Experimental and numerical study on steel wire mesh reinforced concrete slab under contact explosion

Materials and Design 116 (2017) 77–91

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Experimental and numerical study on steel wire mesh reinforced concrete slab under contact explosion Jun Li a,⁎, Chengqing Wu a, Hong Hao b, Yu Su a a b

Centre for Built Infrastructure Research, School of Civil and Environmental Engineering, University of Technology Sydney, NSW 2007, Australia Department of Civil Engineering, Curtin University, WA 6845, Australia

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Beam reinforced by steel wire mesh and micro steel fibres shows high flexure capability • Slab with steel wire mesh reinforcement develops local membrane effect under blast • FE-SPH algorithm can model the fragmentation process with reasonable accuracy • The contact detonation generates fragments with velocity exceeding 100 m/s • The blast shock front velocity detected in the field test exceeds 700 m/s

a r t i c l e

i n f o

Article history: Received 27 July 2016 Received in revised form 24 November 2016 Accepted 26 November 2016 Available online 05 December 2016 Keywords: Steel wire mesh Composite slab Contact detonation SPH algorithm

a b s t r a c t With the rising of terrorism and rapid urbanization around the world, increasingly more structures are exposed to the threats from accidental and hostile explosion loads. To provide adequate structural protection against blast load, novel materials and strengthening techniques are under fast development. In the present study, a composite slab design aiming at high level blast resistance is studied. In the matrix of high strength self-compacting concrete, besides conventional rebars serving as primary reinforcement, steel wire meshes are embedded and served as secondary reinforcements. Moreover, on the concrete cover layer where the tensile cracks locate, steel fibres are added to provide micro crack-bridging effect. Preliminary numerical simulations adopting coupled Finite Element (FE) and Smoothed Particle Hydrodynamics (SPH) are carried out in hydro-code and the results are used as guide for field blast test. Composite slab with optimal design is field tested under 1 kg TNT contact detonation, and the results are compared with slabs made of conventional and ultra-high performance concrete without steel wire meshes. The results demonstrate that slab with steel wire mesh reinforcement develops localized membrane effect when subjected to blast loads and shows better blast resistant capability as compared to the slabs without steel wire meshes. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction

⁎ Corresponding author. E-mail address: [email protected] (J. Li).

http://dx.doi.org/10.1016/j.matdes.2016.11.098 0264-1275/© 2016 Elsevier Ltd. All rights reserved.

Structural response under dynamic loading is a topic of increasing interest in recent decades. Short duration high intensity loads like impact or blast usually cause local response of a structure. The damages

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observed on post-blast structural components are usually in brittle manner [1]. Given there is not necessarily sufficient structural redundancy, damage of individual components can cause disproportional collapse of the entire structure [2], which is now an important concern for structural engineers and researchers. To conduct analysis and provide rational protective design of structures against accidental or hostile explosions, it is critical to understand blast loading amplitude and distributions on the structures. Until now, most information about blast loads is semi-empirical and the most extensively used blast load parameters (including blast overpressure and impulse) are plotted versus the scaled blast standoff distance (R/W1/3) as presented in manual UFC 3-340-02 [3]. The amplitude and distribution of air blast loads are functions of the type of explosive material, weight and shape of the explosive, distance and location of the explosive relative to the structure, and the interaction of the shock front with the ground and the target structure. The most extensive data about blast load parameters are for bare spherical TNT airbursts and bare hemispherical TNT surface bursts. When explosions occur in close proximity to or in contact with the structure, since the loadings on structures from these explosion scenarios are extremely severe and complex, it is very difficult to conduct an accurate measurement, and the curves in UFC manual therefore start at about R/W1/3 = 0.15 ft/lb 1/3 (0.06 m/kg1/3 ). Although the empirical approaches provide predictions of blast load from explosion at a scaled distance less than 1.0 m/kg1/3, previous studies demonstrated that significant variations exist on predicted blast load from different empirical formulae and design charts, indicating it is very difficult to reliably predict blast loads from explosions with scaled distance less than 1.0 m/kg 1/3 [4], let alone predicting loads from contact explosions. In case contact explosions occur, structural components usually suffer highly localized damage such as concrete crushing and spalling, and these damages are induced by stress wave propagation rather than global shear and bending deformation. Upon detonation, high intensity compressive stress wave impinges on the concrete surface which easily exceeds the dynamic compressive strength and induces concrete crushing. When the blast induced compressive stress wave propagating inside the structure strikes the free surface of concrete, it will be reflected and turn into tensile stress wave. At a certain depth of the concrete, if the resultant stress is larger than the dynamic concrete tensile strength, concrete spalling initiates. During the propagation of the stress wave, attenuation, dispersion and divergence occur which change the shape and amplitude of the stress wave. In general, concrete spalling is caused by the shock impedance mismatch during the wave propagation, and it is dependent on the material strength, porosity, reinforcement spacing and other imperfections while it is relatively insensitive to the structural global stiffness and support boundary conditions. Analytical solutions to stress wave induced structural failure is complex. Existing analyses [5–7] are based on simplifications which overlook the influence of wave attenuation and dispersion. Furthermore, these derivations are based on assumption that blast load can be determined and idealized in a specified scenario, however, as mentioned above, blast load is extremely hard, if not impossible, to be reliably predicted in a contact detonation case. McVay [8] proposed an empirical approach for determining if and where a stress wave would cause the concrete to crack in tension. In this method, the changes in the stress caused by stress waves travelling at different velocities, wave attenuation, and dispersion were neglected. The only change in the stress wave propagation that was taken into consideration was wave divergence. Experimental study of this topic has widely been conducted in recent decades. Based on a large database of empirical slab/wall tests, AFRL-MN-EG-TR-1998-7032 Concrete Hard Target Spall and Breach Model [9] details the development of a spall/breaching algorithm for RC slabs and walls. In UFC guideline [3], data from spall tests have been compiled and damage curves are given to predict the concrete

