Structural properties of RC plates damaged by fragmentation impact

Construction and Building Materials 207 (2019) 463–476

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Structural properties of RC plates damaged by fragmentation impact Hezi Y. Grisaro a,⇑, Avraham N. Dancygier a, David Benamou b a b

Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel Fortification Branch, CEC, IDF, Israel

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


RC specimens were subjected to

fragmentation impact in previous field tests.
Specimens were then tested in threepoint bending static tests.
Different behavior was observed for damaged and undamaged elements.
Equivalent cross-section heights were calculated to represent the structural damage.
Quantitative results demonstrate the importance of considering the fragment damage.

a r t i c l e

i n f o

Article history: Received 25 October 2018 Received in revised form 26 December 2018 Accepted 16 February 2019

Keywords: Combined blast and fragments Fragmentation damage Fragmentation impact Protective structures Residual structural behavior

a b s t r a c t This paper describes a second stage of a comprehensive experimental study of the fragment damage effect on the mechanical properties of reinforced concrete (RC) elements. In the first stage, RC elements were exposed to fragmentation impact in a field test series. These specimens were then brought to the laboratory together with reference undamaged specimens, to experimentally study their structural behavior in three-point bending static tests. All specimens exhibited a flexural failure mode and the characteristics of the resulting load-deflection curves are presented and analyzed. The effects of the fragmentation impact from the preceding field tests show differences between the behavior of the undamaged and damaged specimens with respect to their flexural moment capacity, stiffness, deflection capacity and structural ductility. Additionally, evaluation of an equivalent cross-section height is presented, which enables flexural analysis of RC elements under a combined loading of blast and fragments, in cases where the fragments reach the element before the blast (or at the same time). The quantitative results that have been obtained in this study emphasize the importance of considering the damage due to the fragmentation impact, which cannot be neglected, at least within a certain standoff distance. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Detonation of cased charges is one of the threats on protective structures. Although the blast wave from a cased charge has lower peak overpressure and impulse than those from the same charge without casing [1–3] (because of the energy dissipation due to the casing expansion and eventual fragmentation), a cased charge ⇑ Corresponding author. E-mail address: [email protected] (H.Y. Grisaro). https://doi.org/10.1016/j.conbuildmat.2019.02.096 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

generates an additional threat in the form of fragments that are created as a result of the casing rupture. Experiments, as well as numerical and simplified models, show that there is a synergistic effect of this combined loading of blast and fragments [4–8]. This effect is expressed by a damage and structural response, which are more severe than that caused by the same charge without a casing. This phenomenon of combined loading is commonly neglected or dealt in a simplified manner. The fragments have dual effect on the structure. The first is the momentum that they transmit to the structure, which sometimes

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may be negligible, and the second is the physical damage inflicted by their penetration into the structure. The times of arrival of the blast and the fragments are different [6,9,10], yet it can be shown that for very short distances, the blast will reach it before the fragments [6]. When, for other distances, the blast wave reaches a structure, which has already been struck by the fragments, a damaged structure is exposed to that blast, and thus, its global response may be more severe than it would have been under higher blast loading but with no fragments. Moreover, the penetration time of a fragment into a reinforced concrete (RC) element is shorter than the duration of a blast wave pressure. Thus, even when the blast and fragments reach the structure at different times (yet approximately the same), it can be assumed that the blast load strikes an already damaged structure. For the analysis of the response of a RC element to the combined loading of blast and fragments, the parameters of the damage, which is caused by the fragments, should be considered. This can be done by employing equivalent parameters of a reduced cross-section height, which represents the effect of the penetrations of the fragments [11]. Yet, studies that consider the fragmentation effects are very rare [6,8,12], and commonly the fragmentation damage is neglected, yielding a non-conservative design. In this paper, the second stage of a comprehensive experimental study of the fragmentation damage effect on RC elements is presented and discussed. While the first stage included field tests in which RC specimens were subjected to the loading of fragmentation (and blast) from detonated steel-cased explosives, the second stage was aimed at studying the effect of this loading on the structural properties of the specimens. Thus, the motivation for this stage was to measure the global structural behavior of reference (undamaged) and damaged RC elements through static tests and to analyze the resulted measurements. The results of such tests provide information on various structural parameters such as flexural moment capacity and stiffness, which should be used in structural analysis that includes also other parameters (such as inertia) under blast and fragmentation loading. It is emphasized that observations and insights regarding the consideration of the fragment damage in the global response is commonly not included in such analyses. Accordingly, an important goal of the current research stage was to obtain equivalent parameters to analyze RC elements under combined loading of blast and fragments, in cases where the fragments reach the element before the blast or at the same time (where these cases are most common [10]). It should be noted that this study deals with the static response of RC elements that were subjected to combined blast and fragmentation impact. Its main aim was to study the effect of the damage due to fragmentation impact, where this damage should be (but commonly – it is not) part of further dynamic analysis, which is out of the scope of the current study. Thus, a suitable field test series has previously been conducted. These tests were designed such that the damage due to the blast was minor [13]. Thus, the fragmentation damage could be studied separately from the blast. While the field tests provided information on the areas that were

