Passive Control Systems for the Blast Enhancement of Glazing Curtain Walls Under Explosive Loads

2. CURTAIN WALLS

Curtain walls (CW) are largely used in modern practice, due to a multitude of aspects, both in new buildings as well as in the form of re-cladding envelopes for existing structural systems. The typical CW consists of ‘pre-glazed’ units (e.g. manufactured under controlled conditions), that is modular assemblies obtained by connecting metal profiles or steel frameworks with glass panels or other cladding elements (e.g. stainless steel metal panels, insulated spandrels, etc.). Typically spanning from floor to floor, CW modular units are usually attached to the floors by means of special rigid brackets (Fig. 1). Wind and gravity loads, as well as other external pressures, are thus transferred to the building at the level of inter-storey floors.

The method of fabrication and installation of CWs allows classifying this façade typology in ‘stick’ and ‘unitized’ systems. In the first case, the basic modular unit consists of a single glass (or other infill) panel and metal mullions, which is installed on-site piece by piece. Depending on the spacing of columns and the design loads, in the typical stick modular unit the bracing mullions can be spaced from ≈1.2m to ≈1.8m. In ‘unitized’ CWs, conversely, the modular assembly is composed of large units (e.g. more than a single panel). A direct effect deriving from the CWs technology is that stick or unitized CWs can be more or less suitable solutions for large envelopes and building enclosures with modular/repetitive design and/or complex geometries.

2.1. Case Study

In this work, as a reference case study, a modular unit belonging to a stick CW is investigated. In it, four key components are involved, and namely (i) the glass panel, (ii) the supporting frame; (iii) the connection between the glass panel and the frame, as well as (iv) the connection at the interface between the frame restraints and the structural background. The studied façade unit is H= 3m tall and B= 1.20m wide (Fig. 2a). A laminated glass (LG) panel having a total nominal thickness equal to 28.52 mm, e.g. obtained by assembling two 12 mm thick glass lites and a middle 4.52 mm Polyvinyl-Butyral (PVB^®) interlayer, is taken into account. The glass panel is continuously supported along the four edges by means of an aluminum frame (h_m= 135mm, b_m= 70mm, t_h= t_b= 10mm, Fig. (2b)), while the physical interaction between the glass lite and the frame is ensured by a continuous layer of structural sealant (thickness t_joint= 7mm and width h_joint= 21mm). Glazing gaskets are also used to prevent possible rotations and splitting of the sealant joints, so that the original position of the glass panel could be kept fix (e.g. Fig. (2b)). Fully rigid steel brackets provide, finally, a strong restraint between the façade unit and the building, hence ensuring possible local deformations under the effects of high-strain impulsive loads such as explosion.

3.1. Viscoelastic Solid Dampers (VE)

Viscoelastic solid dampers have been largely used in buildings and structural systems (Fig. 3). First applications of VE dampers to structures was in the form of shock absorbers for military and aerospace applications, while successively – due to their intrinsic high damping and flexibility capacities – their application has been extended to buildings and infrastructural systems under seismic, wind or impact vibrations [19-21].

The main advantages of VE dampers are in fact given by (i) activation at very low displacements and incoming impulse, (ii) availability of restoring force and (iii) almost linear mechanical behaviour, thus resulting in simplified design rules and recommendations. Recent applications of VE dampers to glazing systems have been proposed [13, 15], for example, where it was shown through analytical models and FE nonlinear dynamic simulations that VE devices introduced at the points of connection between the glass panels and the metal framework can have multiple benefits on the behavioural trends of the entire system, e.g. mainly deriving from the introduction of additional flexibility and damping capacities. Under well-defined loading conditions (e.g. operating frequency and temperature), the key parameters of a VE device are in fact the damping ratio c_d deriving from the VE compound and the corresponding elastic stiffness k_d ≡ K', where [18]:

(1)

with ω the damper operating frequency, η the loss factor of the VE compound and,

(2)

(3)

the storage and loss stiffnesses respectively, defined as a function of the storage and loss shear moduli G'(ω), G'(ω); the total shear area A_d of the VE layer and its thickness h_d.

Based on Eqs. (1)-(3), once the operating frequency ω and expected loading conditions (e.g. temperature and strain level) are known, a given VE solid damper can be rationally described in the form of a linear dashpot (e.g. c_d) and spring component (e.g. k_d ≡ K'). At the same time, however, careful consideration should be paid in the design of VE dampers, so that (a) possible failure mechanisms, e.g. maximum shear strains γ or deformations s_d,max in the VE layer would not provide tearing in the layer itself (Fig. 3):

(4)

and (b) possible delaminations at the interface between the VE layer and the steel supports could be avoided.

