- Email: [email protected]
Dynamic response of a volcanic shelter subjected to ballistic impacts
ARTICLE IN PRESS
International Journal of Impact Engineering 34 (2007) 681–701 www.elsevier.com/locate/ijimpeng
Dynamic response of a volcanic shelter subjected to ballistic impacts Mauro Dolce, Donatello Cardone, Claudio Moroni, Domenico Nigro Department of Structure, Geotechnics and Applied Geology, University of Basilicata, Macchia Romana, 85100 Potenza, Italy Received 10 September 2005; received in revised form 10 January 2006; accepted 14 January 2006 Available online 4 April 2006
Abstract This paper presents the results of a series of experimental tests, aimed at investigating the impact and dynamic response of a volcanic shelter. Similar shelters are to be installed in the Stromboli island (Aeolian archipelago, Sicily, Italy), to protect human lives from the pyroclastic eruptions of the volcano. Basically, the Shelter consists of two homologous reinforced concrete shells, interconnected by rubber-based special devices, which absorb and dissipate most of the impact energy. The Shelter has been specifically designed to resist, without damage, an impact with a 150 kg mass rock, knocking the surface of the external shell at 62.5 m/s speed. The experimental tests were carried out on a 1:2-scale model, using a testing apparatus purposely realised to simulate impact conditions comparable with those considered in the design. Impact energy and mass ratio between projectile and reinforced concrete shell were assumed as main experimental parameters and varied during the tests. A finite element model of the Shelter was also implemented and direct-integration time-history analyses were performed, to validate the experimental results. Reference to the Hertz’s law was made to simulate the impact between the two bodies. The experimental tests proved the ability of the Shelter to resist impacts without damage. Acceptable agreement between numerical predictions and experimental results was found. r 2006 Elsevier Ltd. All rights reserved. Keywords: Impact testing; Dynamic response; Hertz’s law; Impact-absorbing devices; Numerical analyses
1. Introduction On September 2003, the Italian Dept. of Civil Protection (DPC) entrusted the University of Basilicata (USB) to make theoretical and experimental studies finalised at designing and engineering a volcanic shelter to be installed in the Stromboli island, near Sicily (Italy), where an active volcano frequently produces pyroclastic eruptions [1]. Several monitoring, research and tourist activities are carried out in the area of the volcano. In order to protect the human lives from the risks of a pyroclastic eruption, the DPC planned to place a series of Shelters in strategic sites that can be reached in few seconds by people nearby, along paths traced on the flanks of the volcano. Corresponding author. Tel.: +39 0971 205052; fax: +39 0971 205052.
E-mail address: [email protected] (M. Dolce). 0734-743X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2006.01.002
ARTICLE IN PRESS 682
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
The main performance requirement demanded by DPC for the Shelter was the capability of resisting, without significant damage, an impact with a 0.5 m diameter rock (approximately 150 kg mass), arriving from 400 m distance, after reaching a maximum height of 100 m. The aforesaid basic assumptions result in an impact velocity of the falling rock of about 62.5 m/s (corresponding to an impact energy of some 293 kN m) and in an attack angle of 451, as obtained from the well-known equations describing the motion of a projectile [2]. The other requirements demanded in the design of the Shelter were related to specific concerns (i.e. transportation and assembling operations by helicopter, durability in an aggressive environment, low visual impact in a protected landscape), which are of lesser importance for the scope of this paper, though they played an important role at the design stage. The activities for the complete development of the final design of the Shelter required three phases: Phase 1: Conceptual design of the Shelter, numerical modelling of the impact between falling rock and Shelter, response analysis, design of the Shelter; Phase 2: Design and construction of a reduced-scale model of the Shelter, to be tested under the impact conditions similar to those considered at the design stage; Phase 3: Test set up, experimental testing, analysis of the results. The theoretical and numerical studies carried out during Phase 1 are described in [3]. They led to the design and implementation of a shield-structure (i.e. the Shelter), consisting of two homologous R/C shells, interconnected by suitable impact-absorbing devices. This paper describes the experimental activities carried out during Phase 3 and the most important related results. The experimental tests were carried out on a 1:2-scale model of the Shelter, using a particular testing apparatus, purposely designed and realised at the USB Lab, to simulate impact conditions similar to those considered at the design stage. Eight impact tests were performed, with two different levels of impact energy and four different mass ratios between projectile and R/C shell, as described below. The dynamic response of the Shelter to the considered impact conditions was captured through 18 sensors, i.e., 10 displacement transducers and 8 accelerometers. The finite element model of the Shelter, implemented during Phase 1, was updated based on the experimental outcomes of the impact tests. Direct-integration time-history analyses were then performed, by SAP2000 [10], and the numerical results compared to the corresponding experimental ones. 2. Description of the shelter The impact resisting structure for volcanic shelters basically consists of two homologous R/C shells, connected by suitable impact-absorbing devices. The external shell resists the falling rock elastically, with possible minor damages (e.g. spalling of concrete cover) limited to the impact area. Most of the impact energy is absorbed, and then dissipated, by special devices connecting internal and external shell. The internal shell, where people are recovered, is thus practically not affected by the impact. Fig. 1 shows the different parts composing the Shelter. They include: (i) the foundation, consisting of a Cshaped reinforced concrete 290 mm thick basement, equipped with a backside tie tooth, 300 mm thick and 1 m high (see Fig. 1(d)); (ii) the internal R/C 100 mm thick shell, equipped with two lateral 150 mm thick R/C panels (see Fig. 1(a)); (iii) the external R/C 180 mm thick shell (see Fig. 1(e)), connected to the internal one by means of two lateral 10 mm thick steel plates; (iv) four impact-absorbing devices (two each side, as shown in Fig. 1(b)), based on rubber and viscous material, sandwiched between the steel plates of the external shell and the R/C panels of the internal shell (see Fig. 1(c)). Each structural component of the Shelter has a specific function. The external shell is deputed in front of the falling rocks. The impulse of force developing during the impact results in kinetic energy for the external shell and, as a consequence, gives rise to an initial (translational+rotational) velocity. The impact-absorbing devices provide the necessary stiffness and energy dissipating capability to control and damp the free vibrations of the external shell. The internal shell transfers the forces transmitted by the devices to the foundation. The overall stability to sliding and overturning movements is guaranteed by the foundation, with the help of the backside tooth. The overall dimensions of the Shelter (foundation included) are 4.16 m in the longitudinal direction (Y-direction in Fig. 1), 2.46 m in the transverse direction (X-direction), 3.25 m in the vertical direction
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
683
z
y
x
(a)
(b)
(c)
(e)
(d)
(f)
(g) Fig. 1. Assembling of the Shelter: (a) internal R/C shell, (b) installation of the impact-absorbing devices, (c) installation of the lateral coupling plates, (d) foundation structure, consisting of a R/C basement equipped with a backside tooth, (e) external R/C shell, (f) sub-assemblage including the foundation structure plus the internal shell, (g) Shelter as a whole.
ARTICLE IN PRESS 684
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
(Z-direction). The clean height off-ground in the rear part is 1 m, due to the partial embedment of the Shelter in the earth from behind, in order to reduce the visual impact. The clean internal dimensions are about 3 m length, 1 m width and 1.8 m height, so that at least 10 people can be safely arranged inside, in case of danger. Visco-elastic devices, referred to as Added Damping Rubber Isolators (ADRIs) [4], have been used as impactabsorbing devices. Originally conceived for seismic isolation, ADRI basically consists of a cylindrical laminated rubber bearing with the central hole filled with highly viscous material. ADRIs are mounted in the shelter to be shear-strained when the external shell moves, due to the impact of falling rocks. The shear stiffness of ADRI is a function of the ratio between the cross-sectional area of the device and the total thickness of rubber. It also depends on the shear modulus of rubber, which progressively reduces while increasing shear strain [4]. The damping provided by ADRI is a function of the ratio between inner and outer diameter, as well as of the infill viscosity. Damping ratios of the order of 20% can be easily obtained at high frequency [4]. Besides having no mechanical moving parts, a main advantage of ADRI is the nature of damping, which is mainly viscous rather than hysteretic, so that it does not accumulate inelastic residual deformations after the impact. Moreover, the maximum force exerted by the viscous infill is out-of-phase with respect to the elastic force of the rubber component, so that the energy dissipation is almost quadratic with displacement. Other favourable features of ADRI are its compactness and limited sensitivity to temperature variations. More detailed information on the characteristics of the Shelter structure can be found in [3].
3. Test model and sensor set up A 1:2-scale model of the Shelter has been realised at USB to be tested under impact conditions. The test model was derived from the full-scale prototype, by applying the requirements for geometrically similar scaling [5,6]. Table 1 summarises the scale factors to be used for perfect similitude with a full-scale structural model working in the elastic range under dynamic loading. Practically, there are only two independent scale factors: that relevant to lengths (SL) and to the Young’s modulus of material (SE). All the other scale factors can be expressed as a function of the previous two. For R/C models, the reinforcement of the structural members is usually made of ordinary steel. This implies that a scale factor SE ¼ 1 must be used for both concrete and steel. In Table 1, two different sets of scale factors are reported. This is because the experimental tests described in this paper consists of three parts: (i) the reproduction of the effects due to self-weight, (ii) the simulation of the
Table 1 Similitude requirements for reduced-scale test models working in elastic regime under dynamic loading Parameter
Dimension
Scale factora
Scale factorb
Length Stress Strain Modulus of elasticity Stiffness Force Energy Mass Acceleration Velocity Displacement Time Period of vibration Frequency of vibration
L FL2 — FL2 FL1 F FL FT2L1 LT2 LT1 L T T T1
SL SE 1 SE SESL SES2L SES3L S3L S1 L 1 SL SL SL S1 L
SL SE 1 SE SESL SES2L SES3L S2L 1 S1/2 L SL S1/2 L S1/2 L S1/2 L
a
Reduction factors for perfect similitude of impacts. Reduction factors for perfect similitude of self-weight and free-vibrations.
b
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
685
impact between falling rock and external shell and (iii) the simulation of the free-vibrations of the external shell following the impact. As a matter of fact, the scaling law which applies for (ii) is different from that which applies for (i) and (iii) [5]. In impact engineering, experimental tests are generally carried out on small-scale specimens, geometrically similar to the full-scale prototype and subjected to the same impact velocity. In this case, times are reduced by SL and masses by S3L. As a consequence, accelerations are amplified by SL. The gravity acceleration, however, does not change. This introduces a distortion in the model. Actually, impact tests are primarily conducted with the scope of investigating phenomena like penetration, perforation, buckling, etc. Gravitational forces are not significant, when compared to the dynamic forces generated in the impact, and can be neglected [6]. When the problem is governed by the frequency of vibration of the structure (e.g. free-vibrations, response to harmonic and periodic excitations, seismic-induced vibrations, etc.) and gravity loads are not negligible, a different approach is followed [5]. Experimental tests are carried out on specimens geometrically similar to the full-scale prototype and subjected to the same acceleration. In this case, times are reduced by S1/2 L and masses by S2L. This results in the perfect simulation of inertial, gravity and restoring forces. Further explanations about this concern are given below. Coming back to the test model, it is worth to emphasise that extreme care was taken in choosing the concrete composition for each structural member of the Shelter, as the mechanical properties of a microconcrete can significantly differ from those of a standard concrete [7]. At this aim, a proper selection of (i) granulometry of the aggregate, (ii) aggregate/cement ratio and (iii) water/cement ratio was made. Several mixes were manufactured and tested. The mix selected for the internal and external shell was characterised by a washed sand with grain size lower than 5 mm, a water/cement ratio of 0.32 and an aggregate/cement ratio of 3.68. A fluidifying additive (Multiflux-AximII), about 2% the weight of the cement, was used. The mix selected for the basement was made of washed sand and gravel with grain size lower than 10 mm, a water/cement ratio of 0.44 and an aggregate/cement ratio of 3.68. The fluidifying additive was about 1% the weight of cement. In both cases, cement type 42.5 N [8] was used. Compression tests, carried out just 3 days after casting, provided about 32 N/mm2 average compression strength for the basement and 40 N/mm2 for the shells, to be compared to the design strength of concrete after 28 days, taken equal to 35 N/mm2. Reference to FeB38k steel (375 N/mm2 characteristic yield strength) was made in the design. The same type of steel was adopted for the test model. The steel reinforcement was firstly designed for the full-scale prototype and then reported to the model scale by halving the bar diameter. Ribbed bars of 6 and 8 mm diameter were used in the test model. As an example, Fig. 2 shows the arrangement of the steel reinforcement adopted for the external shell, which is the only component of the Shelter directly impacted by the projectile. As can be seen, the reinforcement of the external shell consists of two grids (one each face) realised by means of 8 mm diameter bars at 50 mm spacing. The grids are connected by 6 cross-ties per square meter, 8 mm diameter, not shown in the figure. For simplicity, the spacing of the reinforcing bars has been maintained constant over the whole shell. The structural elements of the model were cast by using common wooden form works. This produced some imperfections in the shape of the shells, which were accurately surveyed. In particular, the weight of the external shell, which assumes great importance in the impact response of the Shelter, was measured by a dynamometer. It resulted equal to about 8.4 kN, i.e. about 25% greater than expected. Similarly, the actual position of the centre of mass was evaluated by suspending the external shell from the bridge crane. A shift of several millimetres, in both the horizontal and vertical direction, was found, in comparison with the theoretical position of the centre of mass. All that was properly taken into account in view of the experimental tests. First of all, the additional masses to be used to satisfy the mass-similitude requirements for gravity loads and free-vibrations (see Table 1, column 4), were proportioned by referring to a self-weight of the external shell of 8.4 kN. Thus, 4 kN (400 kg mass) were added to get a total weight of 12.4 kN, corresponding to the weight of the external shell in the prototype scale divided by 4. To this end, 40 steel masses (10 kg each) were placed on the external shell, as shown in Fig. 3. The steel masses were inserted inside threaded bars, pre-arranged along the lateral thickness of the external shell. Moreover, the relative position of external and internal shell was revised, in order to eliminate the accidental additional eccentricity between centre of mass of the external shell and centre of
ARTICLE IN PRESS 686
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
Fig. 2. Arrangement of steel reinforcement in the external shell.
