Experimental and numerical study of CFRP protective RC piers under contact explosion

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Experimental and numerical study of CFRP protective RC piers under contact explosion ⁎

Lu Liua, Zhouhong Zonga, , Chao Gaob, Sujing Yuanc, Fan Loud a

School of Civil Engineering, Southeast University, Nanjing 211189, China Institute of Defense Engineering, AMS, PLA, Luoyang 471023, China c School of Highway, Chang'an University, Xi'an 710064, China d Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., Shanghai 200092, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Blast experiment Numerical simulation CFRP RC piers Contact explosion

In the wake of the event of September 2001, the increasing terrorist attacks have been a destabilizing threat around the world. Public infrastructures, such as tall buildings and traffic facilities, have become attractive bombing targets for terrorists. Crucial bridges subjected to great destruction from bomb attacks can contribute to casualties, property loss and interruption of the transportation system. Bridge piers are the main axial bearing components that are common in bridge construction, and it can readily suffer damage under blast loading. Therefore, it should be necessary to explore protective measures for reinforced concrete (RC) piers to resist blast loading. In this paper, carbon fibre reinforced polymer (CFRP) is chosen to protect RC piers under contact explosion. Five piers, consisting of two unprotected piers and three CFRP protective piers, were constructed and the explosion testing was conducted in the field. Additionally, finite element models of CFRP protective piers were built, considering the contact between concrete and CFRP as well as the anisotropy of CFRP composite material. The models were calculated using the Arbitrary Lagrange Euler (ALE) algorithm and validated by experimental acceleration as well as damage extent. Then, the damage development and CFRP protective effect for RC piers were further analysed. Finally, all specimens experienced local failure under contact explosion and the simulative models were proved accurate for depth analysis.

1. Introduction In the wake of the event of September 2001, the increasing terrorist attacks have been a destabilizing threat around the world [1]. Public infrastructures, such as tall buildings and traffic facilities, have become attractive bombing targets for terrorists. Crucial bridges subjected to great destruction from bomb attacks can contribute to casualties, property loss and interruption of transportation system [2,3]. The number of bridge collapses caused by explosion is 2.7 times greater than that caused by earthquake worldwide [4]. Bridge structures mainly consist of superstructures and bridge piers that are important components supporting the superstructure. Meanwhile, seriously damaged piers under blast loading can lead to bridge collapse. There are few design codes to guide the explosive protection of bridge piers. First, it is necessary to study the damage model and the mechanism for piers under blast loading. RC piers are common in bridge constructions, resulting in many researches focusing on RC piers. The National Cooperative Highway Research Program

⁎

(NCHRP) [5,6] has investigated the failure mode of piers under blast loading, testing ten half-scale RC columns at a small standoff in the field. It was concluded that the pier foot experienced shear failure when the explosives were located near the ground. However, most piers had sufficient shear capacity and experienced limited spalling without breaching [7,8]. Yi et al. [9] have also studied RC piers under blast loading, building a three-span RC bridge numerical model. The results showed that bridge piers have six types of damage mechanisms including the eroding of pier bottom concrete, shear of a pier from the footing, rebar severance, breakage of the pier, spalling of the concrete surface, and plastic hinge formation. There are few researches on RC piers in bridge structures, but there are some studies on RC columns in building structures, with many similar conclusions. Codina et al. [10] constructed a RC specimen with a square section and tested it in the field under a close-in blast loading with results of concrete spalling at one end of the column and cracks developing at the mid-height. In addition, Kyei et al. [11] studied the effects of transverse reinforcement spacing on the blast resistance of RC

Corresponding author at: No.2 Southeast University Road, Jiangning District, Nanjing 211189, China. E-mail address: [email protected] (Z. Zong).

https://doi.org/10.1016/j.compstruct.2019.111658 Received 19 August 2018; Received in revised form 26 September 2019; Accepted 3 November 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Lu Liu, et al., Composite Structures, https://doi.org/10.1016/j.compstruct.2019.111658