damaged by the fragments and of the damage level, this paper describes a further study of the residual performance of the damaged specimens in terms of static structural behavior and moment bearing capacity. 2. Experiments 2.1. Previous field tests To experimentally study the fragment damage and its influence on the global behavior of an element, which is exposed to their impacts, a comprehensive experimental study has been conducted. The first stage of the research included field tests, which were previously reported [13]. In these tests, full scale, 20-cm thick, 2.2  1.0-m2 RC T-wall elements were exposed to the combined loading of blast and fragment impacts from detonation of 5-kg cased charges. There were total of 4 tests, whose main parameters are summarized in Table 1. For clarity, an example of one of the arenas that included RC wall specimens that were exposed to the cased charge detonation is presented in Fig. 1. The arena, which is shown in the figure, comprised four specimens, two that were located at a standoff distance of 2 m from the charge and two - at 4 m. These tests were planned such that the damage caused by the blast was minor and most of it was inflicted by the fragments that were generated from the steel pipe casing of the explosive. Thus, this first-stage of the experimental program included two ’control tests’, where one of them was aimed to verify proper fragmentation. Therefore, this control test included a cased charge and only witness plates as ’specimens’ (no RC walls), whereas the other included a bare charge without casing, with the same amount of explosive and a single RC specimen, in order to examine the damage of the blast without fragments. In the latter test, the measured blast wave had higher peak overpressure and impulse than the same charge with a casing (as expected) but the RC wall did not show any visible damage (see specimen ‘140 in Fig. 2). This result verified the planned experimental program of the field tests, of fragmentation-inflicted damage while diminishing the damage

Witness plates

Charge

Water containers

T-Wall specimens

Fig. 1. Test setup example of one of the field tests (Test 3 arena, based on [13]).

Table 1 Main parameters of the field tests [13].

* **

Test #*

Casing mass (kg)

Explosive mass (kg)

Height of charge bottom (cm)

1 3 4

0.345** 6.065 6.110

5.050 5.025 5.050

79.5 80.0 85.0

Test 2 did not include RC wall specimens. The charge was covered with a plastic wrap.

Number of walls 2-m

3-m

4-m

0 2 0

0 0 2

1 2 1

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due to the blast from the cased charge detonations, at least for distance of 4 m from the charge. The experimental test with the bare charge did not include specimens located at 2 or 3 m from the charge, and thus there is not direct experimental evidence that the damage due to the blast at these distances is minor. However, we still think that the vast majority of the structural damage was caused by the fragments. Several arguments for this deduction are given in [13], with the main reason being the clearing effect, according to which, for the dimensions, distances and separate positioning of the specimens, the blast flows around them. The fragmentation that was generated by the charges in the field tests was monitored by recovery of fragment samples in some of the test arenas. The fragmentation cumulative mass distribution was analyzed, and it was also found that they had a maximum velocity of about 2000 m/s in all activations [13]. Together with the damage that was caused to the specimens, these findings indicate typical generation of fragmentation masses and velocities. The damage that was caused to the front and rear faces of the wall specimens in the field tests is shown in Fig. 2. For the full details of the field tests the reader is referred to [13].