stiffness of the impact-absorbing devices. After these adjustments, the test configuration can be considered to reproduce the design configuration satisfactorily. The test model was directly placed on the laboratory floor and then fixed, on the rear, through a couple of threaded bars (see Fig. 3). The threaded bars transfer their action on a UPN steel section, which simulate the presence of the backside tooth. Fig. 4 shows the experimental force vs. displacement behaviour, under cyclic loading, of one impactabsorbing device (ADRI) used in the Shelter during the impact tests. It is characterised by two rubber layers of 48 mm thickness each, an interposed steel shim of 5 mm thickness, outer diameter of 225 mm and inner diameter of 150 mm. In the cyclic test in Fig. 4, the frequency of loading is 0.5 Hz while the displacement amplitude increases from 10 to 30 mm, corresponding to a rubber shear strain of 5% and 15%, respectively.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
687
Reacting wall
Longitudinal jack
Gun
Additional masses
Transverse jack Steel cap
Fig. 3. Test apparatus, including an Enerpac actuator for pre-loading the spring placed inside the gun and a Technotest jack for removing the stop which restrains the projectile put at the top of the spring.
As can be seen, ADRI exhibits a visco-elastic mechanical behaviour which in principle could be described by just two numerical parameters: effective stiffness and effective damping [9]. Their values are reported in the same figure, for each displacement amplitude considered. The effective stiffness practically halves, passing from 0.43 to 0.21 kN/mm, when the displacement amplitude increases from 10 to 30 mm. The effective damping is around 17% at 10–20 mm, then reducing to 15.5% at 30 mm. The effective stiffness of ADRI was found to increase while increasing the strain rate (i.e. frequency of loading) [4]. It is expected that the values provided in Fig. 4 underestimate the actual stiffness exhibited by the devices during the tests, as the frequencies of loading experienced by ADRIs after the impacts are considerably greater than 0.5 Hz.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
688
8
0.5
Effective stiffness 6
0.3 0.2
Shear force (KN)
(KN/mm)
0.4
0.1 0.0 5 mm
20 mm
30 mm
4
2
0 -40
-30
-20
-10
0
10
20
30
40
Displacement (mm) -2
20
-4
Effective damping
-6
(%)
15 10 5 0 -8
5 mm
20 mm
30 mm
Fig. 4. Experimental force–displacement behaviour, under cyclic loading of increasing amplitude, of the impact-absorbing device used in the Shelter. Frequency of loading equal to 0.5 Hz. The inner bar-diagrams show the effective stiffness and the effective damping exhibited by the device as a function of displacement amplitude.
As shown in Fig. 5, 18 sensors were used to capture the dynamic response of the Shelter after the impacts, namely: (a) eight Celesco wire transducers (T1x, T2x, T3z, T4z in Fig. 5), measuring absolute displacements of specific points of the external shell (b) two Penny-Gauss LVDTs (T5x in Fig. 5), measuring possible sliding movements of the basement, (c) eight Columbia accelerometers, with 72 g range (A1x, A2x, A3y, A4x in Fig. 5), measuring the longitudinal and transverse accelerations experienced by the internal and the external shell. The sensors were arranged symmetrically on the left and right side of the Shelter, as shown in Fig. 5. Starting from the displacements recorded by the wire transducers T1x, T2x, T3z, T4z during each test, the rigid-body displacements and rotations of the external shell have been derived. Subsequently, the maximum displacements in the four impact-absorbing devices have been obtained, as in the graphical construction shown in Fig. 6. The initial configuration of the external shell is identified by the initial position of the wire transducers (marked by 1, 2, 3 and 4 in the figure), directly assessed on the model before the tests. The deformed configuration of the external shell is obtained by translating and rotating it, up to comply with the displacements measured by all the transducers (points 10 , 20 , 30 and 40 in Fig. 6). Finally, the displacements generated in the devices are assumed equal to the distance between the points a–a0 and b–b0 . As shown in Fig. 6, the initial configuration of the external shell depends also on the effects of the selfweight, which can be summarized in about 40 mm vertical displacement of the mass centre and in about 71 rotation, around the Y-axis. This, in turn, produced different vertical displacements in the devices, of the order
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
689
right z
x
T1x
y
A4x
left
T2x T3z
A3y
T1x
A1x
T5x
A2x T4z T2x T3z
T5x Fig. 5. Sensor set up. T1x, T2x, T3z and T4z are wire-transducers measuring absolute displacements of the external shell. A1x, A2x, A3y, A4x are accelerometers, measuring the longitudinal and transversal accelerations experienced by internal and external shell. T5x are LVDTs measuring possible sliding movements of the basement.
of 30 mm in the upper ones, and practically negligible in the lower ones. Due to the dependence on the displacement, therefore, the two couples (upper and lower) of ADRIs had different effective stiffness under the impact, according to the diagram shown in Fig. 4. The effects of the self-weight may be eliminated by adding a couple of auxiliary steel components, as discussed in [3]. 4. Experimental program and test apparatus In the experimental program under considerations, tests were carried out on two different configurations of the Shelter, i.e. with or without (w/o) additional masses. The configuration with additional masses intended to reproduce the effects of self-weight and the freevibrations of the external shell following the impact. Obviously, the greater mass of the external shell (about 1240 kg instead of 625 kg) was expected to significantly attenuate the effects caused by the impact and in particular the initial velocity of the external shell. In order to substantially comply with the real impact conditions, the projectile mass was increased from about 19 kg (i.e. 150 kg divided by 8) to about 37 kg. In this way, the same mass ratio between projectile and external shell (about 3%) and the same kinetic energy of the projectile (about 36.6 kN m), as the design impact, was obtained. By assimilating the impact between projectile and shell to a head-on elastic impact between two spheres, the initial velocity of the external shell after the
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
690
4 4’
T1x
up b b’
down a a’
2 2’
3 3’
1 1’
T2x
T3z
T4z
Fig. 6. Graphical construction for the evaluation of the maximum displacements in the devices from the peak displacements in the wiretransducers. The points 1,2,3 and 4 indicate the positions of the sensors at the beginning of the test. The points 10 ,20 ,30 and 40 indicate the positions of the sensors when the maximum displacements are attained.
Table 2 Test program Test no.
Projectile weight (kN)
Impact energy (kN mm)
Impact velocity (m/s)
Additional weight (kN)
Shell weight (kN)
Mass ratio (%)
1 2 3 4 5 6 7 8
0.37 0.37 0.27 0.27 0.37 0.37 0.27 0.27
17,120 25,456 18,946 26,435 17,745 27,555 17,542 25,589
30.4 37.1 37.5 44.3 31.0 38.6 36.0 43.5
0 0 0 0 4 4 4 4
8.4 8.4 8.4 8.4 12.4 12.4 12.4 12.4
4.4 4.4 3.2 3.2 3.0 3.0 2.2 2.2
collision was expected to be 2.56 m/s, i.e. about 30% less than the design value (3.65 m/s). This implies a reduction of the same order of magnitude in terms of both maximum displacements and maximum forces experienced by the Shelter during the free-vibrations following the impact. A further reduction of the order of 15% should be taken into account, due to the real testing conditions (see the impact energy of Test no. 6 in Table 2). The effects of self-weight and the frequency of vibration of the external shell under free-vibrations, instead, are captured with accuracy. The configuration of the Shelter w/o additional masses was aimed at reproducing the perfect similitude during the impact. Thus, in principle, masses were divided by 8 and impact velocity was maintained constant, i.e. equal to 62.5 m/s. The velocity of the external shell resulting from the impact was expected to be exactly 3.65 m/s, while a certain underestimation of the effects due to self-weight and of the frequency of vibration of the external shell was implicitly accepted. In practice, two problems occurred, which led to a significant deviation from the aforesaid test conditions. The first discrepancy was the actual mass of the external shell,
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
691
which resulted equal to about 840 kg, instead of 625 kg. The second discrepancy derived from the operative limits of the hydraulic jack, used to pre-strain the rubber spring placed inside the testing device. The maximum stroke of this jack was 400 mm, corresponding to a maximum strain energy of the spring of about 26–27 kN m, instead of 36.6 kN m. The projectile mass was then increased from about 19 to 26.5 kg, in order to get the same mass ratio (about 3%) between projectile and external shell and the same impulse of force (about 2.3 kNs) as the real impact. By assimilating the impact between projectile and shell to a head-on elastic impact between two spheres, the initial velocity of the external shell is found to be of the order of 2.75 m/s, i.e. about 25% less than the design value (3.65 m/s). Actually, a much greater underestimation of the maximum effects (displacements and forces) experienced by the Shelter during the free-vibrations following the impact is expected, due to the significant overestimation of the frequency of vibration of the external shell. To a first estimation, the maximum displacements observed in the benchmark test on the model w/o additional masses (i.e. Test no. 4 in Table 2) should be multiplied by about 2, to be consistent with the actual response of the Shelter. As a matter of fact, none of the experimental tests carried out on the reduced-scale model of the Shelter exactly reproduces the design impact conditions. However, they provide a clear understanding of the actual response of the Shelter, under impacts still comparable with that considered at the design stage. More importantly, the results of the experimental tests performed on the reduced-scale structural model can be exploited to validate the numerical model used at the design stage for safety verifications [3]. Table 2 summarises the experimental tests carried out on the 1:2-scale model of the Shelter. Eight consecutive tests were performed, differing in the impact energy and in the mass ratio between projectile and external shell. Two different levels of impact energy have been considered, one corresponding to about 25.5–27.5 kN m, the other approximately to 70% of that. In addition, four different mass ratios, ranging from 2.2% to 4.4%, have been considered, by using two different projectiles (having 27 and 37 kg mass, respectively), on two different configurations of the external shell (with or without the additional 4 kN weight). The impact velocity associated to each impact test is also reported in Table 2. A testing device (see Fig. 3) was purposely designed and realised at USB, to simulate the impacts considered at the design stage of the Shelter. Basically, it consists of a steel tube equipped with a mechanical stop driven by two hydraulic jacks (50 kN max. force and 100 mm stroke). The tube is fixed to a stiff reacting wall. A rubber spring of proper stiffness is arranged inside the tube and pre-strained by a hydraulic jack (2000 kN max. force and 400 mm stroke) placed behind it. The spring consists of a series of 10 consecutive rubber cylinders (each with 125 mm diameter and 75 mm height) alternated with 10 thin steel plates (each with 200 mm diameter and 5 mm thickness). The steel plates exert a confining action on the rubber cylinders, which avoids their buckling during the loading phase. Actually, the spring also plays the role of projectile, having a mass of about 19 kg. A supplemental mass of 8 or 18 kg, consisting of a cylindrical block with 200 mm diameter, made of Fe510 tempered steel, is placed at the top of the spring, to get a total mass of 27 or 37 kg, respectively. When the mechanical stop is removed, the projectile is shot, at a given velocity, against the external shell. The impact point was located in the middle of the Shelter, approximately where the normal to the surface of the external shell passes through its centre of mass. Actually, other five impact conditions, differing from that reproduced during the experimental tests, were considered at the design stage. They included impacts on the lower and upper extremity of the external shell, both in the middle and in the lateral section of the Shelter [3]. The impact position considered for the experimental tests was selected being the more dangerous in terms of stresses induced in the external shell. A steel cap with spherical surface was placed on the surface of the R/C shell and centred in the impact point (see Fig. 3). Between the steel cap and the surface of the shell, a 10 mm thickness rubber layer is interposed, with the scope of avoiding localized damages (e.g. spalling of concrete cover), in view of the numerous tests to be conducted. The presence of the rubber layer surely caused a certain loss of the energy transferred to the Shelter during the impact. Another consequence is a longer duration (to the detriment of the peak force) of the impulse generated during the impact, compared with the case of direct contact between rock and concrete surfaces. A series of numerical analyses have been carried out to examine this aspect, as discussed below. Fig. 7 shows the loading curve of the rubber spring placed inside the testing device for one test (Test no. 4 in Table 2). The force–displacement relationship in Fig. 7 was obtained by applying (with the longitudinal
ARTICLE IN PRESS 692
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
210
180
150
(KN)
120
90
60
30
0 0
60
120
180
240
300
360
420
(mm) Fig. 7. Loading curve of the spring for one significant test (Test no. 4 in Table 2).