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columns and showed transverse reinforcement spacing and axial loading significantly affected RC column behaviour under blast loading at low-scaled distances. However, it is difficult to completely resist blast loading for RC columns in buildings and bridges. Therefore, it should be taken some measures to protect RC piers, such as CFRP sheet protection. There are many available types of polymer composite materials for strengthening and retrofitting RC structures [12], such as glass fibre reinforced polymer (GFRP) and carbon fibre reinforced polymer (CFRP). GFRP was made into an FRP tube, whose material characteristics were fully utilized to protect RC columns. They have been applied in many fields. For example, Fang et al. [13] used the GFRP to design a large-scale composite bumper system (LCBS) for bridge against ship collision and simulative analysis showed LCBS could increase the energy dissipation during collision for protecting bridge piers. Parghi et al. [14] conducted nonlinear static pushover analysis for RC bridge pier retrofitted with FRP composites under seismic loading. From the explosion testing [15,16], the stability of columns can be improved by GFRP tubes and local failures as well as global lateral displacements can be reduced. Wood [17] used the traditional FRP tube and developed a new type of FRP-VE tube with a visco-elastic hardening, damping, and wave-modulating system, which was employed to protect RC columns with a reduced scale of 1:4. Finally, the blast experiments showed that FRP-VE tubes could effectively decrease local failures as well as permanent deformations of columns and FRP could confine concrete destruction. Another blast experiment on an FRP protective concrete column was done by Echevarria et al. [18], followed by residual bearing capacity testing. The post-explosive residual bearing capacity of FRP tube protective concrete columns was remarkably improved compared to unprotected columns. Based on the simulation, Mutalib et al. [19] evaluated the failure mode and residual bearing capacity of FRP protective RC columns and concluded that the blast-resistance capacity of FRP protective columns can be obviously improved. Although GFRP is more economical, Crawford et al. [20] recommended that CFRP was more available than GFRP for wrapping piers due to the high tensile strength and stiffness that can protect the concrete from expansion and it has been widely used for seismic strengthening of bridge piers [21–23]. CFRP was also used to wrap circular, rectangular, square and rhombus cross-section columns in finite element software, which showed that the bending capability of CFRP protective columns can be improved under blast loading [24]. There are relatively few experimental studies with an emphasis on numerical studies. Elsanadedy et al. [25] only studied CFRP protective circular RC columns through simulation. The results showed that the lateral residual deformations of CFRP protective columns decreased under blast loading. Pan et al. [26] selected three different CFRP protective methods to protect circular RC columns under blast loading by LS-DYNA, showing that the global bearing capacity and the resistance capacity to local failure of circular RC columns were markedly improved. Furthermore, CFRP can be used to protect concrete-filled steel tube (CFST) columns in simulations [27] and have a confinement effect on CFST columns, demonstrating that the global lateral deformation and bending failure of columns can be effectively reduced. According to the above research, RC piers are still the main research object for researchers in explosion field. Various protective measures for RC piers to resist blast loading have been proposed. Among these measures, CFRP is a common composite material for piers, especially circular piers. However, the dynamic response and damage mechanism of CFRP protective RC piers under contact explosion are not understood due to much attention on non-contact explosion. Therefore, this paper mainly concentrates on studying the dynamic response and damage model of CFRP protective RC piers under contact explosion using blast experiment and numerical simulation. Five piers with a reduced scale of 1:3, consisting of two unprotected RC piers and three CFRP protective RC piers, were tested in the field under contact explosion. The corresponding numerical models considering the anisotropic material,

Table 1 Essential parameters of RC piers.

Number of CFRP layers Thickness of CFRP/mm H0/mm D/mm Concrete strength/Mpa Longitudinal bars size/mm Yield strength of longitudinal reinforcement/Mpa Stirrup size/mm Yield strength of stirrup/Mpa

S1

S2

None –

None –

JS5

JS6

One Two 0.163 0.326 3500 400 40 10φ12 400

JS7 Three 0.489

φ8 300

Note: H0 is effective height; D is cross-sectional diameter.

contact connection and strain rate were built using the Arbitrary Lagrangian-Eulerian (ALE) method according to experimental cases. The accuracy of the models was validated by the experimental acceleration and damage extent, so the models can be used to analyse the damage development mechanism and CFRP protective effect for RC piers. 2. Blast experiment preparation 2.1. Specimen design In this paper, to study the CFRP protective effect for RC piers under blast loading, five circular RC piers are designed and constructed, whose numbers are S1, S2, JS5, JS6 and JS7. S1 and S2 are the same without any protection and JS5, JS6 and JS7 are protected by one, two and three layers of CFRP sheet, respectively [28–31]. The five piers are designed with a reduced scale of 1:3, whose essential parameters are shown in Table 1. According to standard bridge drawing and bridge design code in China, the pier diameter of urban bridge is generally from 1200 mm to 1500 m. In order to obtain the failure mode of pier easily, the specimen diameter is set to 400 mm by the reduced scale in this study, while our group also consider other section sizes in reference [29,30]. Then there are various pier heights in bridge construction, therefore, the specimen height is designed based on the height of reaction frame, which is set 3500 mm. To fix the top of the pier, 200 mm of height is added to the top, so the actual height of the pier is 3700 mm. Bridge pier is axially compressed component, so its reinforcement design should meet the design of axially compressed component and constructional requirement in code for design of reinforced concrete in China. The longitudinal bars are ten hot-rolled ribbed bars (HRB400) with a diameter of 12 mm and its reinforcement ratio is 0.9%, whose yield strength is 400Mpa. The stirrups are hot-rolled plain bars (HPB300) with a dimeter of 8 mm, whose yield strength is 300Mpa. The distance between stirrups at the mid-span pier is 150 mm, and the distance at the two ends is 100 mm. The longitudinal reinforcements are evenly arranged in the cross-section of the pier and extend to the base. The thickness of the concrete cover is 30 mm and the axial compressive strength of concrete is 40Mpa, which can meet the axial compressive strength in the code. To fix the bottom of the pier, a cubic base is also constructed, with dimensions of 1000 mm × 1000 mm × 500 mm. The geometric dimensions of the RC piers and reinforcement arrangement are illustrated in Fig. 1. CFRP sheet is used to protect the pier due to its pliability for circular pier and glued to the concrete in the surface by epoxy resin adhesive. Three specimens without any damage are separately attached one layer, two layers and three layers of CFRP sheet as a confinement ratio parameter, provided by the mechanical properties of CFRP. It cannot cause cumulative damage for a pier because each explosion test may cause serious damage to a pier. While the piers are warped by the CFRP sheet from bottom to top due to the random characteristic of blast 2