Front face

Rear face

2.2. Preparation of the specimens for the static tests The purpose of the field tests was to generate fragmentation damage at different standoff distances (from the same given charge). Consequently, after the field tests, the damaged and reference specimens were transported to the laboratory of the National Building Research Institute (NBRI) at the Faculty of Civil and Environmental Engineering at the Technion, as shown in Fig. 3. Efforts were made to ensure that no further damage would be caused to the specimens during their transportation. The bases of the walls were sawed, leaving remaining 1.0x1.8-m2, 20-cm thick plates. The sawing process is shown in Fig. 4. The walls were reinforced at each side with 8-mm deformed steel meshes, with rebars spaced at 150 mm (i.e., seven rebars at each side of the cross-section). A sketch of the sawed plate crosssection is shown in Fig. 5. The sawed plate specimens were tested in a three-point bending flexural test setup, where the front damaged face, which was exposed to the fragmentation impact, was loaded by a rigid steel beam across its width (more details are given in following text).

Front face

Rear face

Test 1: specimen '14', standoff distance = 4 m Front face Rear face

Test 3: specimen '34A', standoff distance = 4 m Front face Rear face

Test 3: specimen '32A', standoff distance = 2 m

Test 3: specimen '34B', standoff distance = 4 m

Fig. 2. Damaged specimens after the field tests (based on [13]; Tests numbers refer to their numbers in [13]).

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Front face

Rear face

Front face

Rear face

Test 3: specimen '32B',

Test 4: specimen '43E',

standoff distance = 2 m Front face Rear face

standoff distance = 3 m

Test 4: specimen '43W', standoff distance = 3 m Fig. 2 (continued)

The specimen ID terminology is ’X1X2X30 , which refers to the field tests as follows:
X1 is the field test number,
X2 is equal to 2, 3 or 4 and it denotes the horizontal standoff distance between the charge and the wall (m),
X3 marks the difference between two walls, positioned at the same standoff distance at the same test (if there was only one specimen this mark is omitted). For example, ‘‘34A” denotes one of two walls in test 3, which was placed at a standoff distance of 4 m from the charge. 2.3. Material properties and specimens The T-wall specimens were cast by a local contractor and the following details were given by this contractor. 2.3.1. Concrete The concrete mixture was made of Portland cement type CEM I52.5N with a maximum aggregate size of 19 mm. The mixture ingredients are given in Table 2.

Each wall was cast from different concrete batches that were prepared at different dates. During the walls casting, six cubes of concrete were taken from each mixture to measure the uniaxial compressive strength. Three of them were 100  100  100 mm3 cubes, that were wet-cured for 7 days and then used for compressive strength measurements at 28 days, according to [14]. These cubes were tested by the local contractor. The other three were 150  150  150-mm3 cubes that were cured 28 days in water, according to [15]. The compressive strength for each mixture is given in Table 3. 2.3.2. Reinforcing steel A sample from the steel mesh was taken from the local constructor to the NBRI laboratory and three rebars were cut from the mesh to measure the mechanical properties of the steel in tension. In addition, one steel rebar was taken and cut from the edge (near the support) of specimen ‘32B’ after the test (i.e., this sample was taken from part of the specimen, where the bending moment was minimal). Stress-strain measurements of the rebar specimens were taken in a tensile test setup and their resultant curves are shown in Fig. 6. The curves shown in Fig. 6 are characterized by an elastic phase

467

1000

34

200

7φ8@150 7φ8@150

132

34

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Fig. 5. Scheme of the sawed plate cross-section (dimensions in mm).