hydraulic jack in Fig. 3) an increasing compression force on the spring. The force was increased up to reaching the maximum stroke of the spring (400 mm). Then, the mechanical stop was removed by the transverse jacks. The strain energy accumulated before removing the mechanical stop is given by the area under the curve. Under the hypothesis of energy conservation, the strain energy of the spring is equal to the kinetic energy of the projectile when it impacts the Shelter. As can be noted in Table 2, a certain scatter in the impact energy of the tests has been observed, due to a slight hysteresis of the spring (see Fig. 7). This has been accepted and then taken into account when comparing the results of the tests, as explained below. 5. Summary of the experimental outcomes The most important experimental outcome is that the Shelter resisted eight impacts, comparable with that assumed in the design, without suffering significant damage. Actually, the damages observed at the end of the test program, through an accurate visual inspection of the structure, were limited to some hairline cracking in the concrete of the external shell, close to the impact area. Two major parameters have been considered to describe the dynamic response of the external shell caused by the impacts, namely: the peak accelerations experienced by the internal and the external shells and the maximum displacements attained in the four impact-absorbing devices. Fig. 8 shows the maximum displacements of ADRIs as a function of the mass ratio between projectile and external shell. Two different diagrams are reported, each relevant to a different level of impact energy. In particular, Fig. 8(a) refers to the lower energy-content tests (Test nos. 1-3-5-7 in Table 2), while Fig. 8(b) refers to the higher energy-content tests (Test nos. 2-4-6-8 in Table 2). The ith displacement of each diagram is slightly modified by a normalisation factor, equal to the ratio between the impact energy associated to Test no. 7 or 8, respectively, and that associated to the ith test. The four devices are identified by their location inside the Shelter, i.e. on the right or left side (see Fig. 5), up or down (see Fig. 6) in the same side. As can be seen, the trend is practically linear with the mass ratio and the slope of the tendency lines is quite similar, being a bit greater for the higher energy-content tests. The maximum displacements increase, on average, by about 10%, for the upper-placed devices, and by about 18%, for the lower-placed devices, while
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
693
Maximum displacements of ADRI’s (mm)
25
20
15
10
Right_down Right_up
5
Left_down Left_up
0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 Mass ratio (%)
(a)
Maximum displacements of ADRI’s (mm)
25
20
15
10
Right_down Right_up
5
Left_down Left_up
0 (b)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 Mass ratio (%)
Fig. 8. Maximum displacements attained in the devices after the impacts. The maximum displacements are reported as a function of the mass ratio between projectile and external shell (see Table 2), for two different levels of impact energy, approximately equal to (a) 17,550 kN mm and (b) 25,600 kN mm, respectively.
the input energy increases by about 48% (compare Fig. 8(a) with Fig. 8(b)). It should be noted that the slight deviation from the linear trend, observed in Fig. 8, is probably due to the different configuration of the Shelter, as the tests associated to 4.4% and 3.2% mass ratios have been performed before the others, with a reduced additional mass. The addition of 4 kN weight (see Table 2) caused about 25 mm further vertical displacement of the mass centre and about 21 rotation of the external shell. This slight change in the Shelter geometry had some influence on the test results. Fig. 9 reports the ratio between the peak transverse accelerations of external and internal shell, as a function of the mass ratio between projectile and external shell. Each curve refers to a different level of impact energy, as pointed out in the diagram. For each test, the peak accelerations of external and internal shell have been obtained by averaging the peak values measured by the relevant accelerometers, i.e. the four sensors labelled with A1x and A2x and the two sensors labelled with A4x in Fig. 5, respectively. It is worth to note that the aforesaid sensors are designed to record accelerations along a given direction, which, in the case under consideration, was the X-direction in Fig. 5. The initial deformed configuration of the external shell, due to the effects of self-weight, however, determines a not perfect correspondence between the two directions of
ARTICLE IN PRESS 694
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
0.8
Peak acceleration ratio (internal vs. external shell)
0.7 0.6 0.5 0.4 0.3 0.2 0.1
Impact energy = 70% Emax Impact energy = Emax
0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 Mass ratio (%) Fig. 9. Ratio between the peak acceleration of the external shell and that of the internal shell, as a function of the mass ratio between projectile and external shell and for two different levels of impact energy.
measurement. As a matter of fact, the external shell is rotated by 8–101 with respect to the horizontal line. On the other hand, the rigid-body displacements of the external shell occurred along a direction rotated by about 46–511 with respect to the horizontal line. As a consequence, the acceleration components recorded by the sensors placed on the internal shell form an angle of about 46-511 with respect to the motion direction, while those recorded by the sensors placed on the external shell form an angle 8–101degrees greater. This implies that the acceleration ratios reported in Fig. 9 are a little overestimated, by about 20–25%. In any case, Fig. 9 clearly shows a de-amplification, of the order of 30–50% (depending on the mass ratio between projectile and external shell), of the peak acceleration experienced by the internal shell, compared to that recorded on the external shell. The input energy seems to play a negligible role on the effectiveness of the impact-absorbing devices, in reducing the effects transferred to the internal shell. 6. Comparison between experimental results and numerical predictions A refined finite-element model of the Shelter was realised, during the design phase, in order to verify the compliance of the structure with the main design requirements (i.e., resistance of the structural members, compatibility of the displacements of the external shell with the available distance—about 150 mm—from the internal shell, overall stability of the Shelter to sliding and overturning movements, etc.). A condition of elastic impact between falling rock and Shelter, with negligible friction between the surfaces of the impacting bodies (i.e. impact force directed orthogonally to the surfaces of the bodies, in the contact point), was assumed in the design. In the calculations, the falling rock was assumed to behave like a ball, with mass m1 ¼ 18.75 kg and initial velocity v1 ¼ 62.5 m/s, impacting on a steady body (i.e. the Shelter) with mass m2 ¼ 625 kgbm1. A force impulse of about 2.28 kNs was then obtained. The impact force vs. time relationship was supposed to follow a triangular law, characterised by two identical branches, with slope equal to 2*(Fmax/tmax). The duration of the collision (i.e. tmax) and the maximum force exchanged between the two impacting bodies (i.e., Fmax) were estimated by the Hertz’s law [11], as a function of the radii of curvature of the two impacting bodies in the contact point and of the Young’s modulus and Poisson’s ratio [12], resulting equal to 0.017 s and 268 kN, respectively. In the Hertz’s law, reference was made to a steel-rubber contact, assuming Es ¼ 210 kN/mm2 and n ¼ 0:3 as Young’s modulus and Poisson’s ratio of steel, Er ¼ 0.02 kN/mm2 (experimental value) and n ¼ 0:49 as Young’s modulus and Poisson’s ratio of rubber, Rp ¼ 100 m as radius of curvature of the projectile and Rs ¼ 0.5 m as radius of curvature of the external shell in the impact point. The model was implemented in the finite-element program SAP2000_Nonlinear [10] and a series of nonlinear direct-integration time-history analyses were then carried out, taking into account geometrical
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
695
nonlinearities through the hypothesis of large displacements, while material behaviour was considered linear. Reference to [3] can be made for a comprehensive description of the analytical model. In this paper, the numerical model is used to compare and validate reciprocally experimental and numerical results. At this end, the attention is focused on the external shell, whose movement is restrained by the four impact-absorbing devices, assuming that the internal shell is a rigid body perfectly fixed to the ground. Fig. 10 shows the finite-element mesh of the external shell. The elements used to describe the visco-elastic behaviour of the impact-absorbing devices are reported in the same figure. Three different types of finite element have been used, namely: (i) Shell-type elements (i.e. three-dimensional quadrilateral four-node elements), modelling the external shell, lateral steel plates included, (ii) Frame-type elements (i.e. threedimensional beam–column elements connecting two joints), modelling the elastic behaviour of ADRI and (iii) Damper-type elements (i.e. a two-joint connecting link with pure viscous behaviour), modelling the energy dissipating capacity of ADRI. The numerical model is made of 563 joints, 408 shell-type 90 mm thick elements, meshing the external shell, and 186 shell-type 5 mm thick elements, meshing the lateral closing steel plates of the external shell. The mass contributed by each element is lumped at the element joints. The additional masses are taken into account by properly adjusting the mass per unit volume of the shell elements. A linear elastic constitutive law has been adopted for reinforced concrete and structural steel. The dynamic response of the Shelter is mostly governed by the visco-elastic behaviour of ADRIs, which in turn can be described through two main parameters, i.e. the effective stiffness and the effective damping. Their values, as exhibited by ADRIs under cycling loading at 0.5 Hz and displacement amplitudes comparable with those recorded during the impact tests, are shown in Fig. 4. In this study, however, the availability of the impact experimental results allows the authors to identify the visco-elastic parameters of ADRIs from the acceleration response of the Shelter during each test. In this paper the attention is focused on just one test (Test no. 4 in Table 2), with the only scope of demonstrating the consistency of the experimental and theoretical results. Fig. 11 shows the acceleration–time histories recorded during the test under consideration. Figs. 11(a) and (b) refer to the signals recorded by sensors A1x and A2x (see Fig. 5) placed on the external shell, Fig. 11(c) to those recorded by sensors A4x (see Fig. 5) placed on the internal shell. It is interesting to note that the accelerations experienced by the external shell progressively reduce in amplitude, during the damped freevibration of its mass. On the contrary, the accelerations experienced by the internal shell, reduce and then increase in amplitude several times, following the time-profile of the displacements of ADRIs (see Fig 16). Fig. 12 shows the Amplitude Spectra (in RMS2 units) derived from the signals in Fig. 11, by applying the Fast Fourier Transform (FFT) [13]. As known, all the methods for the extraction of modal parameters from Frequency Response Functions (FRFs) are based on the basic assumption that in the vicinity of a resonance
Fig. 10. Finite-element mesh of the external shell.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
696
2500 A1x_right
(mg)
1500 500 -500
0
0.1
0.2
0.3
0.4
0.5
0.6
(sec)
-1500 -2500
A1x_left
(a)
2500 A2x_right
(mg)
1500 500 -500 0
0.1
0.2
0.3 (sec)
0.4
0.5
0.6
0.2
0.3
0.4
0.5
0.6
-1500 -2500
A2x_left
(b)
2500
(mg)
1500
A4x_right
500 -500 0 -1500
0.1
(sec) A4x_left
-2500 (c) Fig. 11. Acceleration–time histories recorded during the Test no. 4 in Table 2 on the (a,b) external and (c) internal shell. Each signal is identified by the label of the corresponding sensor (see Fig. 5).