spall damage. In these tests, a cylindrical charge, cased or bare, is oriented side-on at a standoff distance from a wall slab and oriented end-on in contact with the ground. Foglar and Kovar [10] plotted their experimental results on these spall and breach prediction curves, and they concluded that the observed spall damages in RC specimens agree with the spall and breach prediction curves according to UFC guideline. However, they also noted the spall and breach prediction curves according to UFC are not suitable for predicting the spall damage in fibre reinforced concrete. Moreover, the spall damage severity is not clearly defined in UFC guideline. Therefore it can only predict the occurrence of spall damage in the wall slab under a blast load, but cannot quantify the damage levels. Wang et al. [11] carried out close-in explosion tests on square reinforced concrete slabs and spall damage at different severities was observed. Shi et al. [12] studied the influence from explosive shape on the concrete slab spall damage, and they observed that increase in the height/diameter ratio of the cylindrical TNT charge will significantly increase the spalling damage of the RC slab, although the mass of the TNT charge is unchanged. Ohtsu et al. [13] experimentally and analytically investigated the dynamic failure of fibre-reinforced concrete (FRC) slabs, and it was observed that the averaged diameters and the volumes of the spall failure remarkably decreased with the increase in the flexural toughness of FRC concrete. Ohkubo et al. [14] conducted contact-explosion tests on concrete plates reinforced by carbon or aramid fibre sheet, and it was noted that local spall damage had been significantly reduced with fibre sheet reinforcement, and fibre sheets also had prevented concrete plates from fragmentation. Upon occurrence of spall damage, besides structural damage, the secondary fragments generated with the concrete spall are also of significant importance as these fragments with large momentum can cause severe casualties and property loss. Technical paper [15] details procedures for the collection, analysis and interpretation of explosionproduced debris. It reports that a fragment with an impact kinetic energy of 79 J has a 31% probability of being lethal while an impact kinetic energy of 103 J would generate more than 50% probability of fatality. Later study in [16] gives more discussions about lethality criteria for debris generated from accidental explosions. Clearly, characterization of debris would enable improvement of current guidelines on safe standoff distances from building undergoing demolition or terrorism attack. Fragments velocity and mass distribution are therefore of vital importance when analysing fragment hazards of structures. Under blast loading environment, the concrete fracture and fragmentation result from both impulsive loading by stress waves and explosive gas-driven fracture propagation [17]. Brinkman [18] studied the fragmentation and projectile throwing process of brittle concrete-like material and concluded that stress waves generated by the detonation of an explosive charge are responsible for the development of a damage zone in the concrete material and the subsequent fragment size distribution, while the explosion gases are important in the separation of a crack that has already been formed during the passage of the stress wave, and in the subsequent launch of the fragments. Regarding the fragments mass and size distribution, a well-known analytical model of dynamic fragmentation [19] based on energetic criterion has found an extensive use in describing experimental data in a variety of solid materials. Wu et al. [20] carried out a sieve analysis to investigate the fragments size distributions from the concrete specimens under close-in detonations. It was found that the fragment size followed both a Weibull distribution and a Rosin–Rammler–Sperling–Bennet (RRSB) distribution. In a later experimental study, Li et al. [21] studied the distribution of debris from ultra-high performance concrete under contact detonations. Formulae aiming at crude estimation of the launch velocity of debris that is projected into the far field are proposed in [15]. From the perspective of energy and momentum, Xu and Lu [17] derived a simple formula for predicting velocity of debris generated by an internal explosion. Zhou and Hao [22] developed mesoscale model to analyse the damage and fragmentation of concrete slab under contact detonation. The dynamic

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damage process of the concrete slab under contact detonation was simulated and the fragment size distribution was estimated. Until now, a variety of numerical approaches have been undertaken to numerically simulate blast and more importantly, the fragmentation. When using conventional finite element method towards this purpose, Lagrangian elements are often deleted or eroded when the given failure criterion is achieved so as to avoid computational overflow. Fragmentation has been addressed in this context via post-processing calculations. More realistic methods including cohesive finite element method [23], and discrete element method [24] have been adopted in recent studies to simulate the dynamic deformation and fragmentation of the brittle concrete-like materials. Particle method, which is of particular interest in the present study, has also been used. Smooth particle hydrodynamics (SPH) methods permit simulations of very large distortions in a Lagrangian setting, with local continuum-type quantities such as deformation rates depending upon relative particle motions and smoothing functions. Concrete subjected to explosive loading has been modelled with SPH [25,26]. Previous studies found that contact detonation created large perforation damage of concrete slabs made of normal and high strength concrete even with strong reinforcements [21]. To prevent perforation damage and to increase the capability of concrete slab to resist contact detonation, in this study, steel wire mesh is proposed as additional reinforcements to concrete slab to resist blast loads. In the matrix formed by high strength self-compacting concrete, steel wire meshes as well as the conventional steel reinforcement are embedded and serve as reinforcement. At the concrete cover layers, to improve the tensile crack resistance under both service load and dynamic load, micro steel fibres are mixed into the concrete matrix. Numerical model based on a combined FE and SPH method is developed, and the contact detonation and fragmentation process are modelled. In the field test, contact explosion on the slab is carried out and the detonation and fragmentation process are captured by the high speed camera. Through image processing, the fragments velocities are identified, and the results are compared with the numerical predictions. 2. Material characteristics and experimental investigation 2.1. Steel wire mesh reinforcement In recent decades, high strength self-compacting concrete such as ultra-high performance concrete is under fast development. These concrete materials are known for their high strength, high ductility and high durability. They allow construction of sustainable and economic buildings with extraordinary slim design. However, when designing steel reinforcement for ultra-high performance concrete component, high strength steel rebar is sought after in order to achieve a balanced cross section design. This may inevitably increase the material cost, and conventional reinforcement does not fully exploit the workability of self-compacting concrete. As an alternative to conventional steel rebar, steel wire mesh is prefabricated with welded grid consisting of a series of parallel longitudinal and cross wires with accurate spacing. Comparing with conventional reinforcement, steel wire mesh reinforced concrete (usually self-compacting concrete) enables a wide range of structural shapes with “programmable” performance, and its mechanical properties and physical properties can be adjusted through changing the steel grade and volume fraction. El Debs and Naaman [27] studied bending behaviour of mortar reinforced with steel meshes and polymeric fibres, and they concluded that this combination can satisfy the ultimate strength limit state through the steel mesh reinforcement (main reinforcement) and to control cracking under service loads through fibre reinforcement (secondary reinforcement). As observed in experimental work conducted by Dancygier and Yankelevsky [28], concrete with steel wire mesh reinforcement developed localized membrane effect when subjected to