Finally, (c) design rules of general validity should properly consider the moderate sensitivity of the constitutive VE mechanical properties to frequency, as well as temperature conditions. As a result, Finite-Element numerical studies discussed in this work were carried out by taking into account as a reference configuration the operational frequency ω of the studied CW modular unit, under the hypothesis of constant temperature. Since the aim of this research work is to provide a first assessment of the possible structural effects of VE devices introduced in conventional curtain walls, in first approximation, the elastic parameters of the VE system (e.g. Eqs.(1-3)) were calculated as a function of G'(ω), with ω the fundamental pulsation of the curtain wall modular unit (see Section 3.3) and G'(ω) derived from experimental literature works (G'(ω) ≈ 1MPa and η ≈ 0.6 [20, 22]).

The typical viscoelastic (VE) device consists of two metallic plates and a middle VE layer, namely composed of natural rubber. The VE layer is supposed to have a nominal thickness h_d and a square base shape of surface A_d (with l_d the edge size (Table 1) and (Fig. 4). The lower and bottom plates are directly attached to the structural backup (e.g. the reinforced concrete slab) by means of anchoring bolts, whereas the rigid steel bracket supporting the tubular frame is properly constrained by means of inner steel plates enabling possible crushing of the VE layer and rotations of the steel bracket within the device. In this manner, due to the assigned design explosion, the full VE device is able to slide only in the direction perpendicular to the plane of the curtain wall Fig. 4.

3.2. Elasto-Plastic Devices (PL)

Yielding metal dampers able to dissipate the incoming energy due to inelastic deformation of metals are also widely used in civil constructions [23, 24]. Often, these elasto-plastic mechanisms consist in triangular or X-shaped mild steel plates, so that an almost uniform yielding throughout the device could be offered. ADAS (added-damping-and-stiffness) dampers, for example, have been largely used in civil buildings, especially for the vibration control of buildings under earthquake loads. From a practical point of view, the simplest way to mechanically reproduce the mechanical response of ADAS devices is the use of an elasto-plastic bi-linear constitutive behaviour, in accordance with A.S. Whittaker et al., [23], where the key input parameter are the elastic shear stiffness k_d and the shear yielding force V_y,d.

(5)

(6)

In Eqs. (5 and 6), E_s and σ_y,s denote respectively the Young’s modulus of steel and its yielding stress, while t_d and l_d (with b_d,eq = l_d/2) signify the nominal dimensions of the ADAS yielding components (Fig. 5), n is the number of metal plates and

(7)

represents the yielding shear displacement of the ADAS device.

In Fig. (5), a possible ADAS damper for application in CW assemblies is proposed. The device consists of (i) a rigid metal bracket (e.g. representing the connection between the curtain wall mullions and the device), (ii) a well calibrated number n of X-shaped steel components with l_d and t_d nominal dimensions and (iii) a system of anchoring bolts and rigid plates able to provide a fully rigid connection between the ADAS damper and the sub-structure (e.g. the concrete slab).

When subjected to external loads impacting on the CW surface, the CW modular unit transfers a maximum reaction force to the ADAS device. As far as this reaction force does not exceeds the shear yielding force V_y,d of the ADAS damper, the device behaves as a linear elastic support for the CW assembly. Conversely, when subjected to shear loads exceeding V_y,d, the ADAS mechanism is activated and the bracket slides in the direction perpendicular to the façade, hence providing plastic dissipation of the incoming energy. A bottom steel plate rigidly connected to the concrete slab ensures the appropriate position of the bracket when the dissipative mechanisms activates. The same bottom plate provides an appropriate transmission of vertical loads to the structural background.

3.3. Equivalent Dynamic Properties of the Curtain Wall System

To preliminarily estimate the dynamic behavioural trends of the studied curtain wall equipped by four VE or PL devices introduced at the support points of the CW unit, the dynamic parameters (e.g. equivalent elastic stiffness k_tot, damping c_tot and mass M_tot) may be rationally estimated by considering a simplified single-degree-of-freedom (SDOF) analytical model.