the total response is dominated by the contribution of the mode with the closest natural frequency. Looking at Fig. 12, it can be observed that the modes of vibration of the external shell are well separated from those of the internal shell. Basically, three different resonance peaks (hence modes of vibration) are detected on the Amplitude Spectra relevant to the external shell. The higher contribution to the dynamic response of the external shell must be ascribed to a mode with frequency of vibration approximately equal to 6.63 Hz. The other two modes that seem to give a significant contribution to the dynamic response of the external shell have frequency of vibration around 2 and 9.9 Hz, respectively. The modal analysis associates the previous frequency values to the first, third and fifth mode of vibration of the shelter, which are the primarily excited modes by the impact under consideration. Fig. 13 shows their shapes, as obtained from modal analysis. Table 3 summarises the frequencies of vibration, compared with the experimental values, and the modal participating mass ratios of each mode. As can be seen, a good accordance between numerical and (available) experimental frequency values is found. The first and fifth modes are
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
697
basically rotational modes around the Y-axis (see Fig. 5), while the third mode is a purely translational mode in the XZ plane. The three modes under consideration excite more than 98% of the total mass of the external shell in the X- and Z-directions. The vibration frequency of the dominating mode (i.e. 6.63 Hz) can be used to evaluate the actual shear stiffness of the ADRI system during the impact test. By referring to a SDOF system with 840 kg mass, an effective shear stiffness of about 0.38 kN/mm is obtained for each device. As expected, the effective stiffness exhibited by ADRI in the impact test is greater (by about 50%) than that observed in the cyclic tests of similar displacement amplitudes (i.e. 20 mm, see Fig. 4). This increase must be ascribed to the higher frequency of the movement (4 0.5 Hz) generated in the devices during the impact test. The effective damping associated to the dominant mode of vibration of the external shell has been estimated through the procedure illustrated in Fig. 14, which is based on the evaluation of the maximum value of the curve (i.e., ja0 j) and of the frequency bandwidth of the function (ob 2oa ) corresponding to a response level of
1.E+04 A1x_right
A2x_right
|amp|
8.E+03 6.E+03
A2x_left A4x_right
A2x_right
4.E+03 A1x_left
A4x_left
A1x_right
2.E+03 0.E+00 0
5
10
15
20
25
30
35
40
(Hz) Fig. 12. Amplitude spectra, in the frequency-domain, obtained from the Fast Fourier Transforms of the acceleration–time histories in Fig. 11. Each spectrum is identified by the label of the sensor used to record the signal (see Fig. 5).
Fig. 13. Most important modal shapes of the Shelter and associated frequencies of vibration and participating mass ratios.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
698
Table 3 Frequencies of vibration and modal participating mass ratios of the first six modes of the Shelter, as obtained from modal analysis Mode
1 2 3 4 5 6
Experimental frequencies of vibration (Hz)
2 — 6.63 — 9.9 —
Modal frequencies of vibration (Hz)
2.40 6.51 6.69 8.93 9.37 16.43
Modal participating mass ratios (%) x-dir.
y-dir.
z-dir.
13.5 0.39 64.25 0.67 21.15 —
— 74.37 0.55 0.03 — 16.43
18.1 0.30 55.03 0.80 25.73 —
Comparison with the available experimental results.
pffiffiffi ja0 j= 2. The effective damping of the mode under consideration is then estimated from the following equation [13]: x ¼ ðob oa Þ=ð2or Þ.
(1)
By adopting the previous procedure, a mean value (averaged over the four curves in Fig. 12) of the effective damping equal to 17.1% was found, which matches very well the values previously obtained from cyclic tests (see Fig. 4). Another numerical parameter to be calibrated is the duration of the collision (tmax). The maximum force exchanged between the two impacting bodies (Fmax) is then obtained from the relationship of the impulse of force vs. tmax and Fmax (see Fig. 15). According to the Hertz’s law, indeed, the impulse of force (I) depend on the mass and impact velocity of the projectile only, being equal to 2.28 kNs for the impact under consideration. The duration of the collision (tmax) has been evaluated by a general curve-fitting procedure in the timedomain. The duration of the impulse has been optimised by fitting the numerical displacement–time histories of the external shell to the experimental ones recorded by the wire transducers T1x, T2x, T3z and T4z, through the least-square method. The duration of the impulse was varied from 0.001 to 0.1 s. The optimal value was found to be 0.03 s. It is interesting to note that the duration of the impulse suggested by the Hertz’s law, equal to 0.017 s, results quite similar to the value obtained numerically, through curve-fitting with the experimental outcomes. Fig. 16 compares the experimentally recorded displacement–time histories to those provided by SAP2000, assuming an impulse of force having 0.03 s duration. The experimental curves are identified by the sensor label (i.e., T1x, T2x, T3z and T4z) and by their location on the Shelter (i.e., on the left or right side). The numerical curves are indicated by (a) and (b). Obviously, no difference between the left- and right-side displacements of the external shell are found in the numerical model, due to the symmetry of the structure and of the load condition. The only difference between the two numerical curves reported in each diagram is the magnitude of the maximum impact force. The curves indicated with (a), indeed, refer to an impulse of force equal to 2.28 kNs, corresponding to a maximum impact force of 152 kN, while the curves indicated with (b) refer to an impulse of force equal to 1.6 kNs (i.e. 70% lower), corresponding to a maximum impact force of 106 kN. This reduction could be justified by the loss of energy which surely occurred during the impacts. Part of the input energy, indeed, is absorbed (and then released) through the elastic deformation of the rubber layer, part is dissipated through the plastic deformation of the steel cap (as experimentally observed at the end of the tests) and part is consumed in concrete cracking. The impact modelling, being perfectly elastic, does not take into account the aforesaid aspects. Under the above-mentioned hypotheses, the numerical model seems to be able to capture with reasonable accuracy the experimentally recorded dynamic response of the external shell. It is worth to emphasise that a certain discrepancy between experimental and numerical displacements was expected, due to some differences between test and numerical model (e.g., in the geometry of the external shell), as well as due to the errors inherent in the comparison between experimental and numerical displacements. To this regard, it is sufficient
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
699
α
α' α' /
2
ωb ωr ωa
ω
Fig. 14. Procedure used for the evaluation of the effective damping associated to the dominant mode of vibration of the external shell.
Fig. 15. Schematization of the impulse of force generating during the impact.
to underline two aspects. Firstly, in the numerical model the effects due to the self-weight of the external shell are neglected. As a consequence, at the beginning of the analysis, the devices are assumed to be unloaded and the external shell parallel to the global reference system. Secondly, the numerical displacements in Fig. 16 represent the horizontal (or vertical) components of displacement of the points of the external shell where sensors are connected. Actually, the transducers do not provide horizontal (or vertical) components of displacement, but rather variations of length. For the transducers T1x and T2x (see Fig. 5) the error in assuming the displacement recorded by the sensor as horizontal component of displacement is quite negligible, due to the their large length. The same does not hold for sensors T3z and T4z (see Fig. 5). For this reason, a modification factor has been calculated to transform the signals recorded by T3z and T4z in vertical components of displacement. It has been calibrated by referring to the peak displacement, leading to some approximations for the intermediate displacements. In the light of these considerations, the comparison between experimental and numerical displacements can be considered to be satisfactory. 7. Summary and conclusion An impact-resisting reinforced concrete structure for volcanic shelters has been designed, engineered and tested at the University of Basilicata (USB). It basically consists of two homologous reinforced concrete shells,
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
700
10 5 (mm)
0 -5 -10
T1x_right
-15 -20 -25 59.75
T1x_left
(b) (a) 59.85
59.95
60.05
60.15 (sec)
60.25
60.35
60.45
60.55
60.25
60.35
60.45
60.55
60.25
60.35
60.45
60.55
60.25
60.35
60.45
60.55
10 T2x_left
5
(mm)
0 -5 -10
T2x_right
-15 -20 -25 59.75
(b)
(a) 59.85
59.95
60.05
60.15 (sec)
10 T3z_right
5
(mm)
0 -5 T3z_left
-10 -15 -20 -25 59.75
(b)
(a) 59.85
59.95
60.05
60.15 (sec)
10 T4z_right
5
(mm)
0 -5 -10 -15
T4z_left
-20 -25 59.75
(b) (a)
59.85
59.95
60.05
60.15 (sec)
Fig. 16. Comparison between the displacement–time histories experimentally recorded during the Test no. 4 and the numerical displacement–time histories produced by an impulse of force having 0.03 s duration, and magnitude equal to (a) 100% and (b) 70% of the theoretical value.
interconnected by suitable flexible and highly dissipative devices, which absorb and dissipate most of the impact energy, thus avoiding damages to the reinforced concrete structural members. The Shelter was specifically thought to be installed on the Stromboli volcano (Aeolian archipelago, Sicily, Italy), to protect human lives from pyroclastic eruptions.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
701
In this paper the impact tests carried out at the Laboratory of Structures of the University of Basilicata (USB) are described and the most important experimental results are examined. The experimental tests were performed on a 1:2-scale model of the Shelter, using a testing apparatus, which was purposely realised to simulate impact conditions comparable with that considered at the design stage. Eight different impact tests were conducted, by considering two different levels of impact energy and four different mass ratios between projectile and R/C shell. A refined finite-element model of the Shelter was also implemented and a series of direct-integration time-history analyses were then carried out, to validate the experimental results. The tests clearly proved the ability of the Shelter to resist the impacts without appreciable damage. As a matter of fact, only some minor hairline cracking, close to the impact area, were observed at the end of the tests. The maximum displacements of the external shell (of the order of 20–25 mm for the 1:2-scale model, under the most severe impact) were found to be much lower than the available distance (about 75 mm for the 1:2-scale model) from the internal shell. Actually, the maximum displacements under the design impact conditions are expected to be approximately two times greater than those recorded during the tests. Moreover, impacts may occur at the extremities of the shell. For all these reasons, the clearance between external and internal shell will be kept equal to the design value (i.e. 150 mm) in the full-scale structure. Some additional information was also obtained from the examination of the test results, as well as from the comparison with the numerical simulations. They can be summarised as follows: (i) the maximum displacements of the external shell increase quite linearly with the mass ratio between projectile and external shell, and less than linearly with the impact energy, (ii) a significant de-amplification in the peak acceleration experienced by the internal shell is found, compared to the external shell, (iii) the Hertz’s law is found to predict the impulse of force generated during the impact with reasonable accuracy. Finally, the comparison between numerical and experimental results proves the suitability of the finite-element model used in the design to simulate the dynamic response of the shelter to the impact loading. Further applications for the impact-resisting structure described in this paper, even different from the original aim, may be proposed in the future. Acknowledgements The present study has been funded by the Italian Department of Civil Protection, within a contract with the University of Basilicata. The design of the shelter has been made by M. Dolce, R. Marnetto and D. Cardone. The impact-absorbing devices ADRI have been produced by TIS S.p.A.. The cement and the additives for the test model have been provided by Italcementi S.p.A., that also collaborated in the study of the concrete mix. References [1] Pasquare0 G, Francalanci L, Garduno VH, Tibaldi A. Structure and geological evolution of the Stromboli volcano, Aeolian Islands, Italy. Acta Vulcanol 1993;3:79–89. [2] Halliday D, Resnick R, Walker J. Fundamentals of physics, 6th ed. Wiley; 2002. [3] Dolce M, Cardone D, Marnetto R. Structural design and analysis of an impact resisting structure for volcanic shelters. Engineering Structures, Elsevier Science Ltd: Oxford, UK, in press. [4] Dolce M, Cardone D, Marnetto R, Nigro D, Palermo G. A new added damping rubber isolator (ADRI): experimental tests and numerical simulations. Proceedings of the eighth world seminar on seismic isolation, energy dissipation and active vibration control of structures, Yerevan, Armenia, October, 2003. p.483–92. [5] Harris HG, Sabnis GM. Structural modelling and experimental techniques. Washington, DC: CRC Press; 1999. [6] Jones N. Structural impact. Cambridge, MA: Cambridge University Press; 1989. [7] Woo K, El Atter A, White RN. Small-scale modelling techniques for reinforced concrete structures subjected to seismic loads. Technical report no. NCRRR 88-0041, State University of New York at Buffalo, 1988. [8] EUROPEAN COMMITTEE FOR STANDARDIZATION. pr EN 197-1. Cement—Part 1: Composition, specifications and conformity criteria for common cements, Brussels, February 2000. p. 29. [9] Chopra AK. Dynamics of structures. London: Prentice-Hall International Inc.; 1995. [10] Computers and Structures Inc. SAP2000_Nonlinear: analysis reference manual (Version 9.4), Berkeley (CA), 2004. [11] Hertz H. On the contact of solids—on the contact of rigid elastic solids and on hardness [Translated by D. E. Jones and G. A. Schott]. London: MacMillan and Co. Ltd; 1896. [12] Timoshenko S, Goodier JN. Theory of elasticity. New York: McGraw Hill Inc.; 1951. [13] Ewins DJ. Modal testing: theory and practice. New York: Wiley; 1984.