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impact load and showed good scabbing resistance. Although steel wire mesh reinforcement technology showed some good potentials in structural engineering, the study of utilizing it against blast load especially contact explosions is not found in the open literature yet. 2.2. Material characteristics and experimental investigation The primary objective of the current study is to increase the ductility of structures made of the high-performance self-compacting concrete matrix by adding the micro steel fibres as well as steel wire mesh reinforcements. A key characteristic of the proposed slab design is a significantly increased performance in the energy absorption (material ductility) in comparison to the slab made of standard concretes and other high performance concretes. During the construction of the steel wire mesh reinforced selfcompacting concrete, the liquid self-compacting mortar is poured into a form with designed steel wire mesh. Due to the high flowability of the self-compacting mortar, no vibration and compaction plus levelling of the surface is required. According to static uniaxial compressive tests, the self-compacting mortar itself has a compressive strength of 60 MPa. The steel wire mesh reinforcement is realized by using a number of steel wire mesh layers. As shown in Fig. 1, the mesh grid size is 6.35 × 6.35 mm and the wire diameter is 1 mm. Steel wire mesh was fabricated using 304 stainless steel with tensile strength 500 MPa. The ultimate strain of the steel is 0.15. To investigate the tensile performance and ductility of concrete components after steel wire mesh reinforcement, beam samples with three different steel wire mesh reinforcement, i.e. 10 layers, 20 layers and 30 layers were studied under static four-point bending tests. As shown in Fig. 2a, the samples had a dimension of 400 × 100 × 100 mm with a protective layer of 10 mm thickness on both compressive and tensile surfaces. The steel wire meshes were evenly placed in the beam. No other reinforcement besides the steel wire meshes is provided to the beam. The spacing between the loading points was set to be 1/3 of the clear (outer) span. Within the loading points, no shear acted and the specimens were solely subjected to bending moments in between the loading points. The displacement of the beam element was measured at the centre of the free span with a Linear Variable Differential Transformer (LVDT) device. Fig. 2b–d shows the failure modes of the tested beams. As can be noted beams with high degree of reinforcement (20 layers and 30 layers) did not fail in the intended flexural mode but by shearing. The increment in the beam flexural stiffness outweighed the shear capacity increment, and therefore the beams' failure became shear critical. It can also be seen from Fig. 2e that the beam with 10 layers of steel wire mesh

Fig. 1. Steel wire mesh reinforcement.

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J. Li et al. / Materials and Design 116 (2017) 77–91 Displacement controlled loading

(a) Beam cross seection with 10 layers of steel wire meshes and four-point bending test setup

(b) Beam with 10 layers of steel wire mesh

(c) Beam with 200 layers of steel wire mesh (d) Beam with 30 layers oof steel wire mesh

(e) Force versus mid-span deflection curves Fig. 2. Four-point bending tests on beam samples.

reinforcement showed enormous plastic deformation. After reaching the elastic limit in the bending mode, the beam developed multiple cracks and deformed further before failure. On the other hand, heavily reinforced beams (20 and 30 layers of steel wire mesh) failed at significantly lower deflections. Both of them failed at lower external forces than the beam with 10 layers of steel wire mesh. In Fig. 2e, obvious drop in the load can be observed when the mid-span deflection reached 2.5 mm and 6 mm corresponding to the shear damage. The non-ductile shear failure did not take full advantage of the element flexural capacity. The above observations indicate that providing more layers of steel wire mesh might have adverse effect. It may result in reductions in both the load-carrying capacity and ductility. Similar observations were also made by other researchers based on experiments on

commercially available steel wire mesh reinforced concrete structure. Adding more steel wire meshes change the failure mode of the beam from flexural failure to shear failure. Premature shear failures were observed even on slender concrete beams reinforced with steel wire meshes [29]. These results indicate improvement on the shear capacity of the steel wire mesh reinforced concrete structures is critical for its practical applications. In order to further improve the performance of steel wire mesh reinforced concrete, especially its shear performance, micro steel fibres were mixed into the concrete protective layers in the improved design. There are several benefits that can be expected from this improvement. With addition of the micro steel fibres into the high strength selfcompacting concrete, the composite receives enhanced compressive