Certainly, an accurate analytical calculation of the expected dynamic response for the examined glazing system would require a precise calculation of its equivalent dynamic parameters in both the elastic (e.g. uncracked) and post-cracked stages, due to the typical tensile brittle behaviour of glass plates and almost elasto-plastic constitutive response of the PVB foils. Several studies have been in fact dedicated to the calibration of appropriate transformation coefficients able to take into account – throughout the full dynamic response of a glass panel system – the actual mechanical behaviour of each component [30, 31], so that simplified but accurate dynamic calculations could be developed in accordance with classical theories of structural dynamics [32]. As a result, the formulations here provided are intended for the estimation of the fundamental period of vibration T* only for CW assemblies with fully elastic behaviour. This assumption is rationally justified by the aim of this research contribution, since it is expected that the proposed VE or PL dampers could avoid the development of possible damage mechanisms in the CW assembly components (e.g. glass cracking, interlayer yielding and tearing, frame damage, etc.).

In accordance with the schematic CW modular unit depicted in (Fig. 6) it is in fact expected that – due to the additional VE or PL dissipative dampers – the glazing system would behave as a structural assembly in which:

• M_tot is the equivalent mass, e.g. namely represented by the mass of the glass panel (M_glass), the interlayer (M_int) and the supporting metal frame (M_frame):

(8)

• k_tot represents the elastic stiffness deriving from the VE or PL devices themselves (e.g. assuming a fully rigid continuous support provided by the bracing frame to the glass panel edges):

(9)

where k_d is given by Eqs.(2) or (5), for VE and PL devices respectively;

• c_tot is the total damping of the CW modular unit, and should be properly calculated. Possible damping contributions could in fact derive from material (e.g. the PVB foils bonding together the glass plies, c_int), aeroelastic phenomena (c_air) and dissipation mechanisms deriving from the proposed devices (c_d):

(10)

In Eq. (10), specifically, c_d is given by Eq. (1) in presence of VE devices (c_d for the CW assembly with PL dampers). The aeroelastic, structural and material damping contributions, at the same time, are preliminary neglected. Scarce experimental studies are in fact available in literature for an appropriate assessment of the damping capacities of laminated glass panels and CWs under blast loads. In any case, such data are often in the order of 1-2% [33-37].

In conclusion, once the equivalent mass M_tot and stiffness k_tot of the CW unit are calculated by means of Eqs. (8) and (9), its fundamental period of vibration is given by:

(11)

Based on Eq. (11), it can be noticed that as far as the flexibility provided by devices increases, the fundamental period of the assembled system increases, hence requiring an appropriate calibration of the proposed devices.

In order to assess the accuracy of Eq. (11), extended analytical calculations were carried out on the CW assembly of Fig. (2), by taking into account a wide set of supports stiffnesses k_tot.

The elastic stiffness k_tot, specifically, was expressed in the form of the non-dimensional ratio:

(12)

with,

(13)

representing the bending stiffness of a single tubular mullion, E_a the Young’s modulus of aluminum and h_m, b_m, t_m, t_b its nominal dimensions (Fig. 2b), with H the total CW span (Fig. 2a).

The so calculated vibration periods T* (with 0 < R_K < 10) are collected in (Fig. 7a), and compared with the corresponding T_FE values. These latter fundamental periods of vibration T_FE, in particular, were obtained by means of FE frequency analyses carried out in ABAQUS/Standard, on FE models representative of the CW unit of Fig. (2), assembled and calibrated as discussed in Section 4.3. In the same (Fig. 7a), T₀= 0.0511s represents the fundamental period of the CW modular unit with fully rigid supports (ABAQUS/Standard).

As shown, a rather good agreement was generally found between calculations given by Eq.(11) and the corresponding FE estimations. Parametric calculations highlighted, for the studied CW assembly, that as far as the frame supports behave as rigid restraints (e.g. R_K > ≈5), the fundamental modal shape of the glazing system does not modify and is almost coincident with the deformed configuration of a pinned-pinned beam (e.g. blue-to-red contour plot of (Fig. 7a) (ABAQUS/Standard)). For the same range of stiffness ratios R_K > ≈5, small variations can be seen in terms of the reference vibration period T_o Fig. 7b.

For lower R_K ratios (R_K < ≈5), conversely, the CW assembly almost behaves as a rigid body on flexible supports and T₀ further increases, in accordance with the exponential law provided in Fig. (7b).