International Journal of Impact Engineering 34 (2007) 681–701 www.elsevier.com/locate/ijimpeng
Dynamic response of a volcanic shelter subjected to ballistic impacts Mauro Dolce, Donatello Cardone, Claudio Moroni, Domenico Nigro Department of Structure, Geotechnics and Applied Geology, University of Basilicata, Macchia Romana, 85100 Potenza, Italy Received 10 September 2005; received in revised form 10 January 2006; accepted 14 January 2006 Available online 4 April 2006
Abstract This paper presents the results of a series of experimental tests, aimed at investigating the impact and dynamic response of a volcanic shelter. Similar shelters are to be installed in the Stromboli island (Aeolian archipelago, Sicily, Italy), to protect human lives from the pyroclastic eruptions of the volcano. Basically, the Shelter consists of two homologous reinforced concrete shells, interconnected by rubber-based special devices, which absorb and dissipate most of the impact energy. The Shelter has been specifically designed to resist, without damage, an impact with a 150 kg mass rock, knocking the surface of the external shell at 62.5 m/s speed. The experimental tests were carried out on a 1:2-scale model, using a testing apparatus purposely realised to simulate impact conditions comparable with those considered in the design. Impact energy and mass ratio between projectile and reinforced concrete shell were assumed as main experimental parameters and varied during the tests. A finite element model of the Shelter was also implemented and direct-integration time-history analyses were performed, to validate the experimental results. Reference to the Hertz’s law was made to simulate the impact between the two bodies. The experimental tests proved the ability of the Shelter to resist impacts without damage. Acceptable agreement between numerical predictions and experimental results was found. r 2006 Elsevier Ltd. All rights reserved. Keywords: Impact testing; Dynamic response; Hertz’s law; Impact-absorbing devices; Numerical analyses
1. Introduction On September 2003, the Italian Dept. of Civil Protection (DPC) entrusted the University of Basilicata (USB) to make theoretical and experimental studies finalised at designing and engineering a volcanic shelter to be installed in the Stromboli island, near Sicily (Italy), where an active volcano frequently produces pyroclastic eruptions [1]. Several monitoring, research and tourist activities are carried out in the area of the volcano. In order to protect the human lives from the risks of a pyroclastic eruption, the DPC planned to place a series of Shelters in strategic sites that can be reached in few seconds by people nearby, along paths traced on the flanks of the volcano. Corresponding author. Tel.: +39 0971 205052; fax: +39 0971 205052.
E-mail address: [email protected] (M. Dolce). 0734-743X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2006.01.002
ARTICLE IN PRESS 682
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
The main performance requirement demanded by DPC for the Shelter was the capability of resisting, without significant damage, an impact with a 0.5 m diameter rock (approximately 150 kg mass), arriving from 400 m distance, after reaching a maximum height of 100 m. The aforesaid basic assumptions result in an impact velocity of the falling rock of about 62.5 m/s (corresponding to an impact energy of some 293 kN m) and in an attack angle of 451, as obtained from the well-known equations describing the motion of a projectile [2]. The other requirements demanded in the design of the Shelter were related to specific concerns (i.e. transportation and assembling operations by helicopter, durability in an aggressive environment, low visual impact in a protected landscape), which are of lesser importance for the scope of this paper, though they played an important role at the design stage. The activities for the complete development of the final design of the Shelter required three phases: Phase 1: Conceptual design of the Shelter, numerical modelling of the impact between falling rock and Shelter, response analysis, design of the Shelter; Phase 2: Design and construction of a reduced-scale model of the Shelter, to be tested under the impact conditions similar to those considered at the design stage; Phase 3: Test set up, experimental testing, analysis of the results. The theoretical and numerical studies carried out during Phase 1 are described in [3]. They led to the design and implementation of a shield-structure (i.e. the Shelter), consisting of two homologous R/C shells, interconnected by suitable impact-absorbing devices. This paper describes the experimental activities carried out during Phase 3 and the most important related results. The experimental tests were carried out on a 1:2-scale model of the Shelter, using a particular testing apparatus, purposely designed and realised at the USB Lab, to simulate impact conditions similar to those considered at the design stage. Eight impact tests were performed, with two different levels of impact energy and four different mass ratios between projectile and R/C shell, as described below. The dynamic response of the Shelter to the considered impact conditions was captured through 18 sensors, i.e., 10 displacement transducers and 8 accelerometers. The finite element model of the Shelter, implemented during Phase 1, was updated based on the experimental outcomes of the impact tests. Direct-integration time-history analyses were then performed, by SAP2000 [10], and the numerical results compared to the corresponding experimental ones. 2. Description of the shelter The impact resisting structure for volcanic shelters basically consists of two homologous R/C shells, connected by suitable impact-absorbing devices. The external shell resists the falling rock elastically, with possible minor damages (e.g. spalling of concrete cover) limited to the impact area. Most of the impact energy is absorbed, and then dissipated, by special devices connecting internal and external shell. The internal shell, where people are recovered, is thus practically not affected by the impact. Fig. 1 shows the different parts composing the Shelter. They include: (i) the foundation, consisting of a Cshaped reinforced concrete 290 mm thick basement, equipped with a backside tie tooth, 300 mm thick and 1 m high (see Fig. 1(d)); (ii) the internal R/C 100 mm thick shell, equipped with two lateral 150 mm thick R/C panels (see Fig. 1(a)); (iii) the external R/C 180 mm thick shell (see Fig. 1(e)), connected to the internal one by means of two lateral 10 mm thick steel plates; (iv) four impact-absorbing devices (two each side, as shown in Fig. 1(b)), based on rubber and viscous material, sandwiched between the steel plates of the external shell and the R/C panels of the internal shell (see Fig. 1(c)). Each structural component of the Shelter has a specific function. The external shell is deputed in front of the falling rocks. The impulse of force developing during the impact results in kinetic energy for the external shell and, as a consequence, gives rise to an initial (translational+rotational) velocity. The impact-absorbing devices provide the necessary stiffness and energy dissipating capability to control and damp the free vibrations of the external shell. The internal shell transfers the forces transmitted by the devices to the foundation. The overall stability to sliding and overturning movements is guaranteed by the foundation, with the help of the backside tooth. The overall dimensions of the Shelter (foundation included) are 4.16 m in the longitudinal direction (Y-direction in Fig. 1), 2.46 m in the transverse direction (X-direction), 3.25 m in the vertical direction
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
683
z
y
x
(a)
(b)
(c)
(e)
(d)
(f)
(g) Fig. 1. Assembling of the Shelter: (a) internal R/C shell, (b) installation of the impact-absorbing devices, (c) installation of the lateral coupling plates, (d) foundation structure, consisting of a R/C basement equipped with a backside tooth, (e) external R/C shell, (f) sub-assemblage including the foundation structure plus the internal shell, (g) Shelter as a whole.
ARTICLE IN PRESS 684
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
(Z-direction). The clean height off-ground in the rear part is 1 m, due to the partial embedment of the Shelter in the earth from behind, in order to reduce the visual impact. The clean internal dimensions are about 3 m length, 1 m width and 1.8 m height, so that at least 10 people can be safely arranged inside, in case of danger. Visco-elastic devices, referred to as Added Damping Rubber Isolators (ADRIs) [4], have been used as impactabsorbing devices. Originally conceived for seismic isolation, ADRI basically consists of a cylindrical laminated rubber bearing with the central hole filled with highly viscous material. ADRIs are mounted in the shelter to be shear-strained when the external shell moves, due to the impact of falling rocks. The shear stiffness of ADRI is a function of the ratio between the cross-sectional area of the device and the total thickness of rubber. It also depends on the shear modulus of rubber, which progressively reduces while increasing shear strain [4]. The damping provided by ADRI is a function of the ratio between inner and outer diameter, as well as of the infill viscosity. Damping ratios of the order of 20% can be easily obtained at high frequency [4]. Besides having no mechanical moving parts, a main advantage of ADRI is the nature of damping, which is mainly viscous rather than hysteretic, so that it does not accumulate inelastic residual deformations after the impact. Moreover, the maximum force exerted by the viscous infill is out-of-phase with respect to the elastic force of the rubber component, so that the energy dissipation is almost quadratic with displacement. Other favourable features of ADRI are its compactness and limited sensitivity to temperature variations. More detailed information on the characteristics of the Shelter structure can be found in [3].
3. Test model and sensor set up A 1:2-scale model of the Shelter has been realised at USB to be tested under impact conditions. The test model was derived from the full-scale prototype, by applying the requirements for geometrically similar scaling [5,6]. Table 1 summarises the scale factors to be used for perfect similitude with a full-scale structural model working in the elastic range under dynamic loading. Practically, there are only two independent scale factors: that relevant to lengths (SL) and to the Young’s modulus of material (SE). All the other scale factors can be expressed as a function of the previous two. For R/C models, the reinforcement of the structural members is usually made of ordinary steel. This implies that a scale factor SE ¼ 1 must be used for both concrete and steel. In Table 1, two different sets of scale factors are reported. This is because the experimental tests described in this paper consists of three parts: (i) the reproduction of the effects due to self-weight, (ii) the simulation of the
Table 1 Similitude requirements for reduced-scale test models working in elastic regime under dynamic loading Parameter
Dimension
Scale factora
Scale factorb
Length Stress Strain Modulus of elasticity Stiffness Force Energy Mass Acceleration Velocity Displacement Time Period of vibration Frequency of vibration
L FL2 — FL2 FL1 F FL FT2L1 LT2 LT1 L T T T1
SL SE 1 SE SESL SES2L SES3L S3L S1 L 1 SL SL SL S1 L
SL SE 1 SE SESL SES2L SES3L S2L 1 S1/2 L SL S1/2 L S1/2 L S1/2 L
a
Reduction factors for perfect similitude of impacts. Reduction factors for perfect similitude of self-weight and free-vibrations.
b
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
685
impact between falling rock and external shell and (iii) the simulation of the free-vibrations of the external shell following the impact. As a matter of fact, the scaling law which applies for (ii) is different from that which applies for (i) and (iii) [5]. In impact engineering, experimental tests are generally carried out on small-scale specimens, geometrically similar to the full-scale prototype and subjected to the same impact velocity. In this case, times are reduced by SL and masses by S3L. As a consequence, accelerations are amplified by SL. The gravity acceleration, however, does not change. This introduces a distortion in the model. Actually, impact tests are primarily conducted with the scope of investigating phenomena like penetration, perforation, buckling, etc. Gravitational forces are not significant, when compared to the dynamic forces generated in the impact, and can be neglected [6]. When the problem is governed by the frequency of vibration of the structure (e.g. free-vibrations, response to harmonic and periodic excitations, seismic-induced vibrations, etc.) and gravity loads are not negligible, a different approach is followed [5]. Experimental tests are carried out on specimens geometrically similar to the full-scale prototype and subjected to the same acceleration. In this case, times are reduced by S1/2 L and masses by S2L. This results in the perfect simulation of inertial, gravity and restoring forces. Further explanations about this concern are given below. Coming back to the test model, it is worth to emphasise that extreme care was taken in choosing the concrete composition for each structural member of the Shelter, as the mechanical properties of a microconcrete can significantly differ from those of a standard concrete [7]. At this aim, a proper selection of (i) granulometry of the aggregate, (ii) aggregate/cement ratio and (iii) water/cement ratio was made. Several mixes were manufactured and tested. The mix selected for the internal and external shell was characterised by a washed sand with grain size lower than 5 mm, a water/cement ratio of 0.32 and an aggregate/cement ratio of 3.68. A fluidifying additive (Multiflux-AximII), about 2% the weight of the cement, was used. The mix selected for the basement was made of washed sand and gravel with grain size lower than 10 mm, a water/cement ratio of 0.44 and an aggregate/cement ratio of 3.68. The fluidifying additive was about 1% the weight of cement. In both cases, cement type 42.5 N [8] was used. Compression tests, carried out just 3 days after casting, provided about 32 N/mm2 average compression strength for the basement and 40 N/mm2 for the shells, to be compared to the design strength of concrete after 28 days, taken equal to 35 N/mm2. Reference to FeB38k steel (375 N/mm2 characteristic yield strength) was made in the design. The same type of steel was adopted for the test model. The steel reinforcement was firstly designed for the full-scale prototype and then reported to the model scale by halving the bar diameter. Ribbed bars of 6 and 8 mm diameter were used in the test model. As an example, Fig. 2 shows the arrangement of the steel reinforcement adopted for the external shell, which is the only component of the Shelter directly impacted by the projectile. As can be seen, the reinforcement of the external shell consists of two grids (one each face) realised by means of 8 mm diameter bars at 50 mm spacing. The grids are connected by 6 cross-ties per square meter, 8 mm diameter, not shown in the figure. For simplicity, the spacing of the reinforcing bars has been maintained constant over the whole shell. The structural elements of the model were cast by using common wooden form works. This produced some imperfections in the shape of the shells, which were accurately surveyed. In particular, the weight of the external shell, which assumes great importance in the impact response of the Shelter, was measured by a dynamometer. It resulted equal to about 8.4 kN, i.e. about 25% greater than expected. Similarly, the actual position of the centre of mass was evaluated by suspending the external shell from the bridge crane. A shift of several millimetres, in both the horizontal and vertical direction, was found, in comparison with the theoretical position of the centre of mass. All that was properly taken into account in view of the experimental tests. First of all, the additional masses to be used to satisfy the mass-similitude requirements for gravity loads and free-vibrations (see Table 1, column 4), were proportioned by referring to a self-weight of the external shell of 8.4 kN. Thus, 4 kN (400 kg mass) were added to get a total weight of 12.4 kN, corresponding to the weight of the external shell in the prototype scale divided by 4. To this end, 40 steel masses (10 kg each) were placed on the external shell, as shown in Fig. 3. The steel masses were inserted inside threaded bars, pre-arranged along the lateral thickness of the external shell. Moreover, the relative position of external and internal shell was revised, in order to eliminate the accidental additional eccentricity between centre of mass of the external shell and centre of
ARTICLE IN PRESS 686
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
Fig. 2. Arrangement of steel reinforcement in the external shell.