J. Li et al. / Materials and Design 116 (2017) 77–91

and tensile strength, good anti-abrasion and energy absorption capacity. Due to the micro bridging effect from the fibre material, after initial cracking, the stress is allowed to transfer from concrete matrix to fibres which significantly reduces the crack propagation [30]. In the present study, to make it possible for adding fibres into the protective layer which usually has a limited thickness, micro fibre with a length of 3 mm and diameter of 0.12 mm was chosen to warrant a random distribution and reduce fibre balling. The fibre tensile strength is 4200 MPa. After mixing with 3 vol.% micro steel fibre, the concrete composite used in the protective layer was tested in uniaxial compressive tests and flexural bending tests, and comparison was made against composite with no fibre addition. As shown in Fig. 3a, an improved compressive strength of 85 MPa was achieved while the sample without fibre addition had strength of around 60 MPa. Importantly, material ductility was improved significantly after fibre addition. From fourpoint bending test (the same dimension as shown in Fig. 2a) results shown in Fig. 3b, it is noted that after fibre addition, flexural strength of the concrete composite reached 14 MPa which is much higher than the conventional high strength self-compacting concrete of which the flexural strength is around 2.5 MPa. With fibre material addition into the protective layer, four-point bending test was carried out again to investigate the flexural tensile performance of a new beam sample. Fig. 4a–c shows the four-point bending test on beam sample with 20 layers of steel wire mesh and fibre addition in the protective layer. On contrary to the previous test result shown in Fig. 2c, the improved material performance resulted in the desired flexural failure of the beam as shown in Fig. 4a–b, and the sample sustained much greater mid-span deflection with excellent crack control. From the force-deflection curve shown in Fig. 4c, it can be straightforwardly calculated that the new composite beam has a flexural tensile strength over 60 MPa, and the energy absorption capacity was more than four times higher than the beam sample made of concrete material without micro fibre strengthening the cover layers.

3. Design of slabs with steel wire mesh reinforcement The above material tests and beam sample tests have proved that high strength self-compacting mortar with steel wire mesh reinforcement and fibre addition in the protective layer achieved high material strength and energy absorption capacity. In this section, design of slabs utilizing this reinforcing method is discussed. As shown in Fig. 5, the dimension of slabs considered is: 2000 mm long, 800 mm wide and 120 mm thick. The diameter of the longitudinal reinforcing rebar and stirrup rebar is 10 mm. Both of these two reinforcements are plain round steel bars with 360 MPa yielding strength. The slab is designed with 20 mm concrete cover which is cast with high strength self-compacting concrete with 3 vol.% fibre addition. The fibre material has a length of 3 mm and diameter of 0.12 mm, and its

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tensile strength is 4200 MPa. The intermediate layer of the slab is reinforced by steel wire mesh. Prior to experimental study, preliminary numerical study is carried out in Hydro-code LS-DYNA, and three different volume fractions of the steel wire mesh are considered, i.e. 2 vol.% (10 layers), 4 vol.% (20 layers) and 6 vol.% (30 layers). The considered blast loading scenario is 1 kg TNT contact detonation. 3.1. Numerical model development In the present study, hybrid FE and SPH method is utilized to simulate the damage and associated fragmentation during the contact detonation. It is widely acknowledged that a key issue with the Lagrangian grid based FE model for blast loading is the incapability of modelling large element deformations, which can cause singular Jacobi matrices, leading to high inaccuracy and ultimately the computational overflow [31]. To overcome this problem, so called “erosion algorithm” is widely adopted and elements are eroded when user-defined failure criterion is reached. This method is easy to be used, but lacks physical background as it violates mass conservation, and the criterion must be carefully defined to minimise such influence as premature deletion of elements in the simulations. To better address this problem, numerical methods including interfacial element method and meshfree methods have been developed. One of the most widely used meshless methods is the Smooth Particle Hydrodynamics (SPH) method. Conventional SPH method requires intensive computational effort and therefore it is usually used in conjunction with FE method. There are several benefits from this combination. Firstly, due to its Lagrangian formulation, SPH nodes can be straightforwardly linked to standard finite element. Secondly, SPH method allows tracking of material deformation and the time varying behaviour. Complex material models that are used in traditional FE model can still be allocated to SPH model. Last but not least, this method allows tracking of blast induced fragments formation. In a previous study, Johnson and Stryk proposed a method to resolve the FE mesh distortion problem using coupled SPH and FE method. This method simply converts highly distorted elements into meshless particles during the dynamic response simulation [32]. This approach is suitable for problems involving severe localized distortion such as contact detonation induced structural response, as in such cases effect of the distorted elements to the remaining structure may be rather significant, and with a particle conversion and the associated contact algorithms such an effect could be well preserved [33]. Adopting this hybrid method, numerical model in the current study is shown in Fig. 6a. Concrete material is modelled with solid element while steel wire mesh and steel reinforcement are modelled with beam element. The TNT explosive is modelled with SPH particles. Contact detonation induces localized structural response and damage. To save computational effort, refined mesh size of 5 mm is used in the

Fig. 3. Static performance of concrete composite with fibre addition.