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Fig. 1. Geometric dimensions and reinforcement arrangement of the specimen (Unit: mm).

the front face at the height of 330 mm, as shown in Fig. 4. In this test, the TNT equivalent is 1.0 kg and 2.0 kg, which consists of five and ten small blocks of 0.2 kg-TNT, respectively. An explosion is an energy-releasing process with high temperature and high pressure, which is a transient process. From Fig. 5 recorded using a high-speed camera, the flame around the explosive centre is blue during the initial detonation at 0.2 ms because the temperature around the explosive centre is relatively high. Then, an orange flame spreads at 0.6 ms, when the temperature decreases as energy is released.

loading in the real world and the CFRP strips are attached along circumferential direction. The thickness of different layers are separately 0.163 mm, 0.326 mm, 0.489 mm. 2.2. Experimental setup The pier top is simplified as a hinged constraint with two lateral displacements limited to 3500 mm. The constraint mainly consists of a four-leg steel support fixed on a reaction wall and a steel hoop welded on the support. The pier bottom is assumed to be a fixed constraint in which the entire rotation and translation are limited so the pier base is buried in a pit consisting of a concrete block. The axial force on the top of the bridge pier is caused by the dead weight of the superstructure and vehicular loads. However, a correlation study has proven that the shearing and bending capacity of a pier can be enhanced on the condition that axial force does not exceed the balance point of pier damage [32–35]. Hence, axial force is not considered in this paper. The placement and constraint of the pier are shown in Fig. 2.

3. Blast experiment results 3.1. Acceleration history Contact explosions can produce high overpressure that can directly act on the pier [37], which has a serious effect on the acquisition of accurate test data. Due to strong vibration in the pier, 1# and 2# acceleration transducers are shaken off from all the piers and only 3# acceleration transducer of JS5, JS6 and JS7 record the data in Fig. 6. The intensive vibration of pier transmits from bottom to top when a large impact force strikes the pier bottom. From the acceleration history of 3#, the pier top begins to vibrate at 1.0 ms, meaning the vibration is transmitted from the pier bottom to pier top in one millisecond. The acceleration with high frequency reaches a peak of 1.3 × 104 m/s2, which is 1300 times as high as acceleration of gravity. After one millisecond of consistently intensive vibration, the acceleration rapidly decreases to zero at 2.0 ms. In this vibration process, the pier begins to move back and forth due to external work, which can be quickly transformed to kinetic energy and internal energy as a result of the high vibratory frequency and large damping. When the energy is fully dissipated in a transitory time, the pier vibration stops and the acceleration is decreased to zero.

2.3. Measuring point layout Acceleration is an important indicator in dynamics. Therefore, acceleration transducers are arranged on the back face to record acceleration, where they are protected from being burned out under blast loading. There are three acceleration transducers located at heights of 300 mm, 1750 mm and 3300 mm on the back face, as shown in Fig. 3. 2.4. Experimental cases The typical height of vehicles ranges from 600 mm to 1100 mm, so the height of an explosive ranges from 600 mm to 1100 mm in a car bomb explosion [36]. The height of the explosive in this paper is set equal to 330 mm according to the product of the scale factor of 1/3 and the actual height of 1000 mm. Based on these parameters, contact explosion tests in Table 2 are conducted, in which the explosive is tied to 3

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Fig. 2. Placement and constraint of the specimen.

dynamic response and damage mode of pier under contact explosion, which mainly consist of two classic algorithms, e.g., Lagrangian and Eulerian algorithm. In the Lagrangian algorithm, element meshes can move due to the movement of nodes on the meshes with material points, but in the Eulerian algorithm, element meshes are fixed in space, which cannot deform in the movement of a substance. Therefore, it should be replanned appropriately for large fluid meshes [38]. Combining the advantage of those two algorithms, an Arbitrary-LagrangianEulerian (ALE) algorithm is proposed. The nodes on solid meshes move with the deformation of solids in the Lagrangian algorithm, and the nodes on fluid meshes are fixed in space in the Eulerian algorithm. The ALE algorithm synchronously indicates the dynamic response of solid and the motion of fluid [39–42]. In this algorithm, the Lagrangian and Eulerian meshes must be overlapped to produce better accuracy, but it can be inconsistent for the size of two meshes [43,44]. In this paper, the pier is simulated using the Lagrangian algorithm, then the air and explosive are simulated using the Eulerian algorithm.