stiffness of the impact-absorbing devices. After these adjustments, the test configuration can be considered to reproduce the design configuration satisfactorily. The test model was directly placed on the laboratory floor and then fixed, on the rear, through a couple of threaded bars (see Fig. 3). The threaded bars transfer their action on a UPN steel section, which simulate the presence of the backside tooth. Fig. 4 shows the experimental force vs. displacement behaviour, under cyclic loading, of one impactabsorbing device (ADRI) used in the Shelter during the impact tests. It is characterised by two rubber layers of 48 mm thickness each, an interposed steel shim of 5 mm thickness, outer diameter of 225 mm and inner diameter of 150 mm. In the cyclic test in Fig. 4, the frequency of loading is 0.5 Hz while the displacement amplitude increases from 10 to 30 mm, corresponding to a rubber shear strain of 5% and 15%, respectively.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
687
Reacting wall
Longitudinal jack
Gun
Additional masses
Transverse jack Steel cap
Fig. 3. Test apparatus, including an Enerpac actuator for pre-loading the spring placed inside the gun and a Technotest jack for removing the stop which restrains the projectile put at the top of the spring.
As can be seen, ADRI exhibits a visco-elastic mechanical behaviour which in principle could be described by just two numerical parameters: effective stiffness and effective damping [9]. Their values are reported in the same figure, for each displacement amplitude considered. The effective stiffness practically halves, passing from 0.43 to 0.21 kN/mm, when the displacement amplitude increases from 10 to 30 mm. The effective damping is around 17% at 10–20 mm, then reducing to 15.5% at 30 mm. The effective stiffness of ADRI was found to increase while increasing the strain rate (i.e. frequency of loading) [4]. It is expected that the values provided in Fig. 4 underestimate the actual stiffness exhibited by the devices during the tests, as the frequencies of loading experienced by ADRIs after the impacts are considerably greater than 0.5 Hz.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
688
8
0.5
Effective stiffness 6
0.3 0.2
Shear force (KN)
(KN/mm)
0.4
0.1 0.0 5 mm
20 mm
30 mm
4
2
0 -40
-30
-20
-10
0
10
20
30
40
Displacement (mm) -2
20
-4
Effective damping
-6
(%)
15 10 5 0 -8
5 mm
20 mm
30 mm
Fig. 4. Experimental force–displacement behaviour, under cyclic loading of increasing amplitude, of the impact-absorbing device used in the Shelter. Frequency of loading equal to 0.5 Hz. The inner bar-diagrams show the effective stiffness and the effective damping exhibited by the device as a function of displacement amplitude.
As shown in Fig. 5, 18 sensors were used to capture the dynamic response of the Shelter after the impacts, namely: (a) eight Celesco wire transducers (T1x, T2x, T3z, T4z in Fig. 5), measuring absolute displacements of specific points of the external shell (b) two Penny-Gauss LVDTs (T5x in Fig. 5), measuring possible sliding movements of the basement, (c) eight Columbia accelerometers, with 72 g range (A1x, A2x, A3y, A4x in Fig. 5), measuring the longitudinal and transverse accelerations experienced by the internal and the external shell. The sensors were arranged symmetrically on the left and right side of the Shelter, as shown in Fig. 5. Starting from the displacements recorded by the wire transducers T1x, T2x, T3z, T4z during each test, the rigid-body displacements and rotations of the external shell have been derived. Subsequently, the maximum displacements in the four impact-absorbing devices have been obtained, as in the graphical construction shown in Fig. 6. The initial configuration of the external shell is identified by the initial position of the wire transducers (marked by 1, 2, 3 and 4 in the figure), directly assessed on the model before the tests. The deformed configuration of the external shell is obtained by translating and rotating it, up to comply with the displacements measured by all the transducers (points 10 , 20 , 30 and 40 in Fig. 6). Finally, the displacements generated in the devices are assumed equal to the distance between the points a–a0 and b–b0 . As shown in Fig. 6, the initial configuration of the external shell depends also on the effects of the selfweight, which can be summarized in about 40 mm vertical displacement of the mass centre and in about 71 rotation, around the Y-axis. This, in turn, produced different vertical displacements in the devices, of the order
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
689
right z
x
T1x
y
A4x
left
T2x T3z
A3y
T1x
A1x
T5x
A2x T4z T2x T3z
T5x Fig. 5. Sensor set up. T1x, T2x, T3z and T4z are wire-transducers measuring absolute displacements of the external shell. A1x, A2x, A3y, A4x are accelerometers, measuring the longitudinal and transversal accelerations experienced by internal and external shell. T5x are LVDTs measuring possible sliding movements of the basement.
of 30 mm in the upper ones, and practically negligible in the lower ones. Due to the dependence on the displacement, therefore, the two couples (upper and lower) of ADRIs had different effective stiffness under the impact, according to the diagram shown in Fig. 4. The effects of the self-weight may be eliminated by adding a couple of auxiliary steel components, as discussed in [3]. 4. Experimental program and test apparatus In the experimental program under considerations, tests were carried out on two different configurations of the Shelter, i.e. with or without (w/o) additional masses. The configuration with additional masses intended to reproduce the effects of self-weight and the freevibrations of the external shell following the impact. Obviously, the greater mass of the external shell (about 1240 kg instead of 625 kg) was expected to significantly attenuate the effects caused by the impact and in particular the initial velocity of the external shell. In order to substantially comply with the real impact conditions, the projectile mass was increased from about 19 kg (i.e. 150 kg divided by 8) to about 37 kg. In this way, the same mass ratio between projectile and external shell (about 3%) and the same kinetic energy of the projectile (about 36.6 kN m), as the design impact, was obtained. By assimilating the impact between projectile and shell to a head-on elastic impact between two spheres, the initial velocity of the external shell after the
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
690
4 4’
T1x
up b b’
down a a’
2 2’
3 3’
1 1’
T2x
T3z
T4z
Fig. 6. Graphical construction for the evaluation of the maximum displacements in the devices from the peak displacements in the wiretransducers. The points 1,2,3 and 4 indicate the positions of the sensors at the beginning of the test. The points 10 ,20 ,30 and 40 indicate the positions of the sensors when the maximum displacements are attained.
Table 2 Test program Test no.
Projectile weight (kN)
Impact energy (kN mm)
Impact velocity (m/s)
Additional weight (kN)
Shell weight (kN)
Mass ratio (%)
1 2 3 4 5 6 7 8
0.37 0.37 0.27 0.27 0.37 0.37 0.27 0.27
17,120 25,456 18,946 26,435 17,745 27,555 17,542 25,589
30.4 37.1 37.5 44.3 31.0 38.6 36.0 43.5
0 0 0 0 4 4 4 4
8.4 8.4 8.4 8.4 12.4 12.4 12.4 12.4
4.4 4.4 3.2 3.2 3.0 3.0 2.2 2.2
collision was expected to be 2.56 m/s, i.e. about 30% less than the design value (3.65 m/s). This implies a reduction of the same order of magnitude in terms of both maximum displacements and maximum forces experienced by the Shelter during the free-vibrations following the impact. A further reduction of the order of 15% should be taken into account, due to the real testing conditions (see the impact energy of Test no. 6 in Table 2). The effects of self-weight and the frequency of vibration of the external shell under free-vibrations, instead, are captured with accuracy. The configuration of the Shelter w/o additional masses was aimed at reproducing the perfect similitude during the impact. Thus, in principle, masses were divided by 8 and impact velocity was maintained constant, i.e. equal to 62.5 m/s. The velocity of the external shell resulting from the impact was expected to be exactly 3.65 m/s, while a certain underestimation of the effects due to self-weight and of the frequency of vibration of the external shell was implicitly accepted. In practice, two problems occurred, which led to a significant deviation from the aforesaid test conditions. The first discrepancy was the actual mass of the external shell,
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
691
which resulted equal to about 840 kg, instead of 625 kg. The second discrepancy derived from the operative limits of the hydraulic jack, used to pre-strain the rubber spring placed inside the testing device. The maximum stroke of this jack was 400 mm, corresponding to a maximum strain energy of the spring of about 26–27 kN m, instead of 36.6 kN m. The projectile mass was then increased from about 19 to 26.5 kg, in order to get the same mass ratio (about 3%) between projectile and external shell and the same impulse of force (about 2.3 kNs) as the real impact. By assimilating the impact between projectile and shell to a head-on elastic impact between two spheres, the initial velocity of the external shell is found to be of the order of 2.75 m/s, i.e. about 25% less than the design value (3.65 m/s). Actually, a much greater underestimation of the maximum effects (displacements and forces) experienced by the Shelter during the free-vibrations following the impact is expected, due to the significant overestimation of the frequency of vibration of the external shell. To a first estimation, the maximum displacements observed in the benchmark test on the model w/o additional masses (i.e. Test no. 4 in Table 2) should be multiplied by about 2, to be consistent with the actual response of the Shelter. As a matter of fact, none of the experimental tests carried out on the reduced-scale model of the Shelter exactly reproduces the design impact conditions. However, they provide a clear understanding of the actual response of the Shelter, under impacts still comparable with that considered at the design stage. More importantly, the results of the experimental tests performed on the reduced-scale structural model can be exploited to validate the numerical model used at the design stage for safety verifications [3]. Table 2 summarises the experimental tests carried out on the 1:2-scale model of the Shelter. Eight consecutive tests were performed, differing in the impact energy and in the mass ratio between projectile and external shell. Two different levels of impact energy have been considered, one corresponding to about 25.5–27.5 kN m, the other approximately to 70% of that. In addition, four different mass ratios, ranging from 2.2% to 4.4%, have been considered, by using two different projectiles (having 27 and 37 kg mass, respectively), on two different configurations of the external shell (with or without the additional 4 kN weight). The impact velocity associated to each impact test is also reported in Table 2. A testing device (see Fig. 3) was purposely designed and realised at USB, to simulate the impacts considered at the design stage of the Shelter. Basically, it consists of a steel tube equipped with a mechanical stop driven by two hydraulic jacks (50 kN max. force and 100 mm stroke). The tube is fixed to a stiff reacting wall. A rubber spring of proper stiffness is arranged inside the tube and pre-strained by a hydraulic jack (2000 kN max. force and 400 mm stroke) placed behind it. The spring consists of a series of 10 consecutive rubber cylinders (each with 125 mm diameter and 75 mm height) alternated with 10 thin steel plates (each with 200 mm diameter and 5 mm thickness). The steel plates exert a confining action on the rubber cylinders, which avoids their buckling during the loading phase. Actually, the spring also plays the role of projectile, having a mass of about 19 kg. A supplemental mass of 8 or 18 kg, consisting of a cylindrical block with 200 mm diameter, made of Fe510 tempered steel, is placed at the top of the spring, to get a total mass of 27 or 37 kg, respectively. When the mechanical stop is removed, the projectile is shot, at a given velocity, against the external shell. The impact point was located in the middle of the Shelter, approximately where the normal to the surface of the external shell passes through its centre of mass. Actually, other five impact conditions, differing from that reproduced during the experimental tests, were considered at the design stage. They included impacts on the lower and upper extremity of the external shell, both in the middle and in the lateral section of the Shelter [3]. The impact position considered for the experimental tests was selected being the more dangerous in terms of stresses induced in the external shell. A steel cap with spherical surface was placed on the surface of the R/C shell and centred in the impact point (see Fig. 3). Between the steel cap and the surface of the shell, a 10 mm thickness rubber layer is interposed, with the scope of avoiding localized damages (e.g. spalling of concrete cover), in view of the numerous tests to be conducted. The presence of the rubber layer surely caused a certain loss of the energy transferred to the Shelter during the impact. Another consequence is a longer duration (to the detriment of the peak force) of the impulse generated during the impact, compared with the case of direct contact between rock and concrete surfaces. A series of numerical analyses have been carried out to examine this aspect, as discussed below. Fig. 7 shows the loading curve of the rubber spring placed inside the testing device for one test (Test no. 4 in Table 2). The force–displacement relationship in Fig. 7 was obtained by applying (with the longitudinal
ARTICLE IN PRESS 692
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
210
180
150
(KN)
120
90
60
30
0 0
60
120
180
240
300
360
420
(mm) Fig. 7. Loading curve of the spring for one significant test (Test no. 4 in Table 2).