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J. Li et al. / Materials and Design 116 (2017) 77–91

(a)

(b)

Cover layer with fibre bridging n

(c)

Fig. 4. Four-point bending tests on 20 layers steel wire mesh reinforced samples with and without fibre addition.

centre part of the slab (0.5 m in width direction × 0.6 m in length direction) while a coarse mesh size of 10 mm is used for the remaining part. Steel wire mesh is explicitly modelled in the refined mesh zone. Mesh size in the current study is determined based on convergence test. As shown in Fig. 6b, simulation of slab with 2 vol.% (10 layers) steel wire mesh under 1 kg TNT contact detonation is carried out with three mesh size for the central part of the slab, i.e. 10 mm, 5 mm and 2.5 mm. As shown the central nodal acceleration converges with a decreasing element size, however, 2.5 mm element size requires enormous computational resources and time. When modelling the slab with 6 vol.% (30 layers) steel wire mesh with the 2.5 mm mesh size, the computer memory and calculation are beyond the current computer power (workstation with 4 core 3.0 GHz processor and 16 g memory). In this study, mesh size of 5 mm is adopted. At both ends of the slab, nodes within

100 mm from the free edge are constrained to achieve a fully fixed boundary in the simulation. To explicitly model the fragmentation process, the method discussed by Johnson and Stryk is adopted, and solid elements with large distortion is converted into meshless particles in the numerical simulation. These particles carry velocity and mass of original element, and they are defined with the same material properties. This algorithm does not violate the mass conservation, and can simulate the fragmentation process. Table 1 summarises the material models adopted in the present study. Elastic-Plastic-Hydrodynamic model is adopted by the authors [34–36] and Wang et al. [37] to describe the material behaviour of steel fibre reinforced concrete, and reasonable correlation between the numerical results with blast tests were found in the analysis.

Cross section A-A of reinforced slab

Fig. 5. Dimension and reinforcement of slabs considered in the study.

J. Li et al. / Materials and Design 116 (2017) 77–91

(a)

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(b) 10 layers of steel wire mesh

1 kg contact explosive

Fig. 6. Numerical model and convergence test results.

To use the Material Elastic_Plastic_Hydrodynamic, an Equation of State (EOS) is required. In the present study, the Gruneisen EOS is adopted. With cubic shock velocity-particle velocity, the Gruneisen equation of state defines pressure for compressed material as: h
γ  a i ρ0 C 2 μ 1 þ 1− 0 μ− μ 2 2 2 p¼h i2 þ ðγ0 þ aμ ÞE 3 μ2 −S3 μ 2 1−ðS1 −1Þμ−S2 μþ1

ð1Þ 3.2. Numerical simulation results

ðμþ1Þ

and for an expanded material as: p ¼ ρ0 C 2 μ þ ðγ 0 þ aμ ÞE

ð2Þ

where C is the intercept of the Vs–Vp (shock velocity versus particle velocity) curve, E is the specific internal energy. S1, S2 and S3 are the coefficients of the slope of the Vs–Vp curve, and since the relationship of the shock wave velocity and particle velocity is often linear, only S1 is considered in the present study; γ0 is the Gruneisen gamma; a is the first order volume correction to γ0; and μ = ρ/ρ0 − 1. In addition, a widely adopted Jones–Wilkens–Lee (JWL) EOS model for TNT explosive is used in the present study to model the detonation process. JWL EOS models the pressure generated by chemical energy in an explosive. It can be written in the following form.     ω ω ωE e−r1 V þ B 1− e−r2 V þ p ¼ A 1− r1 V r2 V V

The parameters in the EOS used in the present study are shown in Table 2. Strain rate effect is considered in the present study for both concrete material and steel material. Dynamic Increase Factor (DIF) for the concrete compressive and tensile strength are defined according to [41], and that for steel is defined according to [42].

ð3Þ

The values of the constants A, r1, B, r2 and ω for many common explosives have been determined from dynamic experiments. These values should be considered as a set of interdependent parameters. The parameters in JWL equation of state for TNT used in the present study are listed in Table 2 [38], in which E0 is initial C–J (Chapman– Jouguet) energy per volume as the total chemical energy of TNT.

Figs. 7–9 show the damage of slabs with different steel wire mesh reinforcement. When slab is reinforced by 2 vol.% (10 layers) steel wire mesh, severe concrete cratering and spalling can be observed on proximal and distal surface, respectively. Due to the fracture of all the steel wire meshes, slab perforation failure occurs. The steel reinforcement at slab mid-span also experiences significant deformation. With increment of the steel wire mesh to 4 vol.% (20 layers), the concrete crater and spall areas are smaller than the 2 vol.% (10 layers) steel wire mesh reinforced slab, no slab perforation is observed due to the bridging effect from steel wire mesh. With 6 vol.% (30 layers) steel wire mesh, the slab damage is further reduced, no perforation occurs, and close examination shows only the outmost layers of the steel wire meshes experience fracture. Effect of steel wire mesh on confining the concrete damage is shown in Fig. 7c, Fig. 8c and Fig. 9c. It is observed from Fig. 7c that when 2 vol.% (10 layers) steel mesh is used, the area of steel wire mesh engaged in resisting blast load is limited, all layers of the steel meshes experience fracture and large deformation occurs on steel reinforcement. With the increase of the steel wire mesh volume percentage, tensile membrane effect takes place and more obvious confining effect can be observed. Localized tensile membrane action develops in the steel wire mesh reinforced panels at large deflections caused by contact detonation. It is a self-equilibrating mechanism comprising a tensile net in the central region surrounded by a peripheral compressive ring of

Table 1 Material model in the numerical simulation. Material

Material model

Input values

Magnitude

Cover layer fibre reinforced concrete Core concrete in refined mesh zone Core concrete in coarse mesh zone