3.2. Local damage Fig. 7 shows the local damage phenomena of five piers under contact explosion. S1 is tested under a 1.0 kg-TNT explosion; the front concrete spalls at a height of 60 cm and a maximum depth of 4 cm. Then, transverse and vertical micro-cracks appear in the rear concrete. S2 is tested under a 2.0 kg-TNT explosion, whose damage extent is more serious than S1. The concrete of S2 is completely broken through the cross-section at a height of 70 cm and wider cracks appear in the rear concrete. In addition, the longitudinal reinforcement experiences bending deformation and the stirrup is fractured without any concrete protection. JS5, JS6 and JS7 with CFRP protection are tested under a 1.0 kgTNT explosion. For JS5, the front CFRP sheet is broken and the front concrete spalls at a height of 53 cm, a width of 93 cm and a maximum depth of 12 cm. Then, transverse cracks appear in the rear concrete. However, the stirrup is fractured due to the hook in the front face. For JS6, the front CFRP sheet is broken and the concrete spalls at a height of 46 cm, a width of 92 cm and a maximum depth of 14 cm. Then, transverse cracks appear in the rear concrete with the stirrup fracturing. For JS7, the front CFRP sheet is broken and the concrete spalls at a height of 40 cm, a width of 85 cm and a maximum depth of 13 cm. Then, transverse cracks appear in the rear concrete with the stirrup pulled from concrete. From the local damage of CFRP protective pier, the concrete damage extent decreases as the number of CFRP layers increases.

4.1. Model construction Concrete is simulated by solid 164 with eight-node solid elements, which can get stress in six direction and concrete spalling. All steel bars, including the longitudinal reinforcements and stirrups, are simulated by beam 161 with two-node beam elements, which can get axial stress and bar fracture. In addition, CFRP composite layer and ground are simulated by shell 163 with four-node thin-shell elements, which in-plane stress is dominant. From Fig. 8, the height of top is 200 mm, the effective height of pier is 3500 mm, and the underground foundation is 500 mm. The crosssectional diameter of pier is 400 mm. The size and layout of steel bars are built according to the piers in explosion testing.

4. Numerical simulation To further study the protective effect of CFRP under blast loading, numerical simulation is the most common and effective method. In this study, LS-DYNA finite-element software is employed to simulate the 4

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Fig. 3. Acceleration measurement points.

Fig. 4. Location and dimension of the TNT charge.

The foundation is fixed from all translational displacement and rotational displacement due to large base imbedded into the earth and the top is limited to two transverse translational displacements because these are limited by steel sleeve. All surface of pier is wrapped by CFRP with a height of 3500 mm, whose fibre tension direction is circumferential. The mesh sizes of concrete, steel bar, CFRP and ground are divided into 10 mm. Yuan et al. [45] have investigated the mesh convergence of RC piers and proved that a 10-mm mesh size can achieve a balance between the accuracy and calculation effort. The concrete elements and steel bar elements are coupled with common nodes ignoring relative slippage due to a fairly short blasting time [31], furthermore, concrete may be broken early before the development of slippage between different elements. The adhesive contact connection between CFRP element and concrete element is set by the keyword AUTOMATIC_SURFACE_TO_SURFACE_TIEBREAK in LS-DYNA [19]. The contact in LS-DYNA is an algorithm, which considers non-interpenetration between two adjacent interfaces (concrete and CFRP). Traditional contacts transmit only normal compressive force and tangential force, but

cannot transmit normal tension. However, not only normal compressive force and tangential force but also normal tension should be considered between concrete and CFRP. This connection is a typical glued surface that can transmit both tensile and compressive forces until the glue fails. The contact between CFRP and concrete is valid before a failure criterion predefined by equation (1) is reached, which originates from the strength of epoxy based on its normal tensile and shear stresses at failure. The mechanical properties of the epoxy adhesive shown in Table 3 are provided by Sayed-Ahmed [46]. In other words, when the normal stress and the shear stress between CFRP and concrete exceed the tensile strength and shear strength of epoxy adhesive, the contact connection between CFRP and concrete will be lost, so that the CFRP can be separated from the concrete. In addition, the friction coefficient between CFRP and concrete did not be considered. Firstly, it is extremely short to acting on the structure for blast loading, therefore, there is no sliding development between CFRP and concrete under contact blast loading before the contact connection is lost. Then the epoxy adhesive is considered a brittle failure in a very short time.

Table 2 Main test cases. Test case

No.

TNT equivalent/kg

Height of explosive center/mm

Case1 Case2 Case3 Case4 Case5

S1 S2 JS5 JS6 JS7

1.0 2.0 1.0 1.0 1.0

330 330 330 330 330

5

Blast type Contact Contact Contact Contact Contact

explosion explosion explosion explosion explosion

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Fig. 5. Explosion process.

Fig. 6. Acceleration history. 6

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Fig. 7. Damage phenomena. 2 2 ⎛ |σn | ⎞ + ⎛ |σs | ⎞ ≥ 1 NFLS SFLS ⎝ ⎠ ⎝ ⎠

1600 mm × 2000 mm × 1020 mm with a mesh size of 20 mm, and the dimensions of 1.0 kg-TNT and 2.0 kg-TNT explosives are 80 mm × 80 mm × 100 mm and 120 mm × 100 mm × 100 mm, respectively. The explosive, ground and pier with a height of 1000 mm are in the air domain, in which the ground can reflect shock wave. The partial air domain has been validated to reasonably simulate explosion cases under contact explosion [45,47], since most energy released by explosive is absorbed directly by the pier leading to small shock wave