hydraulic jack in Fig. 3) an increasing compression force on the spring. The force was increased up to reaching the maximum stroke of the spring (400 mm). Then, the mechanical stop was removed by the transverse jacks. The strain energy accumulated before removing the mechanical stop is given by the area under the curve. Under the hypothesis of energy conservation, the strain energy of the spring is equal to the kinetic energy of the projectile when it impacts the Shelter. As can be noted in Table 2, a certain scatter in the impact energy of the tests has been observed, due to a slight hysteresis of the spring (see Fig. 7). This has been accepted and then taken into account when comparing the results of the tests, as explained below. 5. Summary of the experimental outcomes The most important experimental outcome is that the Shelter resisted eight impacts, comparable with that assumed in the design, without suffering significant damage. Actually, the damages observed at the end of the test program, through an accurate visual inspection of the structure, were limited to some hairline cracking in the concrete of the external shell, close to the impact area. Two major parameters have been considered to describe the dynamic response of the external shell caused by the impacts, namely: the peak accelerations experienced by the internal and the external shells and the maximum displacements attained in the four impact-absorbing devices. Fig. 8 shows the maximum displacements of ADRIs as a function of the mass ratio between projectile and external shell. Two different diagrams are reported, each relevant to a different level of impact energy. In particular, Fig. 8(a) refers to the lower energy-content tests (Test nos. 1-3-5-7 in Table 2), while Fig. 8(b) refers to the higher energy-content tests (Test nos. 2-4-6-8 in Table 2). The ith displacement of each diagram is slightly modified by a normalisation factor, equal to the ratio between the impact energy associated to Test no. 7 or 8, respectively, and that associated to the ith test. The four devices are identified by their location inside the Shelter, i.e. on the right or left side (see Fig. 5), up or down (see Fig. 6) in the same side. As can be seen, the trend is practically linear with the mass ratio and the slope of the tendency lines is quite similar, being a bit greater for the higher energy-content tests. The maximum displacements increase, on average, by about 10%, for the upper-placed devices, and by about 18%, for the lower-placed devices, while
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
693
Maximum displacements of ADRI’s (mm)
25
20
15
10
Right_down Right_up
5
Left_down Left_up
0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 Mass ratio (%)
(a)
Maximum displacements of ADRI’s (mm)
25
20
15
10
Right_down Right_up
5
Left_down Left_up
0 (b)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 Mass ratio (%)
Fig. 8. Maximum displacements attained in the devices after the impacts. The maximum displacements are reported as a function of the mass ratio between projectile and external shell (see Table 2), for two different levels of impact energy, approximately equal to (a) 17,550 kN mm and (b) 25,600 kN mm, respectively.
the input energy increases by about 48% (compare Fig. 8(a) with Fig. 8(b)). It should be noted that the slight deviation from the linear trend, observed in Fig. 8, is probably due to the different configuration of the Shelter, as the tests associated to 4.4% and 3.2% mass ratios have been performed before the others, with a reduced additional mass. The addition of 4 kN weight (see Table 2) caused about 25 mm further vertical displacement of the mass centre and about 21 rotation of the external shell. This slight change in the Shelter geometry had some influence on the test results. Fig. 9 reports the ratio between the peak transverse accelerations of external and internal shell, as a function of the mass ratio between projectile and external shell. Each curve refers to a different level of impact energy, as pointed out in the diagram. For each test, the peak accelerations of external and internal shell have been obtained by averaging the peak values measured by the relevant accelerometers, i.e. the four sensors labelled with A1x and A2x and the two sensors labelled with A4x in Fig. 5, respectively. It is worth to note that the aforesaid sensors are designed to record accelerations along a given direction, which, in the case under consideration, was the X-direction in Fig. 5. The initial deformed configuration of the external shell, due to the effects of self-weight, however, determines a not perfect correspondence between the two directions of
ARTICLE IN PRESS 694
M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
0.8
Peak acceleration ratio (internal vs. external shell)
0.7 0.6 0.5 0.4 0.3 0.2 0.1
Impact energy = 70% Emax Impact energy = Emax
0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 Mass ratio (%) Fig. 9. Ratio between the peak acceleration of the external shell and that of the internal shell, as a function of the mass ratio between projectile and external shell and for two different levels of impact energy.
measurement. As a matter of fact, the external shell is rotated by 8–101 with respect to the horizontal line. On the other hand, the rigid-body displacements of the external shell occurred along a direction rotated by about 46–511 with respect to the horizontal line. As a consequence, the acceleration components recorded by the sensors placed on the internal shell form an angle of about 46-511 with respect to the motion direction, while those recorded by the sensors placed on the external shell form an angle 8–101degrees greater. This implies that the acceleration ratios reported in Fig. 9 are a little overestimated, by about 20–25%. In any case, Fig. 9 clearly shows a de-amplification, of the order of 30–50% (depending on the mass ratio between projectile and external shell), of the peak acceleration experienced by the internal shell, compared to that recorded on the external shell. The input energy seems to play a negligible role on the effectiveness of the impact-absorbing devices, in reducing the effects transferred to the internal shell. 6. Comparison between experimental results and numerical predictions A refined finite-element model of the Shelter was realised, during the design phase, in order to verify the compliance of the structure with the main design requirements (i.e., resistance of the structural members, compatibility of the displacements of the external shell with the available distance—about 150 mm—from the internal shell, overall stability of the Shelter to sliding and overturning movements, etc.). A condition of elastic impact between falling rock and Shelter, with negligible friction between the surfaces of the impacting bodies (i.e. impact force directed orthogonally to the surfaces of the bodies, in the contact point), was assumed in the design. In the calculations, the falling rock was assumed to behave like a ball, with mass m1 ¼ 18.75 kg and initial velocity v1 ¼ 62.5 m/s, impacting on a steady body (i.e. the Shelter) with mass m2 ¼ 625 kgbm1. A force impulse of about 2.28 kNs was then obtained. The impact force vs. time relationship was supposed to follow a triangular law, characterised by two identical branches, with slope equal to 2*(Fmax/tmax). The duration of the collision (i.e. tmax) and the maximum force exchanged between the two impacting bodies (i.e., Fmax) were estimated by the Hertz’s law [11], as a function of the radii of curvature of the two impacting bodies in the contact point and of the Young’s modulus and Poisson’s ratio [12], resulting equal to 0.017 s and 268 kN, respectively. In the Hertz’s law, reference was made to a steel-rubber contact, assuming Es ¼ 210 kN/mm2 and n ¼ 0:3 as Young’s modulus and Poisson’s ratio of steel, Er ¼ 0.02 kN/mm2 (experimental value) and n ¼ 0:49 as Young’s modulus and Poisson’s ratio of rubber, Rp ¼ 100 m as radius of curvature of the projectile and Rs ¼ 0.5 m as radius of curvature of the external shell in the impact point. The model was implemented in the finite-element program SAP2000_Nonlinear [10] and a series of nonlinear direct-integration time-history analyses were then carried out, taking into account geometrical
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
695
nonlinearities through the hypothesis of large displacements, while material behaviour was considered linear. Reference to [3] can be made for a comprehensive description of the analytical model. In this paper, the numerical model is used to compare and validate reciprocally experimental and numerical results. At this end, the attention is focused on the external shell, whose movement is restrained by the four impact-absorbing devices, assuming that the internal shell is a rigid body perfectly fixed to the ground. Fig. 10 shows the finite-element mesh of the external shell. The elements used to describe the visco-elastic behaviour of the impact-absorbing devices are reported in the same figure. Three different types of finite element have been used, namely: (i) Shell-type elements (i.e. three-dimensional quadrilateral four-node elements), modelling the external shell, lateral steel plates included, (ii) Frame-type elements (i.e. threedimensional beam–column elements connecting two joints), modelling the elastic behaviour of ADRI and (iii) Damper-type elements (i.e. a two-joint connecting link with pure viscous behaviour), modelling the energy dissipating capacity of ADRI. The numerical model is made of 563 joints, 408 shell-type 90 mm thick elements, meshing the external shell, and 186 shell-type 5 mm thick elements, meshing the lateral closing steel plates of the external shell. The mass contributed by each element is lumped at the element joints. The additional masses are taken into account by properly adjusting the mass per unit volume of the shell elements. A linear elastic constitutive law has been adopted for reinforced concrete and structural steel. The dynamic response of the Shelter is mostly governed by the visco-elastic behaviour of ADRIs, which in turn can be described through two main parameters, i.e. the effective stiffness and the effective damping. Their values, as exhibited by ADRIs under cycling loading at 0.5 Hz and displacement amplitudes comparable with those recorded during the impact tests, are shown in Fig. 4. In this study, however, the availability of the impact experimental results allows the authors to identify the visco-elastic parameters of ADRIs from the acceleration response of the Shelter during each test. In this paper the attention is focused on just one test (Test no. 4 in Table 2), with the only scope of demonstrating the consistency of the experimental and theoretical results. Fig. 11 shows the acceleration–time histories recorded during the test under consideration. Figs. 11(a) and (b) refer to the signals recorded by sensors A1x and A2x (see Fig. 5) placed on the external shell, Fig. 11(c) to those recorded by sensors A4x (see Fig. 5) placed on the internal shell. It is interesting to note that the accelerations experienced by the external shell progressively reduce in amplitude, during the damped freevibration of its mass. On the contrary, the accelerations experienced by the internal shell, reduce and then increase in amplitude several times, following the time-profile of the displacements of ADRIs (see Fig 16). Fig. 12 shows the Amplitude Spectra (in RMS2 units) derived from the signals in Fig. 11, by applying the Fast Fourier Transform (FFT) [13]. As known, all the methods for the extraction of modal parameters from Frequency Response Functions (FRFs) are based on the basic assumption that in the vicinity of a resonance
Fig. 10. Finite-element mesh of the external shell.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
696
2500 A1x_right
(mg)
1500 500 -500
0
0.1
0.2
0.3
0.4
0.5
0.6
(sec)
-1500 -2500
A1x_left
(a)
2500 A2x_right
(mg)
1500 500 -500 0
0.1
0.2
0.3 (sec)
0.4
0.5
0.6
0.2
0.3
0.4
0.5
0.6
-1500 -2500
A2x_left
(b)
2500
(mg)
1500
A4x_right
500 -500 0 -1500
0.1
(sec) A4x_left
-2500 (c) Fig. 11. Acceleration–time histories recorded during the Test no. 4 in Table 2 on the (a,b) external and (c) internal shell. Each signal is identified by the label of the corresponding sensor (see Fig. 5).
the total response is dominated by the contribution of the mode with the closest natural frequency. Looking at Fig. 12, it can be observed that the modes of vibration of the external shell are well separated from those of the internal shell. Basically, three different resonance peaks (hence modes of vibration) are detected on the Amplitude Spectra relevant to the external shell. The higher contribution to the dynamic response of the external shell must be ascribed to a mode with frequency of vibration approximately equal to 6.63 Hz. The other two modes that seem to give a significant contribution to the dynamic response of the external shell have frequency of vibration around 2 and 9.9 Hz, respectively. The modal analysis associates the previous frequency values to the first, third and fifth mode of vibration of the shelter, which are the primarily excited modes by the impact under consideration. Fig. 13 shows their shapes, as obtained from modal analysis. Table 3 summarises the frequencies of vibration, compared with the experimental values, and the modal participating mass ratios of each mode. As can be seen, a good accordance between numerical and (available) experimental frequency values is found. The first and fifth modes are
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
697
basically rotational modes around the Y-axis (see Fig. 5), while the third mode is a purely translational mode in the XZ plane. The three modes under consideration excite more than 98% of the total mass of the external shell in the X- and Z-directions. The vibration frequency of the dominating mode (i.e. 6.63 Hz) can be used to evaluate the actual shear stiffness of the ADRI system during the impact test. By referring to a SDOF system with 840 kg mass, an effective shear stiffness of about 0.38 kN/mm is obtained for each device. As expected, the effective stiffness exhibited by ADRI in the impact test is greater (by about 50%) than that observed in the cyclic tests of similar displacement amplitudes (i.e. 20 mm, see Fig. 4). This increase must be ascribed to the higher frequency of the movement (4 0.5 Hz) generated in the devices during the impact test. The effective damping associated to the dominant mode of vibration of the external shell has been estimated through the procedure illustrated in Fig. 14, which is based on the evaluation of the maximum value of the curve (i.e., ja0 j) and of the frequency bandwidth of the function (ob 2oa ) corresponding to a response level of
1.E+04 A1x_right
A2x_right
|amp|
8.E+03 6.E+03
A2x_left A4x_right
A2x_right
4.E+03 A1x_left
A4x_left
A1x_right
2.E+03 0.E+00 0
5
10
15
20
25
30
35
40
(Hz) Fig. 12. Amplitude spectra, in the frequency-domain, obtained from the Fast Fourier Transforms of the acceleration–time histories in Fig. 11. Each spectrum is identified by the label of the sensor used to record the signal (see Fig. 5).