Fig. 3. Transportation of the walls to NBRI laboratory.

with a modulus of elasticity of 200 GPa, a yield stress that ranges between 500 and 600 MPa, and an ultimate stress - between 600 and 700 MPa. The rupture strain is 2% indicated by bars #2 and #3, while bar #1 showed rupture strain of 1.5% (see Fig. 6). 2.4. Test setup The sawed plates were tested in a three-point bending, quasistatic test setup, as shown in Fig. 7. The specimens were supported by 5-cm wide steel plates, welded to cylindrical bars, to enable support rotation. The axial span between the support midpoints was 1.6 m. The three-point bending test was chosen to allow sufficiently long shear span of a = 800 mm (i.e., a/d > 4, where d is the effective depth) in order to ensure flexural response and failure of the specimens (rather than shear failure). The plates were loaded by a uniform line load, which was generated by the controlled displacement of a hydraulic jack stroke, through a rigid steel beam that transferred the load to the specimen along a 6cm wide steel plate (see Fig. 7). While the line load over the width of the undamaged reference specimens was easily applied, its application over the damaged faces of the other walls was challenging because of the craters that were caused by the fragments.

For this purpose, a 6-cm strip of gypsum mortar was cast between the loading plate and the specimen, as shown in Fig. 8. The instrumentation system, presented in Fig. 7, included the following measurements: The load was recorded by a 25-ton load-cell (Tedea-120) that was placed between the stroke and the steel beam. The mid-span deflection was recorded by two vertical position transducer gauges (POT) that were connected to the bottom face of the specimen. In order to verify that the gypsum distributed the load properly and to monitor any development of possible relative deformations between the steel beam and the specimen, two vertical linear variable differential transformers (LVDT, Measurement Specialties-3000HR, range ±76.2 mm) were connected between the loading beam and the laboratory floor (see LVDT1 in Fig. 7). Horizontal LVDT gauges were also set near the top and the bottom of the specimen, on each of its two sides (total of four LVDT gauges, see LVDT2 in Fig. 7; Measurement Specialties-500HR, range ±12.07 mm, and Measurement Specialties-1000HR, range ±25.4 mm). The top LVDT gauges were attached at the level of the top reinforcement mesh (i.e., 34 mm from the top fiber of the cross-section; refer to Fig. 5) and their readings were used later for validation of the cross-sectional calculations (see Section 4.4). The bottom LVDT gauges were placed parallel to the location of the longitudinal tension rebars, thus providing direct evaluation of the strain at these rebars. Note that in some cases, in specimens whose sides were heavily damaged, the initial length of the LVDT had to be increased (such that it spanned over the damaged zone) or, in cases of severe damage, this gauge was not installed at all. In the undamaged specimens, two strain gauges (TML- PL-120-11-1L, range 2%) were placed on the top of the specimen under the loading plate, parallel to the span of the slab (special care was taken to install these strain gauges under the loading plate). In some of the tests, four vertical LVDT gauges (model Measurement Specialties-200HR, range ±5.08 mm) were also connected between the specimen edges and the concrete blocks that served as supports to the setup, at each side of the specimen (see LVDT3 in Fig. 7) to measure possible displacement of the slab edges relative to the supporting blocks. The stroke displacement rate varied during each test from 0.03 to 0.4 mm/min.

180 220

20

20 20

Sawed cross-secon

45 20 45 110 Fig. 4. Sawing process of the T-walls (dimensions in cm).

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Table 2 Concrete mixture proportion. Amount (kg/m3) Water 155 *

Cement 300

Natural Sand 245

Crush sand 200

Aggregate 1350

Fly ash 150

WRA* 3

Total 2403

Water reducing agent

Table 3 Concrete compressive strength results. 100  100  100-mm3 cubes

Specimen ID

Control1 Control2 14 32A 32B 34A 34B 43E 43W *

150  150  150-mm3 cubes *

Age (days)

Compressive strength (MPa)

Age (days)

Compressive strength* (MPa)

28

51.1 43.1 52.6 47.3 47.2 47.8 51.6 52.6 42.8

36 33 41 29 34 42 35 28 30

44.1 37.5 51.2 39.5 45.9 47.2 46.5 46.3 33.7

(1.1) (0.4) (1.4) (2.0) (2.2) (0.9) (2.6) (1.3) (1.6)