(1)

where σn is the normal stress and σs is the shear stress at the interface surface; NFLS is the corresponding tensile stress and SFLS is the corresponding shear stress at failure. The air and explosive are simulated by solid 164 with eight-node solid elements, and the Eulerian element is also coupled with common nodes. The physical dimensions of air domain are 7

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Table 3 Mechanical properties of the epoxy adhesive [46]. Property

Value

Tensile strength (NFLS)/MPa Tensile modulus/GPa Shear strength (SFLS)/MPa Compressive strength/MPa Poisson’s ratio

32 11.7 29.4 60 0.2

interaction between fluid and solid. Then, the keyword CONTROL_ALE is chosen to set the global control parameters for the Arbitrary Lagrangian-Eulerian (ALE) and Eulerian calculations. The keyword BOUNDARY_NON_REFLECTING is chosen to set the non-reflecting boundaries, which are used on the exterior boundaries of infinite air domain, such as a partial air domain to prevent artificial shock wave reflections generated at the air domain boundaries from re-entering the air domain and contaminating the results.

4.2. Material model 4.2.1. Concrete The concrete uses material model MAT_CONCRETE_DAMAGE_REL3 (MAT_72R3), called KCC model, which can analyse the dynamic performance of a concrete structure under high strain rate [48]. This

Fig. 7. (continued)

Fig. 8. Finite element model of the pier.

constitutive model is modified in accordance with pseudo-tensor concrete material, including three independent failure surfaces, a strain rate effect and a damage effect [49]. The strain rate effect can be considered based on the relationship between strain rate and dynamic increase factor (DIF) of material strength, where DIF comes from the

generated by air. Therefore, the shock wave propagating to the upper part has little effect on the pier, which can be ignored to save computing time. The air and pier are linked by the keyword CONSTRAINED_LAGRANE_IN_SOILD to provide the coupling mechanism for 8

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modified CEB model. The tension dynamical increase factor (TDIF) of concrete strength is as follows [50].

TDIF =

TDIF =

TDIF =

ftd fts ftd fts ftd fts

Table 5 Material properties of CFRP composites [53]. Mechanical Properties

= 0.26(lgεḋ ) + 2.06, εḋ ≤ 1/ s

(2)

= 2(lgεḋ ) + 2.06, 1/ s < εḋ ≤ 2/ s

= 1.44331(lgεḋ ) + 2.22766, 2/ s < εḋ ≤ 150/ s

Density/kg·m Youngs modulus/GPa

(3)

Shear modulus/GPa

Poisson’s ratio

(4)

where ftd is the dynamic tension strength of concrete at strain rate εḋ , fts is the static tension strength of concrete at strain rate εtṡ (εtṡ = 10−6/ s ). The compressive dynamical increase factor (CDIF) of concrete strength is as follows [50].

CDIF =

CDIF =

fcd fcs fcd fcs

= 0.0419(lgεḋ ) + 1.2165, εḋ ≤ 30/ s

= 0.8988(lgεḋ )2 − 2.8255(lgεḋ ) + 3.4907, εḋ > 30/ s

1580 138 9.65 9.65 5.24 2.24 5.24 0.021 0.021 0.49 1440 2280 228 57 71 1.38 1.175

Ea Eb Ec Gab Gbc Gca Prba Prca Prcb

Transverse compressive strength/MPa Transverse tensile strength/MPa Vertical compressive strength/MPa Vertical tensile strength/MPa In-plane shear strength/MPa Maximum strain for fiber tension/% Maximum strain for fiber compression/%

(5)

Note: a is the transverse direction; b is the vertical direction; c is the throughthickness direction.

(6) 4.2.4. CFRP The CFRP can be simulated as a type of anisotropic composite material. The tensile direction of fibre is the principal stress direction and the other two directions are the subordinate stress directions due to adhesive bonding. MAT_ENHANCED_COMPOSITE_DAMAGE (MAT_54) is chosen to model the CFRP composite, which has been widely used [19,51,52]. This material model is based on the Change-Chang failure criterion for evaluating lamina failure, in which there are four failure modes including the tensile fibre mode, compressive fibre mode, tensile matrix mode and compressive matrix mode. The CFRP composites shown in Table 5 consist of a CFRP sheet and epoxy (AS4/3501-6), whose material properties are provided by Chan et al [53]. The confinement ratio [54] of different CFRP layers can be got by equation (8), which is separately 0.0465 (one layer), 0.0929 (two layers), 0.1393 (three layers).

where fcd is the dynamic tension strength of concrete at strain rate εḋ , fcs is the static compressive strength of concrete at strain rate εcṡ (εcṡ = 30 × 10−6/ s ). In LS-DYNA, only unconfined compressive strength (UCS), concrete density and Poisson’s ratio can be input to the KCC model. Other material parameters are automatically generated. The material parameters are shown in Table 4. MAT_ADD_EROSION is chosen to define the failure mode of concrete by principal strain. 4.2.2. Steel bar The steel bar uses material model MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_24), which is an elastoplastic material with an arbitrary stress vs strain curve and an arbitrary strain rate dependency that can be defined. In this model, failure based on a plastic strain can also be defined. The dynamical increase factor that scales the yield stress can be used to account for strain rate. In this paper, the dynamical increase factor (DIF) of the steel bar is as follows [50].

fy ε̇ α DIF = ⎛ −4 ⎞ , α = 0.074 − 0.04 10 414 ⎝ ⎠

Carbon/Epoxy (AS4/3501-6)

−3

ρc = 2σf t / dfco

(8)

where σf is transverse tensile strength of CFRP, t is thickness of CFRP, d is diameter of cross-section, fco is the uniaxial compressive strength of concrete.