Mat_Elastic_Plastic_Hydrodynamic Mat_Concrete_damage_REL3 Mat_Pseudo_Tensor

Steel reinforcement

Piecewise_linear_plasticity

Steel wire mesh TNT explosive

Piecewise_linear_plasticity Mat_High_Explosive_Burn

Tabulated compressive stress strain curve as shown in Fig. 3a Uniaxial compressive strength Uniaxial compressive strength for concrete and volume fraction for mesh reinforcement Mass density Elastic modulus Poisson's ratio Yield stress Failure plastic strain Same with steel reinforcement but with 500 MPa yield strength Material density Detonation velocity C–J pressure

60 MPa 60 MPa/2%, 4%, 6% reinforcement ratio 7800 kg/m3 2.00E + 11 0.3 360 MPa 0.15 500 MPa 1630 kg/m3 6900 m/s 2.1E + 10 Pa

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Table 2 Parameters for the equation of state. EOS_Gruneisen [39]

C0 S1 γ0

2600 1.4 2

EOS_JWL [38,40]

A B r1 r2 ω E0

3.71E + 11 3.23E + 9 4.15 0.95 0.3 7E + 9

concrete. Tensile membrane action is not a common phenomenon and only occurs in severe conditions such as explosion, and this mechanism is able to provide alternate load path in mitigating blast effects. The engagement of more steel wire mesh effectively transfers the blast energy into the elastic and plastic strain energy of the steel meshes, and therefore less concrete damage occurs. Besides consuming blast energy due to steel mesh fracturing, the close-spaced steel wire meshes and rebars also provide shock reflections and shock wave interference that effectively reduce the blast energy propagating within the slab, leading to reduced damage. The slab central part consists of the steel wire meshes experiences the most significant deformation and damage under the contact blast loads. The following plots illustrate the energy evolution with respect to time for the steel wire meshes in the three slabs. For the internal energy, it is indicating that increasing steel wire mesh reinforcement results in an increase of the internal energy of steel wire meshes (Fig. 10). Unlike the other two cases, the kinetic energy of 2 vol.% steel wire meshes does not drop to zero, and this is because in this case the fractured steel wire meshes preserve certain amount of kinetic energy as shown in Fig. 7c. In the slabs with 4 vol.% and 6 vol.% steel wire meshes reinforcement, the kinetic energy drops back to zero as the movement of steel wire meshes stops soon after the blast loads. It is worth noting that the deceleration of the movement in 6 vol.% steel wire meshes is higher than 4 vol.% steel wire meshes. Due to the fact that steel wire meshes are only explicitly modelled in the central region of the slab, the energy evolution plot cannot serve as an indication of the energy

26 cm dimeter crater

absorbed by the steel wire meshed. However, it can be used to indicate the sensitivity of the internal energy absorption to the steel wire mesh volume fraction changes in each design case. Fragmentation process is simulated for the slab with 6 vol.% (30 layers) steel wire mesh reinforcement. As shown in Fig. 11, failed elements transform into SPH particles and fly with high velocity. These SPH particles inherit all the properties of the Lagrangian element, e.g. mass, constitutive relations and kinetic variables. In the present model set-up, mass of each failed element is 0.35 g, depending on the SPH particle size, which is a shortcoming of particle method in simulating fragmentation process of structures because the fragment size and shape depend on the predefined particles. However, the approach does not erode away elements therefore the mass and energy conservation are maintained. The maximum horizontal velocity of the fragment in the simulation is measured to be around 600 m/s. It should be pointed out that, due to the missing of the air domain and inaccurate prediction of the fragment shape, the air drag force which is related to the particle shape and velocity is not modelled in the present study, and this leads to an over prediction of the fragment velocity. 4. Experimental study of slab with steel wire mesh reinforcement In the experimental verification, slab with dimension as shown in Fig. 5 was cast with 6 vol.% (30 layers) steel wire mesh reinforcement. Apparatus used in the contact explosion are shown in Fig. 12. Bolting clamping system was used to stabilize the slab during the test. Besides direct compressive failure in the proximal surface beneath the charge, contact detonation also induces three-dimensional shock wave propagation within the slab. Upon reaching the boundaries where shock impedance mismatch exists, e.g. the distal slab surface, side surface in the free edge and the fixed end, and also the steel wire meshes and rebar, shock wave reflects and interacts with the upcoming wave. Material spallation occurs if the net stress magnitude is larger than the material dynamic tensile strength. In the present study, major damage is anticipated to be directly beneath the contact explosion including both material crush and spallation. After the slab was firmly clamped, the whole system was elevated and stabilized into the vertical position as shown in Fig. 13, and both

45 cm dimeter spall

Slab t=10 ms

Area of steel wire mesh engaged in resisting blast load

Steel wire mesh t=10 ms

(a) top view t=10 ms

(b) bottom view t=10 ms

(c) side view

Fig. 7. Slab with 2 vol.% (10 layers) steel wire mesh reinforcement.

J. Li et al. / Materials and Design 116 (2017) 77–91

22 cm dimeter crater

38 cm dim meter spall

85

Slab t=10 ms

Area of steel wire mesh engaged in resisting blast load

Steel wire mesh t=10 ms

(a) top view t=10ms

(b) bottom view t=10 ms

(c) side view

Fig. 8. Slab with 4 vol.% (20 layers) steel wire mesh reinforcement.

sides of the slab were painted with different colours. According to the original plan, fragments after the test would be collected and grouped according to the projectile distance and colour, however, due to the site limitation including unlevelled sandy ground and bushes, the collection process was not successful. Cylindrical TNT explosive with height of 6 cm and diameter of 12 cm was placed with its end on the centre of the slab. High speed camera (Photron SZ) was used to record the fragmentation process, and the frame rate was set to 10,000 fps (frames per second), and the data was post-analysed through Photron Fastcam Analysis (PFA) software.