The close agreement between analytical estimations given by Eq.(11) was then further assessed by means of frequency modal analyses carried out in ABAQUS on additional CW modular units. In this latter case, in order to emphasize the general validity of Eq. (11), variation of the R_K ratio was taken into account (with 0 < R_K < 10) for several CW modular units. The difference between these latter CW assemblies and the case study of Fig. (2) was represented by (i) the tubular section of the frame elements (t_h= t_b= 6mm, 8mm, 15mm, 20mm; h_m= 100mm, 150mm), (ii) the thickness of the glass panels (10mm, 15mm, 19mm), (iii) the overall BxH dimensions of the CW unit (H= 2.5m, 3.5m; B= 1.5m, 1.8m). The so obtained comparisons are collected in Fig. (7c).

4.1. General Numerical Approach

Nonlinear dynamic Finite-Element numerical simulations were then carried out on the examined façade modular unit, by taking into account several possible applications of VE or PL devices, as well as various blast loading scenarios.

Tables 1 and 2 summarize a selection of the main input parameters considered throughout the performed exploratory numerical investigations.

4.2. Air Blast Loading Scenarios

In order to assess the dynamic behaviour of the studied façade module to impact pressures of various intensities, as well as the structural efficiency of VE or PL devices, several air blast loading scenarios were taken into account. Although the pressure wave impacting on a building depends on several parameters (e.g. the equivalent mass M_TNT of explosive, the stand-off distance H_TNT of the explosive from the building, etc.), the corresponding time-pressure waves can be idealized by means of approximating fitting curves.

In this work, explosive air blast waves corresponding to the free field detonations of 150kg, 75kg and 25kg respectively – at a stand-off distance of 30m from the CW surface – were taken into account. (Fig. 8) shows the corresponding pressure-time idealized curves, with BLAST-150, BLAST-75 and BLAST-25 denoting the respective M_TNT charges. The positive phase is calculated in accordance with the semi-empirical modified Friedlander equation [38, 39]:

(14)

with

• p_o denoting the maximum peak of reflected pressure
• b the decay parameter, e.g. a coefficient able to describe the rate of decay of the pressure-time curve
• t⁺_d signifying the positive phase duration of the air blast wave

while the negative phase, typically characterized in terms of negative duration t^-_d and under-pressure peak p_o,min, is described in the form of a bi-linear relationship.

4.3. FE-Model Assembly of the Curtain Wall Modular Unit

Careful consideration was paid for a rational assembly and mechanical calibration of each façade unit component, as well as their reciprocal interaction, in order to correctly reproduce the expected dynamic and preserve the computational cost of nonlinear dynamic simulations. First, the modular unit with fully rigid brackets was investigated (M01 model, (Fig. 9). The difference between the so assembled and calibrated M01 model was then given by the introduction, at the point supports of the metal frame, of equivalent springs and dashpots able to reproduce – both in the case of VE or PL devices – the mechanical behaviour of dampers with geometrical and mechanical properties listed in Tables 1 and 2 (detail of Fig. 9).

In accordance with C. Amadio et al., [15], the laminated glass panel was modelled in the form of S4R 4-node type, composite quadrilateral stress/displacement shell elements with reduced integration and large-strain formulation. Five integration points through the thickness of the composite section were taken into account, while the nominal cross section of the panel was considered. This modelling approach, typically characterized by low computational cost compared to fully 3D models, is also in agreement with Larcher et al. [6], where the comparison of FE numerical results obtained from laminated glass layered shell models or 3D solid models showed a close agreement between them, especially in the case of failure of both the glass plies. The supporting frame (e.g. the aluminium mullions and transoms) was then modelled of three-dimensional beam elements (B31), with equivalent cross-sectional properties able to reproduce the actual geometry and inertial contributions of the examined case study (Fig. 2b).

Meshing of the frame was based on beam elements with 50mm of length. In the case of the laminated glass panel, a free meshing technique was used, so that the reference element size l_mesh could be set equal to 50mm along the panels edges, and decreased up to 15mm towards the centre of the panel (e.g. where maximum tensile stresses were expected). In this manner, mechanical connectors able to reproduce the effects of continuous sealant joints were introduced along the panel edges, in the form of node-to-node joints interconnecting each glass edge node and the corresponding mesh node in the metal frame (Fig. 9). These equivalent springs, representative the bead of silicone sealant interposed between the glass panel and the frame, were characterized in terms of in-plane stiffness K_x and K_y (Fig. 9), with K_z = ∞ – in accordance with the discussed simplified modelling assumptions – and fully rigid rotational stiffnesses R_x, R_y. The corresponding in-plane stiffnesses K_x and K_y were calculated by taking into account the influence length of each connector and the mechanical properties of sealants of practical use in practice for structural glass applications (see Section 4.3.1).