(7) 4.2.5. Air and explosive The air is simulated as an ideal gas in the LS-DYNA by MAT_NULL (MAT_9) material model, and the state equation is set by keyword EOS_LINEAR_POLYNOMIAL. The linear polynomial state equation is linear in internal energy. The pressure is described by equation (9).

where ε ̇ is the strain rate of reinforcement, f y is yield strength, and the application ranges are 10−4s−1 ≤ ε ̇ ≤ 255s−1 and 270MPa ≤ f y ≤ 710MPa . The material parameters are shown in Table 4. 4.2.3. Ground The ground can be considered a rigid plane to reflect shock wave, whose rotation and displacement in the x, y and z directions is constrained. Therefore, MAT_RIGID (MAT_20) is chosen to simulate the ground, whose material parameters are shown in Table 4.

P = C0 + C1 μ + C2 μ2 + C3 μ3 + (C4 + C5 μ + C6 μ2 ) E

(9)

whereC0 ~ C6 are material parameters; μ = ρ / ρ0 − 1, ρ / ρ0 is the ratio of current density to reference density; E is the initial internal energy per unit reference volume.

Table 4 Material parameters of the concrete, steel bar and ground. MAT_72R3 Parameter

Concrete

Yield strength/MPa Density/kg·m−3 Elastic modulus/MPa Poisson’s ratio Tangent modulus/MPa Failure strain UCS/MPa

– 2.5 × 103 – 0.2 – – 40

MAT_24 Longitudinal bar 2

4.0 × 10 7.85 × 103 2.0 × 105 0.3 2.0 × 103 0.15 –

9

MAT_20 Stirrup

Ground 2

3.0 × 10 7.85 × 103 2.0 × 105 0.3 2.0 × 103 0.15 –

– 2.5 × 103 3.25 × 104 0.2 – – –

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Table 6 Material parameters for the explosive. Parameter

A /GPa

Value

3.738 × 10

ω

B /GPa 2

3.747

0.35

R1 4.15

R2 0.9

ρ E ρ0

(10)

The explosive is simulated as a TNT charge in the LS-DYNA by MAT_HIGH_EXPLOSIVE_BURN (MAT_8) material model, and the state equation is set by the keyword EOS_JWL. The pressure is defined by equation (11).

ω ⎞ −R1 V ω ⎞ −R2 V ωE p = A ⎛1 − e + B ⎛1 − e + R V R V V 1 2 ⎝ ⎠ ⎝ ⎠ ⎜

⎟

⎜

1

E /kJ·m−3 6

6.0 × 10

ρ /kg·m−3 1.63 × 10

3

vD /m·s−1 6.93 × 10

3

PCJ /GPa 21

of structures due to the linear characteristics of mesh. Meanwhile, the vibration frequency can be affected by the stiffness and mass in dynamics. The stiffness is linked with the size, number, and shape of mesh and boundary condition of structure. The mass is linked with volume and density. As we can see, the localized blast effects cause the erosion and fracture of mesh, and the reduction of mass. In addition, the data transmission needs more time in the process of calculation due to a large number of grid element, so there is time lag effect between simulation and experiment, which is less than 0.5 ms. Although there is some limitation for this model, it can be improved in the future according to several aspects. It should be increased for the sampling frequency of acquisition system to get more continuous data. Then, numerical model can set infinitesimal mesh, add nonlinear elements at local locations, and adjust the boundary condition. Lastly, it should be further to study the erosion criterion to simulate accurate mass-loss of structure.

In this study, the gamma law state equation can be used to simulate the ideal gas, which can be achieved by setting C C0 = C1 = C2 =C3 = C6 = 0 and C4 = C5 = γ − 1, where γ = CP is the v ratio of specific heats. Therefore, the pressure for a perfect gas is given by equation (10). In this study, γ = 1.4 , the initial air density is 1.225 kg/m3 and the initial internal energy of air per unit volume is 0.2068 × 106 kJ/kg [55].

P = (γ − 1)

V

⎟

(11)