In the test, the supporting frame was covered with dark green canvas cloth, and the gap between the slab and canvas cover was carefully sealed. The setup was to prevent overexposure in the high speed camera image. Upon detonation, fire with strong light could cause overexposure that made the image in the high speed camera too bright to be analysed. As shown in Fig. 13, the camera was placed 30 m away from the slab centre with shooting angle parallel to the slab surface. The TNT explosive was electrically initiated through a detonator. The detonator was bonded in the core of the TNT explosive through pre-drilled hole as shown in Fig. 13. The detonation point is of key

36 cm dimeter spall

a 19 cm dimeter crater

Slab t=10 ms Area of steel wire mesh engaged in i resisting blast load

Steel wire mesh t=10 ms

(a) top view t=10ms

(b) bottom view t=10 ms

(c) side view

Fig. 9. Slab with 6 vol.% (30 layers) steel wire mesh reinforcement.

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Fig. 10. Energy evolution in slabs with varying steel wire mesh reinforcement.

importance in directing the explosive wave, and this experimental setup is consistent with the previous numerical investigation in which the detonation was initiated in the core of the TNT. The explosive in the detonator is Hexogen (RDX) with TNT equivalence of 1.58. One detonator contains 0.4–0.6 g RDX with NEQ (net explosive quantity) less than 1 g TNT per detonator. Comparing with the explosive charge weights used in the current test, the effects from the detonator is deemed not prominent and can be neglected. The energy releasing process of a high explosive detonation is almost instantaneous. To determine the parameters of explosive loading, a system of differential equations describing the conservation laws of mass, momentum and energy as well as material equation of state under high pressure need to be solved using numerical integration techniques [43] and specialized computer programs, e.g. LS-DYNA, AUTODYN, SAP and SHARC. Simplified engineering-level relationships for explosive loads [44] hypothesized that detonation is an instantaneous process where the

volume, initially occupied by the condensed matter, is filled instantaneously by hot, highly compressed detonation product gases. The mean detonation pressure within the charge can be determined as P0 ¼

ρ0 D20 2ðk þ 1Þ

ð4Þ

where ρ0 is the density of explosive; D0 is detonation velocity; k is the polytropic exponent of the detonation products. The polytropic exponent typically used is k ≈ 3. The exact value of k lies within the range of 2.54 ≤ k ≤ 3, depending on the kind of explosive. In contact detonation case, the pressure acting on the structure equals to the mean detonation pressure, which in this case is as high as 9 GPa. Under such high explosive loads, concrete in contact with the explosive failed under compression as shown in Fig. 14a. The remaining portion of the explosive energy continued propagating in the structure in the form of stress wave causing localized structural

Fig. 11. Concrete fragment simulation and velocity prediction.

J. Li et al. / Materials and Design 116 (2017) 77–91

Fig. 12. Supporting frame.

response, upon deformation, steel wire mesh developed localized tensile membrane action which enhanced the local blast resistance. In the present experiment, despite the stress wave propagation was partially mitigated by the close-spaced steel wire mesh, the remaining stress wave continued propagating within the slab and caused the concrete spallation in the distal surface as shown in Fig. 14b. Fracture of steel wire mesh on both surfaces was also observed in the test. The spall diameter on the distal surface was 40 cm which was slightly larger than that predicted by the numerical simulation shown in Fig. 9b. The steel wire mesh fracture on the distal surface was not well predicted by the numerical simulation. This could be because the simulation time is insufficient. The simulation stops at 10 ms, which well captures the forced response phase of the slab but not the free-vibration phase, because it is extremely time consuming to perform such simulations. Primary damages at the centre of the slab caused by direct contact explosion are captured by the simulation because they occur quickly in the 10 ms duration. Free vibration might cause further damage on steel wire mesh. Another reason is the insufficient confinement from the steel reinforcement owing to the poor workmanship in casting the test specimen. Fig. 9b and Fig. 9c show that the excessive deformation of steel wire mesh on the distal surface is restrained by the longitudinal and stirrup steel rebar. Nevertheless, as can be noted from Fig. 14, due to inadequate workmanship, the stirrup reinforcement shifted 12 cm and 7 cm from the designated location on the proximal and distal

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surface, respectively. The missing of the stirrup reinforcement had a direct influence on the steel wire mesh deformation. Contact detonation induces highly localized damage and response, and the dislocation of the steel reinforcement made the passive confinement of steel wire mesh less effective and therefore more fractures were observed. In addition, in the numerical simulation, failed concrete elements are transformed into SPH particles, and these SPH particles inherit all the properties of the Lagrangian element, e.g. mass, constitutive relations and kinetic variables. However, due to the limitation of SPH algorithm, they are incapable of transmitting the tensile stress wave caused by impedance mismatch at material boundaries (between steel wire mesh and concrete, steel rebar and concrete) afterwards. This may lead to underestimation of the responses. Under contact detonation, steel wire mesh reinforced concrete slab with steel fibre in the concrete cover area performs better than normal strength concrete and ultra-high performance concrete as presented in the previous study [21,34]. Fig. 15 shows the comparison of slab damage after an identical 1 kg TNT contact detonation. Both the normal strength concrete slab (Fig. 14a–b) and ultra-high performance concrete slab (Fig. 15c–d) have the same dimension as the present slab shown in Fig. 14. It is clearly observed that perforation failure occurred on both normal strength concrete slab and ultra-high performance concrete slab. In addition, the crater and spall area on these two slabs are larger than those on the steel wire mesh reinforced concrete slab presented in the current study. The improvement mainly comes from the following aspects. Firstly, during the wave propagation in the steel wire mesh reinforced slab, due to shock impedance mismatch at the material boundaries (steel wire mesh/concrete, steel rebar/concrete), the closely spaced steel wire meshes effectively dispersed the stress wave which in turn retarded wave propagation. Secondly, kinetic energy of particle movement was transferred to slab deformation and fracture of steel wire mesh absorbed energy leading to reduced damage. Finally, when local large deformation occurred, the tensile membrane effect from multilayers of the steel wire mesh increased the scab and spall resistance. Fig. 16 shows the high speed camera images which were obtained with the PFA software by Photron. A thin and very light layer of aluminium foil was placed 10 m in front of the test slab. This setup was aiming at monitoring the arrival time for calculation of the propagation speed of the shock wave. Upon interacting with the shock front, aluminium foil which is thin and light would deform and reflect light into the camera so that the arrival time can be determined. Close examination of the video footage indicates a transparent shock front with compressed air layer interacted with the aluminium foil at 14.2 ms after detonation. The shock front velocity is therefore determined as 704 m/s.