Structural, material and aeroelastic damping terms, based on Eq. (10), were fully neglected in this exploratory investigation, so that the main contributions of VE or PL dampers could be emphasized and assessed.

4.3.1. Materials

Regarding the mechanical characterization of materials, both the aluminum and the silicone sealant were described in the form of idealized elasto-plastic constitutive behaviours, by taking into account nominal or experimental parameters available in literature. In the case of aluminum, the Young modulus, Poisson ratio and density were assumed equal to E_a = 70GPa, ν_a= 0.3 and ρ_a= 2700 Kg/m³, respectively, with σ_y,a= 200MPa the yielding stress and σ_u,a= 280MPa the stress at failure [40]. Concerning the structural silicone joints, otherwise, average elastic mechanical properties of sealants of typical use in the practice of glazing systems were considered. An average Young modulus E_joint= 0.7MPa was taken into account, with σ_joint,u = τ_joint,u = 1.2MPa and ε_joint,u =400% the corresponding tensile/shear resistance and ultimate strain [41, 42]. A tensile brittle mechanical damage model was also implemented in the equivalent connectors, so that at the first attainment of the ultimate stress (e.g. σ_joint,max = σ_joint,u) or strain (e.g. ε_joint,max = ε_joint,u) configurations, the single connector could be deactivated and the possible detachment of the glass panel from the tubular frame could be considered.

4.3.1.1. Glass

The tensile brittle behaviour of glass was then taken into account by means of the ‘brittle cracking’ material model available in ABAQUS/Explicit library [16]. In it, a Rankine failure criterion is used for the crack detection and glass is assumed to behave linear elastically until the maximum principal tensile stress exceeds the characteristic tensile strength σ_Rk,g. As input parameters, glass was described as homogeneous, isotropic material with nominal Young modulus (E_g= 70GPa), Poisson ratio (ν_g= 0.23) and density (ρ_g= 2500 Kg/m³) [43]. A fully indefinitely linear elastic behaviour was then considered to characterize the compressive response of glass. This assumption was justified by the typically high compressive resistance of glass (with σ_c,g ≈ 1000MPa the theoretical value [43]), as well as by the specific loading and boundary conditions taken into account in this research work. Careful consideration, conversely, was given to assessment of the characteristic tensile strength. As also discussed in detail by Bedon et al., [44], due to the impulsive nature of explosive loads, strain rate effects should be properly taken into account. A possible tool is represented by the use of magnified nominal characteristic tensile strengths given by production standards. The tensile strength of glass strictly depends in fact on the duration of the applied loads. Under exceptional high-speed loads like explosions, with a typical duration of ≈0.005-0.025 seconds, tensile strengths of glass are generally assumed higher than the corresponding nominal values, due to the increased reference probability of failure. In this paper, in accordance with Bedon et al., [44], the static bending strengths σ_Rk,g of annealed glass (45MPa) was replaced with “dynamic” reference strength of ≈85MPa.

The post-cracked behaviour was then described by means of the “brittle shear” retention model available in ABAQUS/Explicit [16]. Consequently, the cracked shear modulus of glass was estimated in each simulation as a fraction of the uncracked shear modulus G_g:

(15)

For the shear retention factor , being its value dependent on the crack opening strain ( , with before crack initiation and at the complete loss of aggregate interlock), an exponential low was used:

(16)

with the ultimate crack opening strain. The material parameter p, based on earlier calibration [44, 45], was assumed equal to p= 5. The “brittle failure” sub-option was also taken into account in simulations, so that the cracked glass elements were physically removed from the mesh at the attainment of a critical displacement u_ck:

(17)

with G_f,g the glass fracture energy equal to G_f,g= 3J/m² [44, 45].

4.3.1.2. PVB

The mechanical behaviour of PVB foils is also strictly strain-rate and temperature dependent. Differing from the typical non-linear viscoelastic behaviour under low-strain rates, impulsive and high-strain rates are commonly associated to an elasto-plastic mechanical response for PVB-films and high elastic stiffness E_int.

As also highlighted by Bedon et al. [44], based on dynamic test results of literature, a detailed and rigorous description of its constitutive characteristic curve would require the implementation of hyperelastic material laws. X. Zhang et al. [46], for example, the mechanical constitutive response of PVB foils in laminated glass windows under the dynamic impact of wood debris (e.g. for application to automotive products) has been deeply investigated – throughout the full pre-cracked and post-cracked phases –by means of high-strain rate experiments and calibrated FE-numerical models.