Fig. 13. Most important modal shapes of the Shelter and associated frequencies of vibration and participating mass ratios.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
698
Table 3 Frequencies of vibration and modal participating mass ratios of the first six modes of the Shelter, as obtained from modal analysis Mode
1 2 3 4 5 6
Experimental frequencies of vibration (Hz)
2 — 6.63 — 9.9 —
Modal frequencies of vibration (Hz)
2.40 6.51 6.69 8.93 9.37 16.43
Modal participating mass ratios (%) x-dir.
y-dir.
z-dir.
13.5 0.39 64.25 0.67 21.15 —
— 74.37 0.55 0.03 — 16.43
18.1 0.30 55.03 0.80 25.73 —
Comparison with the available experimental results.
pffiffiffi ja0 j= 2. The effective damping of the mode under consideration is then estimated from the following equation [13]: x ¼ ðob oa Þ=ð2or Þ.
(1)
By adopting the previous procedure, a mean value (averaged over the four curves in Fig. 12) of the effective damping equal to 17.1% was found, which matches very well the values previously obtained from cyclic tests (see Fig. 4). Another numerical parameter to be calibrated is the duration of the collision (tmax). The maximum force exchanged between the two impacting bodies (Fmax) is then obtained from the relationship of the impulse of force vs. tmax and Fmax (see Fig. 15). According to the Hertz’s law, indeed, the impulse of force (I) depend on the mass and impact velocity of the projectile only, being equal to 2.28 kNs for the impact under consideration. The duration of the collision (tmax) has been evaluated by a general curve-fitting procedure in the timedomain. The duration of the impulse has been optimised by fitting the numerical displacement–time histories of the external shell to the experimental ones recorded by the wire transducers T1x, T2x, T3z and T4z, through the least-square method. The duration of the impulse was varied from 0.001 to 0.1 s. The optimal value was found to be 0.03 s. It is interesting to note that the duration of the impulse suggested by the Hertz’s law, equal to 0.017 s, results quite similar to the value obtained numerically, through curve-fitting with the experimental outcomes. Fig. 16 compares the experimentally recorded displacement–time histories to those provided by SAP2000, assuming an impulse of force having 0.03 s duration. The experimental curves are identified by the sensor label (i.e., T1x, T2x, T3z and T4z) and by their location on the Shelter (i.e., on the left or right side). The numerical curves are indicated by (a) and (b). Obviously, no difference between the left- and right-side displacements of the external shell are found in the numerical model, due to the symmetry of the structure and of the load condition. The only difference between the two numerical curves reported in each diagram is the magnitude of the maximum impact force. The curves indicated with (a), indeed, refer to an impulse of force equal to 2.28 kNs, corresponding to a maximum impact force of 152 kN, while the curves indicated with (b) refer to an impulse of force equal to 1.6 kNs (i.e. 70% lower), corresponding to a maximum impact force of 106 kN. This reduction could be justified by the loss of energy which surely occurred during the impacts. Part of the input energy, indeed, is absorbed (and then released) through the elastic deformation of the rubber layer, part is dissipated through the plastic deformation of the steel cap (as experimentally observed at the end of the tests) and part is consumed in concrete cracking. The impact modelling, being perfectly elastic, does not take into account the aforesaid aspects. Under the above-mentioned hypotheses, the numerical model seems to be able to capture with reasonable accuracy the experimentally recorded dynamic response of the external shell. It is worth to emphasise that a certain discrepancy between experimental and numerical displacements was expected, due to some differences between test and numerical model (e.g., in the geometry of the external shell), as well as due to the errors inherent in the comparison between experimental and numerical displacements. To this regard, it is sufficient
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
699
α
α' α' /
2
ωb ωr ωa
ω
Fig. 14. Procedure used for the evaluation of the effective damping associated to the dominant mode of vibration of the external shell.
Fig. 15. Schematization of the impulse of force generating during the impact.
to underline two aspects. Firstly, in the numerical model the effects due to the self-weight of the external shell are neglected. As a consequence, at the beginning of the analysis, the devices are assumed to be unloaded and the external shell parallel to the global reference system. Secondly, the numerical displacements in Fig. 16 represent the horizontal (or vertical) components of displacement of the points of the external shell where sensors are connected. Actually, the transducers do not provide horizontal (or vertical) components of displacement, but rather variations of length. For the transducers T1x and T2x (see Fig. 5) the error in assuming the displacement recorded by the sensor as horizontal component of displacement is quite negligible, due to the their large length. The same does not hold for sensors T3z and T4z (see Fig. 5). For this reason, a modification factor has been calculated to transform the signals recorded by T3z and T4z in vertical components of displacement. It has been calibrated by referring to the peak displacement, leading to some approximations for the intermediate displacements. In the light of these considerations, the comparison between experimental and numerical displacements can be considered to be satisfactory. 7. Summary and conclusion An impact-resisting reinforced concrete structure for volcanic shelters has been designed, engineered and tested at the University of Basilicata (USB). It basically consists of two homologous reinforced concrete shells,
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
700
10 5 (mm)
0 -5 -10
T1x_right
-15 -20 -25 59.75
T1x_left
(b) (a) 59.85
59.95
60.05
60.15 (sec)
60.25
60.35
60.45
60.55
60.25
60.35
60.45
60.55
60.25
60.35
60.45
60.55
60.25
60.35
60.45
60.55
10 T2x_left
5
(mm)
0 -5 -10
T2x_right
-15 -20 -25 59.75
(b)
(a) 59.85
59.95
60.05
60.15 (sec)
10 T3z_right
5
(mm)
0 -5 T3z_left
-10 -15 -20 -25 59.75
(b)
(a) 59.85
59.95
60.05
60.15 (sec)
10 T4z_right
5
(mm)
0 -5 -10 -15
T4z_left
-20 -25 59.75
(b) (a)
59.85
59.95
60.05
60.15 (sec)
Fig. 16. Comparison between the displacement–time histories experimentally recorded during the Test no. 4 and the numerical displacement–time histories produced by an impulse of force having 0.03 s duration, and magnitude equal to (a) 100% and (b) 70% of the theoretical value.
interconnected by suitable flexible and highly dissipative devices, which absorb and dissipate most of the impact energy, thus avoiding damages to the reinforced concrete structural members. The Shelter was specifically thought to be installed on the Stromboli volcano (Aeolian archipelago, Sicily, Italy), to protect human lives from pyroclastic eruptions.
ARTICLE IN PRESS M. Dolce et al. / International Journal of Impact Engineering 34 (2007) 681–701
701
In this paper the impact tests carried out at the Laboratory of Structures of the University of Basilicata (USB) are described and the most important experimental results are examined. The experimental tests were performed on a 1:2-scale model of the Shelter, using a testing apparatus, which was purposely realised to simulate impact conditions comparable with that considered at the design stage. Eight different impact tests were conducted, by considering two different levels of impact energy and four different mass ratios between projectile and R/C shell. A refined finite-element model of the Shelter was also implemented and a series of direct-integration time-history analyses were then carried out, to validate the experimental results. The tests clearly proved the ability of the Shelter to resist the impacts without appreciable damage. As a matter of fact, only some minor hairline cracking, close to the impact area, were observed at the end of the tests. The maximum displacements of the external shell (of the order of 20–25 mm for the 1:2-scale model, under the most severe impact) were found to be much lower than the available distance (about 75 mm for the 1:2-scale model) from the internal shell. Actually, the maximum displacements under the design impact conditions are expected to be approximately two times greater than those recorded during the tests. Moreover, impacts may occur at the extremities of the shell. For all these reasons, the clearance between external and internal shell will be kept equal to the design value (i.e. 150 mm) in the full-scale structure. Some additional information was also obtained from the examination of the test results, as well as from the comparison with the numerical simulations. They can be summarised as follows: (i) the maximum displacements of the external shell increase quite linearly with the mass ratio between projectile and external shell, and less than linearly with the impact energy, (ii) a significant de-amplification in the peak acceleration experienced by the internal shell is found, compared to the external shell, (iii) the Hertz’s law is found to predict the impulse of force generated during the impact with reasonable accuracy. Finally, the comparison between numerical and experimental results proves the suitability of the finite-element model used in the design to simulate the dynamic response of the shelter to the impact loading. Further applications for the impact-resisting structure described in this paper, even different from the original aim, may be proposed in the future. Acknowledgements The present study has been funded by the Italian Department of Civil Protection, within a contract with the University of Basilicata. The design of the shelter has been made by M. Dolce, R. Marnetto and D. Cardone. The impact-absorbing devices ADRI have been produced by TIS S.p.A.. The cement and the additives for the test model have been provided by Italcementi S.p.A., that also collaborated in the study of the concrete mix. References [1] Pasquare0 G, Francalanci L, Garduno VH, Tibaldi A. Structure and geological evolution of the Stromboli volcano, Aeolian Islands, Italy. Acta Vulcanol 1993;3:79–89. [2] Halliday D, Resnick R, Walker J. Fundamentals of physics, 6th ed. Wiley; 2002. [3] Dolce M, Cardone D, Marnetto R. Structural design and analysis of an impact resisting structure for volcanic shelters. Engineering Structures, Elsevier Science Ltd: Oxford, UK, in press. [4] Dolce M, Cardone D, Marnetto R, Nigro D, Palermo G. A new added damping rubber isolator (ADRI): experimental tests and numerical simulations. Proceedings of the eighth world seminar on seismic isolation, energy dissipation and active vibration control of structures, Yerevan, Armenia, October, 2003. p.483–92. [5] Harris HG, Sabnis GM. Structural modelling and experimental techniques. Washington, DC: CRC Press; 1999. [6] Jones N. Structural impact. Cambridge, MA: Cambridge University Press; 1989. [7] Woo K, El Atter A, White RN. Small-scale modelling techniques for reinforced concrete structures subjected to seismic loads. Technical report no. NCRRR 88-0041, State University of New York at Buffalo, 1988. [8] EUROPEAN COMMITTEE FOR STANDARDIZATION. pr EN 197-1. Cement—Part 1: Composition, specifications and conformity criteria for common cements, Brussels, February 2000. p. 29. [9] Chopra AK. Dynamics of structures. London: Prentice-Hall International Inc.; 1995. [10] Computers and Structures Inc. SAP2000_Nonlinear: analysis reference manual (Version 9.4), Berkeley (CA), 2004. [11] Hertz H. On the contact of solids—on the contact of rigid elastic solids and on hardness [Translated by D. E. Jones and G. A. Schott]. London: MacMillan and Co. Ltd; 1896. [12] Timoshenko S, Goodier JN. Theory of elasticity. New York: McGraw Hill Inc.; 1951. [13] Ewins DJ. Modal testing: theory and practice. New York: Wiley; 1984.