4.3.2. Damage verification The damage extent of pier is also an important validation indicator between simulative results and experimental phenomenon. From Fig. 10, the damage extent of S1, S2, JS5, JS6 and JS7 is obtained in the simulation. There is no global deformation, but highly localized failure occurring for all piers. It is showed that the concrete is cracked with a spalling of a crystal shape, and the steel bar is bent. The damage height of S1 under a 1.0 kg-TNT contact explosion is 54 cm in the simulation and 60 cm in the test, in which the concrete cover is peeled off. The damage height of S2 under a 2.0 kg-TNT contact explosion is 65 cm in the simulation and 70 cm in the test, in which the concrete is completely broken through the cross-section and the longitudinal reinforcement is bent. The damage height of JS5 under a 1.0 kg-TNT contact explosion is 53 cm in the simulation and 53 cm in the test, the damage height of JS6 under a 1.0 kg-TNT contact explosion is 53 cm in the simulation and 52 cm in the test, and the damage height of JS7 under a 1.0 kg-TNT contact explosion is 38 cm in the simulation and 40 cm in the test. These three specimens all develop concrete cover spalling and CFRP fracture. According to Fig. 10(f), the damage heights of simulative specimens and experimental specimens are in good agreement for the five piers with an error of less than 20%. Therefore, the simulative model can be used to analyse the damage mechanism of a pier. Furthermore, the damage extent is greater for S2 than for S1 based on the damage height of S1 and S2, which is because more TNT is used for S2. In addition, it is a notable result that the damage extent increases with the increasing number of CFRP layers based on the damage heights of S1, JS5, JS6 and JS7.

where p is the hydrostatic pressure; V is the relative volume of the explosive; E is the energy per unit volume; A , B , R1, R2 and ω are material constants for the explosive determined by the experiment. The material parameters for the explosive are shown in Table 6 [56], in which vD is the detonation velocity of the explosive and PCJ is the Chapman-Jouget pressure calculated by the least action detonation model of the explosive in the chemical domain. 4.3. Model verification To verify the reliability of numerical model for analysing the damage mechanism of a pier under contact explosion, the corresponding experimental cases are simulated and the numerical models are validated in accordance with acceleration and damage extent. 4.3.1. Acceleration verification In structural dynamics, acceleration, velocity and displacement are the main dynamic responses of pier. The acceleration histories of JS5, JS6 and JS7 at 3# in the simulation are extracted for comparison with the experiment. From Fig. 9, the peak values and the global vibration trend of simulated acceleration data are in reasonable agreement with the experimental results except for some time lag effect. The peak value and starting times of acceleration are almost identical, which peak value is about 13000 m/s2 and starting time is on about 0.7 ms; in addition, the vibration data is mainly concentrated between the moments of 0.5 ms and 2.5 ms and decreases to zero before the movement of the piers stops. Due to short time of structural vibration and intensive response, pier vibration is a high-frequency response, especially under blast loading. Relative study [45] has explained that high-frequency vibration may not be accurately because of the limitation of data acquisition system, and continuous finite element model also has limitation that material fracture is unavoidable under contact blast loading. Based on these, it can be concluded that they are in good agreement and numerical model can give a reasonable prediction for analysis under blast loading. However, there are several reasons why the time is not exactly the same. Firstly, the sampling frequency response of data acquisition system cannot keep up with the natural frequency of the structure that is an ultra-high frequency vibration and the sampling data in the experiment is actually discontinuous. Then, numerical simulation is a hypothetical simulation method, dispersing a continuous structure into small elements. It is difficult to get the higher order vibration frequency

5. Numerical results and discussion 5.1. Damage development To better understand the damage development of a CFRP protective pier, the validated model can be used. In related research [45], the stress wave can propagate in a circular cross-section from the front to rear and reflect off the pier surface. The stress wave can also propagate in the vertical section of Fig. 11 to the above and below height of explosive. When the TNT starts to explode, the front CFRP breaks directly due to the great impact force from the energy release, so the stress wave can be introduced straight into the concrete interior. The stress wave at the height of explosive initially arrives at the rear 10

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Fig. 9. Acceleration verification of 3#.

5.2. Reinforcement stress

surface and reflects off the surface, producing tensile stress. However, the upper and lower stress waves continue to propagate towards the arrow direction in vertical section, producing the compressive stress. This situation contributes to the rear CFRP sheets at the height of explosive experiencing a drag force, so the CFRP is separated from concrete. Then, the CFRP is gradually separated from the height of explosive to the above and below height of explosive. During the detachment process between CFRP and concrete, the rear CFRP is also pulled in the vertical and transverse direction. When the stress value of CFRP element reaches the pre-supposed stress threshold, the element will be invalid that implies the CFRP is broken. In Fig. 12, a shell element in the rear CFRP is selected, which is a failure element. There are vertical and transverse tensile directions for the failure element, whose tensile stress in the two directions is extracted. From the curves, the maximum vertical stress in the history curve is 66 MPa, which is greater than 57 MPa and contributes to the element failure in the vertical direction. However, the maximum transverse stress in the history curve is 630 MPa, which is much larger than the maximum vertical stress but less than 2280 MPa, so the elements in the transverse direction are not fractured and can continue to bear transverse tensile stress. According to the analysis for the rear CFRP, the thin connection lines are broken in vertical direction and the transverse CFRP strips remain intact in the experimental phenomenon.