In this work, in accordance with the FE mechanical calibration proposed [44], a stress-strain characteristic curve with σ_y,int= 11MPa the yielding strength, ε_u,int= 300% the ultimate strain and E_int= 500MPa the Young modulus was used. For FE-modelling purposes, hardening effects were totally neglected and an idealized elasto-plastic σ-ε relationship was taken into account (with σ_u,int≡ σ_y,int the ultimate strength). Material density and Poisson’s ratio were finally set equal to ρ_int= 1100kg/m³ and ν_int= 0.49, respectively.

Certainly, the full post-cracked dynamic analysis of the examined CW modular unit would require careful assessment of the mechanical modelling assumptions for all the CW components (e.g. characteristic behaviour of materials in the post-cracked stage and, for example, proper description of glass-to-interlayer interaction or possible tearing and delaminations in the post-failure stage). The numerical investigations presented in this paper are based in fact on a fully bonding interaction between glass and PVB layers, up to failure. However, since the purpose of this exploratory research is the development of preliminary recommendations for the implementations of VE or PL dampers able to prevent glass failure, these mechanical modelling assumptions were rationally justified.

4.4. Validation of the FE Modelling Approach and Mechanical Calibration of Devices

Preliminary validation of the general FE modelling approach presented in Section 4.3 was performed by taking into account some experimental and FE numerical data available in literature. Finite-Element numerical simulations can in fact be used to develop parametric investigations, sensitivity studies and design optimizations [47]. In the blast response of a glazing system, however, several mechanical and geometrical aspects can manifest in improper predictions, hence requiring – when possible – the validation towards experimental data. In (Fig. 10), time-displacement predictions are proposed for two laminated glass panels subjected to shock tube experiments performed by Hooper et al. [48] and numerically assessed by M. Larcher et al. [6], together with a past FE investigation proposed [6] and the corresponding ABAQUS/Explicit estimations.

In Fig. (10a), comparisons are proposed for a 3/1.52/3 mm laminated glass panel (1.5 m × 1.2 m the nominal sizes) subjected to 12.8kg of C4-explosive (e.g. 15kg of equivalent TNT) at a distance of 10m. The glass panel was connected by means of a 6mm thick and 20mm wide silicone joint to a rigid frame. (Fig. 10b), otherwise, refers to a laminated glass specimen of identical nominal dimensions and mechanical properties, subjected to 12.8kg of C4-explosive at a distance of 13m. For FE purposes, the corresponding time-pressure waves were calculated in accordance with Section 4.2, and implemented in the corresponding ABAQUS/Explicit models in the form of impulsive distributed pressures.

As shown, close agreement was generally found between test results and corresponding FE predictions, both in terms of uncracked stiffness of the panel and (especially for (Fig. 10a) maximum deflections. Partial overestimation of maximum displacements was conversely found for (Fig. 10b), hence suggesting the rational pre-cracked FE modelling assumptions (e.g. appreciable time-displacement estimations for the initial instants of the dynamic response) but emphasizing the intrinsic possibilities and limitations of FE studies, typically related to the use of simplified layered shell models. Especially in the post-cracked phase, several aspects can markedly affect the obtained test and FE data (e.g. the possible PVB foil tearing after glass cracking, or the failure of the sealant joints along the panel’ edges, etc.).

For both the experiments of (Fig. 10) [48], for example, no tearing of PVB foils was observed after glass cracking, but a joint failure mechanism occurred along the panel’ edges (after a further glass panel rebound, in the case of (Fig. 10b)). Appropriate post-cracked FE simulations should be consequently able to take into account and properly describe a multitude of possible damage scenarios that are not fully included in the current ABAQUS/Explicit models, based on the purpose of this research project (e.g. full prevention of damage and cracking in CW units by means of the proposed VE or PL devices). As also highlighted [6, 48], apart from the mechanical and geometrical calibration of all the FE model components and the FE model assembly (e.g. composite shell elements rather than full 3D solid models, etc.), it should be noticed that large sensitivity of FE results and their agreement with the corresponding experimental data is often given by small variations in the time-pressure waves input parameters (e.g. Eq. (14)).

In order to assess the major effects of VE and PL devices on a typical CW modular unit, however, the validation of FE models collected in (Fig. 10) was considered satisfactory.

Further FE assessment was in fact successively carried out towards the design concept for the VE and PL dampers proposed in (Figs. 4 and 5). In order to verify the mechanical calibration of the VE or PL devices, preliminary FE simulations were in fact carried out in ABAQUS/Explicit on full 3D solid models representative of possible damper prototypes, with geometrical properties, assembly concept and nominal dimensions according to (Figs. 4 and 5) and Tables 1 and 2. Some results are proposed in Fig. (11).

