is unknown whether the FEA truly captures the reaction structure’s movement, as insufficient data of the reaction structure’s movement was recorded in the experiments. To limit computational requirements, only a portion of the reaction structure was modeled. This simplification likely underestimated the energy dissipated by the test frame’s movement. Consequently, resulting in a higher rebound magnitude than was physically observed.

The debonding of the CFRP and the cracking of concrete are processes that consume significant fracture energy. Mesh refinement may affect how much energy is dissipated during these processes. While the interface between the concrete and CFRP were modeled with merged nodes to accurately simulate how debonding was initiated and propagated in the experiments, the mesh refinement used in these simulations may have been too coarse. This could lead to inaccuracies in capturing the amount and timing of the damage in the concrete and subsequent debonding, potentially resulting in discrepancies between the simulated and experimental peak rebound displacements.

FEA exploration for direct comparison of mechanical anchorage systems

Direct comparisons between the two mechanical anchorage systems are challenging due to the different airblast loads they were subjected to in the experiments. However, since the FEA demonstrated good agreement with the experimental results for inbound behavior and overall damage, it can be used as a tool to facilitate a direct comparison between the systems. To achieve this, a numerical study was conducted where the simulated specimens were swapped between the two loading environments. Specifically, the S1 specimen (strap anchorage system) was simulated in the S2 reaction structure and loading environment, while the S2 specimen (plate anchorage system) was simulated in the S1 reaction structure and loading environment. This approach enables a direct comparison between the two anchorage systems under identical loading conditions.

Figure 14 presents the displacement-time histories of the simulated mechanical anchorage systems. The results show that the inbound behavior of the two systems is nearly identical for each loading environment and reaction structure, with minimal differences observed. However, the rebound behavior exhibits some variation, with the simulated plate anchorage specimen showing a 16% higher rebound displacement under S1 loading, and the simulated strap anchorage specimen exhibiting a 20% higher rebound displacement under S2 loading. These findings suggest that the type of mechanical anchorage system used may influence the slab’s behavior as damage to the retrofit initiates. Nevertheless, the comparison indicates that the use of a strap or plate mechanical anchorage system has little impact on the overall expected displacement of the slab for the two loading environments investigated.

Conclusions

Two live explosive tests were conducted at Fort Johnson, Louisiana, to investigate the behavior of RC slabs retrofitted with CFRP and equipped with different mechanical anchorage systems subjected to blast. One anchorage system employed nine epoxy anchors and three steel straps that spanned the width of the specimen on the non-blast side (S1). The other anchorage system employed 17 epoxy anchors and 17 small steel plates dispersed throughout the non-blast side of the specimen (S2). Anchorage systems were used on each specimen to prevent wide-spread delamination of the CFRP. Each specimen exhibited different failure modes, but both specimens exhibited delamination of the retrofit. In both specimens, delamination was not caused by an adhesive failure between the CFRP and the concrete but by failure initiated in the concrete. Under these specific loading conditions, the epoxy anchors exhibited no visible movement and performed well for this test.

In the S1 test, tearing occurred in the CFRP near the three straps and spanned almost the entire width of the specimen. Furthermore, the steel strap anchorage system exhibited long cracks in the CFRP. Additionally, the installation process for this system was extremely challenging, which could pose significant difficulties if this retrofit were to be applied to large-scale slabs. The weight and bulk of the steel straps would become increasingly problematic for larger slabs, and the process of aligning holes would be cumbersome and time-consuming. In contrast, the S2 specimen’s installation proved to be more practical in this application. Although it required a greater number of epoxy anchors, the installation of the small steel plates was significantly less labor-intensive compared to the installation of the steel straps, resulting in a more streamlined process. This design also resulted in minimal damage to the CFRP, with only small tears observed.

The S1 specimen exhibited a failure mode similar to plate-end debonding, but with noticeable differences; the debonding initiated at the location of the straps in the anchorage system, not at the end of the CFRP application. The S2 specimen exhibited an intermediate flexural and flexural-shear crack-induced interfacial debonding failure mode. Despite the size of the tensile failures in the concrete, the plate mechanical anchorage system prevented wide-spread delamination.

FEA was conducted to further investigate the performance of the mechanical anchorage systems. The FE simulations accurately captured the inbound behavior of the slabs, matching the experimental results in terms of displacement-time histories, peak inbound displacements, and timing of peak displacements. The simulations also successfully replicated the types and magnitudes of damage observed in the experiments, as well as the timing of the peak rebound displacement, although they did not capture the magnitude of the peak rebound displacement. This discrepancy is likely due to limitations in modeling the reaction structure and potentially too coarse mesh refinement in modeling the interface between the concrete and CFRP.

As the FEA was able to accurately capture the inbound behavior and the overall damage of the slabs, the FEA was used to facilitate a direct comparison between the performance of the two mechanical anchorage systems. The results show that the inbound behavior of the two systems is nearly identical for each loading environment and reaction structure, with minimal differences observed. This numerical exploration indicates that for the specific slab geometry and blast loads investigated, the choice between the strap and plate anchorage systems had a minimal effect on the slab’s initial inbound dynamic response. This suggests that other factors, such as constructability, may be a more critical differentiator between these two systems.

To further advance the understanding of the mechanical anchorage retrofits under blast loads, it is recommended that additional tests with a larger variety of mechanical anchorage systems be conducted using a more robust reaction structure. This would enable more accurate modeling by minimizing the impact of the reaction structure motion and provide valuable insights into the performance of CFRP retrofits with mechanical anchors under such loads. As this test series provides preliminary evidence for the feasibility of using epoxy anchors without catastrophic failure for the two investigated blast loads, a dynamic pull-out test series for epoxy anchors for this type of application is also recommended.

Footnotes

Acknowledgements

The authors acknowledge the technical aid of Mr. Omar Flores and Mr. Bob Walker. Permission to publish was granted by Director, Geotechnical & Structures Laboratory.

ORCID iDs

Genevieve L. Pezzola

Lauren K. Stewart

Author contributions

Dr. Pezzola: Conceptualization, Methodology, Data collection, Data Analysis, Computational Modeling, Writing – original draft preparation.

Dr. Stewart: Conceptualization, Writing, Reviewing and Editing, Supervision.

Dr. Stephens: Data analysis, Reviewing and Editing, Investigation.

Mr. Nelson: Data analysis, Computational Modeling, Writing, Reviewing and Editing.

Mr. Judson: Coordinated data collection, Investigation, Reviewing and Editing.

All authors approved the final manuscript as submitted and agree to be accountable for all aspects of the work.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The experiments described and the resulting data presented herein were funded under PE 06022784, Project AT40, Task 22 “Force Protection in the Urban Environment,” and managed and executed by the U.S. Army Engineer Research and Development Center.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data that support the findings of this study are available upon reasonable request from the authors.*

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