(2.1) (1.6) (0.4) (2.0) (1.8) (0.9) (2.6) (1.1) (1.0)

Values in brackets denote standard deviations

their average was taken as the mid-span measured deflection. The LVDT gauges that measured the displacements of the rigid loading beam edges, relative to the floor (LVDT1) also showed almost the same deflections as those that were measured by the POT gauges, which means that the gypsum layer, between the loading beam and the specimen, did not develop deformations that may have affected the results. In specimens that were installed with LVDT gauges between the specimen edges and the supporting concrete blocks (LVDT3), the deflections of the supports were subtracted from the mid-span deflection. These deflections (at the supports) were very small and were therefore meaningful with regard to the measured deflections only at very small deformations, at the beginning of the test. All measured load-deflection curves include four characteristic points that are marked on the curves as follows: Fig. 6. Stress–strain curves of the rebars.

3. Results and discussion In all tests, failure was characterized by rupture of one of the steel bars, and there was no crushing of the concrete. The test was then terminated when a second rebar (out of seven, refer to Fig. 5) was ruptured. No shear cracks were observed in all tests, which emphasizes that the response was dominated by flexure and not by shear. The results are presented and analyzed in the following sections with regard to four aspects:





Load-deflection behavior, Cracking, Ductility, Load carrying capacity.

3.1. Load-deflection curves This section deals with the measured load-deflection curves that represent the structural behavior of the plates. Fig. 9 shows the load-deflection curves of the tested specimens, recorded by the mid-span POTs, where the load was directly recorded by the load cell. Measurements from both POT gauges at the bottom of each specimen were almost the same in all cases, and therefore


‘Cr’ - Cracking point. At this load level, the first flexural crack was observed at the bottom of the specimen. After this point, the slope of the curve becomes much lower, as can be seen in Fig. 9 (and as can be expected from cracked cross-sections).
‘Y’ – Yield point. At this point, the tension steel reached its yield strain. It was indicated either by the horizontal LVDTs that were placed at the rebar level or by the sharp slope change in the load-deflection curve.
’U’ – Ultimate point (ULS – ultimate limit state). This point marks the maximum applied load.
’R’ – Rupture point, in which the first rebar was ruptured. Fig. 9 shows that the measured responses of the undamaged specimens (’Control10 and ’Control20 ) are very similar. The differences between them can be related to their different concrete strengths, the actual rupture strain of each bar, or the actual location of the reinforcing mesh in the cross-section. They are both characterized by the same behavior: high slope of the loaddeflection curve up to the cracking point (’Cr’ in Fig. 9a), followed by a lower slope up to the yield point, a plateau (or very small slope) at around 100–110 kN and then failure, denoted by rupture of one of the rebars when the mid-span deflection was 13–14 mm. It can also be observed that the load-deflection curve of specimen ’140 (which was exposed to a bare charge detonation) is very similar to those of the control specimens. It is characterized by the same behavior, where its maximum load is in between the control

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Strain gauges

POT

Top view

Bottom view

Stroke Load cell Loading (steel) beam

Strain gauges RC Specimen

LVDT2

LVDT3

LVDT3

LVDT3

LVDT1

Concrete block

Concrete block

LVDT1

POT

Side view

Typical test setup

Front view

Schematic isometric illustration Fig. 7. Test setup and measurement instrumentation.

Fig. 8. Gypsum casting to uniformly distribute the load over a damaged surface of the test specimen.