Fig. (11a), specifically, presents the expected deformed configuration for the VE-01 prototype (Table 1), under the action of external pressures acting in the direction perpendicular to the façade surface (mid-span transversal cross-section). The corresponding mechanical response is proposed in the form of shear force vs. in-plane displacements of the device, as obtained respectively from analytical calculations (Eq.(2)) and a FE nonlinear dynamic analysis of the device under an impulsive load (‘Full 3D – dynamic’). The VE device, specifically, was subjected to a pressure-time impulse according to (Fig. 8), with a positive phase duration of 0.07s, acting on the bracket end surface (e.g. to reproduce the reaction force deriving from the frame). The obtained cyclic response was then monitored in the time interval 0 ≤ t ≤ 0.2s. The elastic stiffness of the same full 3D model under linearly increasing, static shear loads is also proposed in (Fig. 11a) (‘Full 3D – static’). (Fig. 11b), similarly, refers to the mechanical response of the PL-01 damper. A distribution of Von Mises stresses in the steel components (blue-to-red contour plot) is proposed, together with a comparison of analytical (Eqs.(6)-(7)) and FE numerical calculations obtained for the full 3D model under an impulsive load (‘Full 3D – dynamic’) or static actions (‘Full 3D – static’).

As for the case of the VE-01 device, a rather close agreement was found between the discussed modelling approaches, hence suggesting the validity of the FE models implemented for the nonlinear dynamic simulations on the CW assemblies (see Section 5).

5.1. High-Level Blast Loading Scenarios

Incremental nonlinear dynamic analyses were carried out first on the M01 and VE / PL models subjected to the BLAST-150 air pressure wave of (Fig. 8). Throughout the dynamic simulations, having a total duration of 0.2s (e.g. ≈2 times the assigned pressure-time wave (Fig. 8) and ≥ 4 the fundamental period of vibration T₀ of the CW modular unit), the impulsive pressure was described in the form of a uniformly distributed, impulsive load.

The main results are proposed in (Figs. 12-14) (in the time range comprised between the impact (t= 0) and t=0.1s) and Tables 3 and 4.

In Fig. (12), specifically, the qualitative distribution of maximum principal stresses in glass is proposed for the first instants of the CW dynamic response (maximum stresses tending from blue to red). The correspondence between these (a)-(g) contour plots is provided in (Fig. 13a). As shown, the assigned blast pressure acts as a moving, impulsive load on the glazed system. The BLAST-150 wave pressure, however, clearly involves maximum effects exceeding the M01 curtain wall capacities. The maximum principal stresses are in fact first located near the glass panel supports (e.g. the metal frame, (Fig. 12a)), but rapidly moves towards the panel centre (Fig. 12b and c), leading to the almost simultaneous failure of both the glass plies at about 0.014s (Fig. 12d-g). After glass cracking (Fig. 13a), the dynamic response of the M01 system largely modifies, being characterized by yielding of the tubular mullions (Fig. 13b), a smaller frequency of vibration of the damaged system and largest relative deflections attained in the cracked panel (Fig. 13c), while the effect of glass cracking can be noticed also in terms of distribution in time of the maximum reaction forces transmitted from the damaged CW unit to the structural background (Fig. 13d). In terms of in-plane behaviour of the sealant joints, the FE studies highlighted an almost linear elastic response under the assigned blast load, and no damage occurred in them (Table 3).

A totally different dynamic response was obtained for the same CW unit equipped by VE or PL dampers. In Figs. (13 and 14) and Tables 3 and 4, additional comparative results are in fact proposed for the M01 module towards the glazing system equipped by some of the VE or PL devices configurations collected ion (Tables 1 and 2). The maximum blast effects on the façade components (e.g. supports, bracing frame, sealant joints) are collected in the form of:

• maximum tensile stress in glass (σ_g,max), and possible cracking
• maximum stresses in the bracing mullions (σ_m,max), and possible yielding
• maximum shear stresses in the sealant joints (τ_joint,max)
• reaction forces transmitted to the structural background (V_d,max). In presence of PL devices, V_d,max is also compared with the yielding force V_y,d of the proposed ADAS dampers (Eq.(6))
• deformation ratio u_max/H, defined as the maximum relative deflection at the centre of the glass panel, as a function of the panel height H
• deformation ratio s_d,max/h_d, signifying the maximum shear strain γ in the VE compound (Fig. 3)
• fundamental period of vibration T_FE of the curtain wall modular unit, as obtained from FE simulations and also in accordance with Eq.(11)