For CFRP protective piers under contact explosion, there is some deformation and axial stress for reinforcement after the CFRP is broken and concrete spalls. The axial stress of reinforcement at the height of the explosive in the front face for S1, JS5, JS6 and JS7 is shown in Fig. 13. The axial stress history of stirrup is shown in Fig. 13(a). The peak stress decreases with the increase in CFRP layers for the four piers and the residual stress decreases with the increase in CFRP layers except for S1. The stirrups are important for constraining core concrete when it is in good condition without spalling. For S1 without any protection, the core concrete spalls so that stirrups lose the ability to constrain it and release the residual stress. Therefore, the residual stress is smaller for S1 than for the other piers. The peak stress and residual stress of longitudinal reinforcement for S1 are significantly greater for CFRP protective piers. The peak stress of longitudinal reinforcement for JS5, JS6 and JS7 are almost identical and the residual stress of longitudinal reinforcement decreases to zero, which can be explained by the number of CFRP layers not having an effect on the stress of longitudinal reinforcement and the lack of residual deformation for longitudinal reinforcement in the front face due to separation between the concrete and reinforcement. In the rear face, the peak stress and residual stress of stirrup for S1 are greater than for other piers in Fig. 14(a). The stirrups can still confine the core concrete due to the back-core concrete not spalling. Nevertheless, the number of CFRP layers does not have an effect on the

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Fig. 10. Damage verification.

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100

Experiment Simulation Error

Damage Height (mm)

80

80

60

60

40

40

20

20

0

S2

S1

JS1

JS2

JS3

Error (%)

100

0

(f) Damage height comparison

Fig. 10. (continued)

rear face can produce plastic deformation that is the same as concrete due to the coupling action between reinforcement and concrete without spalling. In general, CFRP can protect RC piers from the axial stress of

axial stress for CFRP protective piers due to the same stress. The peak stress of longitudinal reinforcement is greater for S1 than for other piers in Fig. 14(b) and the residual stress of longitudinal reinforcement for those four piers is nearly identical. Longitudinal reinforcement in the

Fig. 11. Stress-flow process. 13

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Fig. 12. CFRP fracture.

Fig. 13. Axial stress of reinforcement in the front face. 14

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Fig. 14. Axial stress of reinforcement in the back face.

internal energy is greater for S1 than for other piers, and the residual internal energy of S1 is nearly ten times greater than that of the other three piers, as can be interpreted by more concrete deformation and fracture leading to greater residual internal energy of concrete. Therefore, the damage extent of unprotected piers is more serious in accordance with concrete damage. However, the residual internal energy of JS5, JS6 and JS7 are approximate and quite small, which implies CFRP can effectively protect the piers and the number of CFRP layers has little influence on concrete damage under contact explosion.

reinforcement in the front and rear faces, and the protective effect for RC piers is better with an increasing number of CFRP layers. 5.3. Energy Fig. 15 shows the internal energy of S1, JS5, JS6 and JS7 from concrete absorption. The concrete can absorb external energy and translate it into internal energy by concrete deformation and fracture. From the internal energy history, the peak internal energy and residual

Fig. 15. Internal energy of concrete. 15

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Fig. 16. Kinetic energy and internal energy of CFRP.

Declaration of Competing Interest

Fig. 16 shows the kinetic energy and internal energy of CFRP for JS5, JS6 and JS7. There is kinetic energy and internal energy for each CFRP shell element, resulting in the total kinetic energy and internal energy of CFRP. When the CFRP shell element fails, it can vanish including its all characteristics, such as velocity, mass, etc. According to Fig. 16(a), the total kinetic energy of CFRP increases as the number of CFRP layers decreases. Since the decreasing number of CFRP layers can weaken the protective effect for pier, more shell elements will fail. In addition, the kinetic energy finally decreases to zero due to stop-motion with a velocity of zero. From Fig. 16(b), the total internal energy of CFRP increases as the number of CFRP layers decreases. Shell elements without failure can become deformed and store the internal energy in deformation, because the identical external work and the large deformation can cause more energy to be absorbed. Therefore, the CFRP of JS7 can store the most internal energy so that it is the best protective effect for pier.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was supported by the National Natural Science Foundation of China (51678141) and the Fund of State Key Laboratory of Bridge Engineering Structural Dynamics and the Key Laboratory of Bridge Earthquake Resistance Technology, Ministry of Communications, PRC (201801), as well as the Graduate Research and Innovation Projects of Jiangsu Province (KYCX18_0119). The first author also appreciates the financial support provided by the China Scholarship Council. References

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In this paper, the explosion experiment and simulation were conducted to study the dynamic response and damage mechanism of CFRP protective RC piers under contact explosion. Some main conclusions are drawn as follows. Based on the experimental explosion test in the field, the piers present a high-localized damage model in which the concrete spall and reinforcement become deformed. The local damage extent of pier is more serious due to larger TNT equivalents. CFRP can protect RC pier. In addition, the integral structure of pier can vibrate due to local impact. Simulation models are built based on the Arbitrary LagrangianEulerian (ALE) algorithm considering the strain rate effect for concrete and reinforcement and an anisotropic composite for CFRP. The air and explosive are also simulated accurately according to the experimental TNT charge. The models were validated by a comparison of the acceleration and damage extent showing good agreement, so they can be used to further analyse the damage mechanism of CFRP protective RC piers. In accordance with the validated finite element model, the damage development of the piers is studied. The results show that a dragging force caused by a stress wave separates the CFRP from concrete. The vertical CFRP fibre is broken first, followed by transverse fibre. The reinforcement stress and energy of concrete and CFRP are also analysed with a conclusion that CFRP can provide effective protection for RC piers under contact explosion.

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