Camera shield Cylindrical explosive

Diameter 12 cm m Height 6 cm

(a) Frame with canvas cover

(b) 1 kg TNT

(c) Photron SZ

Fig. 13. Test setup and high speed camera.

(d) Slab ready for test

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Misplaced Stirrup

Misplaced Stirrup

7 cm

12 cm

(a) Top surface crater diameter 20 cm

(b) Bottom surface spall diameter 40 cm

Fig. 14. Steel wire mesh reinforced concrete slab after detonation.

Upon detonation, the slab was engulfed firstly by the strong light followed by fireball, and the fire lasted around 50 ms. TNT has the fuel and oxidizer built in, when TNT explodes 2CH3 C6 H2 ðNO2 Þ3 ðsÞ→3 N2 ðgÞ þ 5H2 OðgÞ þ 7COðgÞ þ 7CðsÞ

ð5Þ

It is seen that the products include lots of gases, and it is incomplete combustion as CO is formed rather than CO2, unburnt carbon forms the black cloud which is clearly seen in the figure. The analysis on concrete fragment velocity is a complex problem as it involves many uncertainties. In a previous report [15], based on field tests, one empirical method was proposed. The following equation can

be used to estimate the ejection velocity of the concrete fragments in a blast scenario. V fragment ¼ Am eðBmRÞ

ð6Þ 2

Am ¼ 5:41 þ 1:79  ½ ln ðMÞ þ 0:049  ð½ ln ðMÞÞ M = mass of :304 Bm ¼ 0:053  M − 0 the fragment in grams R = range in meters from the centre of the detonation to the fragments found in field. Given the fragment flying distance and weight are known, the above equation can give crude estimation on the initial velocity of the fragment. where

(a) Top surface crater diameter 44cm

(b) Bottom surface spall diameter 80 cm

(c) Top surface crater diameter 25cm

(d) Bottomsurface spall diameter 45 cm

Fig. 15. Response to 1 kg contact explosion (a–b) normal strength concrete slab, (c–d) ultra-high performance concrete slab [21].

J. Li et al. / Materials and Design 116 (2017) 77–91

Fig. 16. Blast test recorded in high speed camera.

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However, it is noted that, the fragment generated in blast scenario can distribute in a wide range with a diameter of several hundred meters, the collecting process could be very time and resource consuming. In the present study, the particle based numerical approach provides an alternative to estimate the ejecting velocity of the debris, and its feasibility is validated through comparison with the high speed camera results from the field. As shown in Fig. 17a, concrete fragments started to become visible in the camera from 8 ms. Through the image analysis in PFA software, the fragments can be identified and tracked. For instance, the speed of the fragment which is located 1.2 m away from the slab as shown in the Fig. 16a is calculated as 120 m/s. The length of the fragment can be approximately determined from the recorded images in test as 20 mm, and this size equals to four finite elements in the numerical model. Based on this assumption, four adjacent elements in the same location in the numerical model are selected and their velocities are plotted in Fig. 17b, and it is noted that numerical prediction yields a fragment velocity around 145 m/s (averaged from the four adjacent fragments) which is higher than the test observation. As discussed above, numerical simulation does not consider the air drag force which is related to the fragment shape and velocity, therefore it will overestimate the actual fragment velocity. 5. Conclusions and discussions In the present study, a novel design of steel wire mesh reinforced concrete slab is proposed. Although high strength concrete contributes

to the enhanced resistance against dynamic compressive loads, it is prone to fail in a more brittle manner than conventional concrete. In addition, to achieve a balanced cross-section design i.e. concrete crushes at the same time when tensile rebar yields, high strength steel rebar is required to work together with high strength concrete. To overcome the material brittleness and reduce the material cost, in the present study, steel wire mesh is used as additional reinforcement in high strength self-compacting concrete slab and steel fibres are mixed into concrete and applied to the cover layer to provide micro bridging effect. Static test results showed promising mechanical properties of this novel design. Considering different volume fractions of the steel wire mesh, numerical simulation of slabs under contact detonations is carried out and the results are validated with the field blast tests. Key findings in the present research include: 1. Steel wire mesh reinforcement provides additional spall and crater resistance due to the localized membrane effect, also closely spaced steel wire mesh effectively reduces the blast wave propagation leading to less perforation and concrete spall. 2. Numerical simulation based on coupled FE and SPH method captures the test observations, and yields reasonably accurate fragment velocity predictions. However, improvement should be made in the future study to include air domain in the numerical study to consider the drag force. In addition, the fragment size prediction should be considered in the numerical simulation process.

Fig. 17. Fragment velocity determination.

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