The main advantage of VE devices, as also in agreement with past investigations discussed [15], is given by a double beneficial contribution represented by the additional flexibility they introduce at the support points, as well as their significant damping capacity (Eq.(1)). As far as the stiffness of VE devices decreases, specifically, their damping effect increases and an important reduction of maximum stresses in the whole façade components is expected. On the other hand, careful consideration should be paid in the estimation of the optimal VE key parameters, since a high flexibility would also result in maximum deformations of the VE compound leading the device to failure (Table 3). For the CW object of study, in particular, an interesting beneficial effect was obtained with the VE-01 solution (Table 3), while the VE-02 and VE-03 proposals typically resulted in important mitigation effects, but maximum deformations in the VE layer progressively leading the same VE dampers to failure (Fig. 13e).

Interesting structural effects in the CW components were obtained also in presence of PL devices (Fig. 14 and Table 4). In this latter case, however, particular attention should be dedicated in the design of two key parameters, represented by the elastic stiffness k_d and the shear resistance/sliding force V_y,d.

In order to highlight the effects of both PL stiffness and resistance parameters, in accordance with Table 2, (Fig. 14) shows in fact the different effects obtained in the CW assembly by means of PL devices characterized by variable stiffness k_d (Fig. 14a,c,e) or variable shear resistance V_y,d (Fig. 14b,d,f) respectively, together with the cyclic response of the three examined PL configurations (Fig. 15). Comparisons are proposed in terms of maximum (i) principal stresses in glass, (ii) stresses in the tubular mullions, (iii) relative deflections at the centre of the panel.

As also highlighted in (Table 4), the performed FE studies generally emphasized that ADAS devices can provide beneficial structural effects on the examined CW unit under the BLAST-150 wave pressures.

As in presence of VE devices, due to deformations of the ADAS themselves, the maximum relative deflections in the glass panel are almost half the M01 reference configuration (Fig. 14e and f) and yielding of the tubular mullion is preserved (Fig. 14c and d). In terms of maximum stresses in glass (Fig. 14a and b), the application of PL dampers generally avoided the failure of glass plies, for all the studied configurations. While the maximum stresses in glass resulted almost independent on the ADAS elastic stiffness k_d (Fig. 14a and b and Table 4), however, FE comparisons highlighted the importance of a proper calibration of the shear resistance V_y,d of the same dampers. The design of ADAS devices with high shear resistance V_y,d, compared to the incoming reaction forces, would in fact result in PL dampers behaving as fully rigid restraints, hence leading to maximum stresses in glass almost comparable with the M01 reference configuration.

5.2. Medium/Low Level Blast Loading Scenarios

Final preliminary assessment of the proposed VE and PL devices was made by taking into account impulsive pressures of low/medium intensity. Parametric results obtained for the M01, VE-01 and PL-01 systems under the BLAST-75 pressure wave are compared in (Fig. 16), in the form of maximum principal stresses in glass (Fig. 16a), maximum stresses in the tubular mullions (Fig. 16b), reaction forces transmitted to the structural background (Fig. 16c) and relative displacements at the centre of the panel (Fig. 16d).

Additional comparative calculations are also collected in (Fig. 17), for the same glazing assemblies subjected to the BLAST-75 pressure-time wave, while Table 5 summarizes the main outcomes of BLAST-75 and BLAST-25 loading scenarios.

As expected, as far as the blast wave intensity decreases, the effectiveness of PL-01 dampers vanishes, compared to VE-01 devices, due to the intrinsic mechanical behaviour of VE and PL dampers respectively (Section 3). While VE dampers provide additional damping capacities under dynamic loads affecting the CW unit, independently on their amount, the activation of PL dampers strictly depends on their shear resistance V_y,d. As a result, it can be seen that although the M01 curtain wall modular unit behaves fully elastically under the assigned BLAST-75 and BLAST-25 pressure waves (e.g. fully undamaged glass panels and tubular mullions), the investigated VE-01 and (partially) PL-01 dampers can in any case improve the CW dynamic response, compared to the reference M01 system.

In conclusion, it is clear that the design and optimization of VE or PL dampers should be properly calibrated, based on the CW mechanical properties and the expected loading scenarios. The presented FE parametric studies, however, emphasized the feasibility and potentiality of the proposed passive control system applications, hence suggesting further research developments and detailed validations.