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(a)

(d) Fig. 9. Load-deflection curves for: (a) control specimens and the specimen that was exposed to bare charge detonation, and specimens that were subjected to cased charge detonations at standoff distances of (b) 2 m, (c) 3 m and (d) 4 m.

specimens’ results (102.0 kN, which is in a good agreement with the average maximum load of the control specimens – 105.2 kN). Yet, the first rebar of this specimen was ruptured when the deflection was 9 mm, which is lower than that of the control specimens. However, while in the control specimens (and in all other

specimens) the second rebar was ruptured after the first one, without developing further significant deflection, in specimen ’140 the second rebar was ruptured when the deflection was 13–13.5 mm, i.e., after the mid-span deflection at the first rupture increased by 50%. A reasonable explanation for this result is that one of the

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(marked ’Cr’ in the figure), the first crack was observed at the bottom of the specimen. The slab stiffness, depicted by the slope of the load-deflection curve, gradually decreased after this point. As mentioned above, the fact that specimen ’140 exhibited an uncracked phase even though it was exposed to higher pressure (from the bare charge, see Fig. 4 in [13]), indicates that the reason for the main damage inflicted on the walls was the fragmentation impact and not the blast load. It should be noted though, that after the field tests and prior to the static tests, longitudinal cracks on the rear face (across the width) of the walls were observed only on specimens ’32A’ and ’32B’ that were located 2 m from the charge. On the other walls, no visible cracks were found on the rear face (and the fragment penetration depths were not more than 105 mm [13]). Nevertheless, in all specimens that were exposed to cased charge detonations, and as a result of the fragmentation impact, there was no pre-cracked phase in the load deflection curves, as indicated by their relatively reduced stiffness up to yielding of the tension steel (see Fig. 9b–d). Moreover, mid-span flexural cracks did appear immediately at the beginning of the static tests of all damaged specimens. This observation of the absence of an uncracked phase in the response of the damaged specimens, is important because it indicates that analysis of a RC barrier subjected to combined load of

rebars in this specimen had lower rupture strain than the others, and this is the reason for its early rupture (refer also to Bar #1 in Fig. 6). Considering this observation, it can be concluded that specimen ’140 shows similar results to those of the control specimens. Contrary to this behavior, the damaged specimens showed no uncracked phase, lower maximum force (in the range of 60.1– 98.0 kN) and larger deflections (see Section 3.3). Thus, the damage due to the blast load can be neglected in the current test series, while the damage due to the fragments impact is significant. 3.2. Cracking The first cracks in all tests appeared at the mid-span section (or very close to it). Additional flexural longitudinal cracks also appeared at the bottom face of the specimens during the test. After the static tests, the specimens were rolled over and the flexural cracks were marked. A typical example of the cracks is shown in Fig. 10. This crack pattern, which is typical of flexural response, was similar in all specimens (control specimens, as well) and it thus further indicates the flexural response of the specimens. It is evident from Fig. 9 that the cracking point was observed only in the undamaged specimens (’Control10 and ’Control20 ), and in specimen ’140 , which was not exposed to fragmentation impact (at a standoff distance of 4 m) in the field tests. At this point

(a)

(b) Fig. 10. Typical example of flexural cracks in specimen (a) ’140 and (b) ‘34B’ (post-static test pictures).

Table 4 Test results and equivalent height estimation. Specimen

Distance (m)

Fmax (kN)

heq (mm)

c0 (mm)

c0/heq

heq/h0

dU (mm)

dR (mm)

Control1 Control2 14 32A 32B 43W 43E 34A 34B

– – 4 2 2 3 3 4 4

110.5 99.9 102.0 73.0 60.1 87.7 83.3 90.8 98.0

202.6 195.6 195.7 160.3 138.2 184.2 177.3 186.2 192.8

17.2 16.8 14.9 11.4 9.9 14.5 11.2 13.2 14.8

0.085 0.086 0.076 0.071 0.072 0.079 0.063 0.071 0.077

1.013 0.978 0.979 0.802 0.691 0.921 0.886 0.931 0.964

10.8 9.8 7.7 12.4 16.6 21.4 9.6 12.8 10.6

13.1 13.4 8.9 17.0 36.3 27.7 16.6 18.8 14.8

Ductility ratios

Post crack stiffness (kN/mm)

dR/dY

dU/dY

3.45 3.53 3.08 2.79 3.07 3.22 3.76 4.00 4.04

2.85 2.58 2.03 1.41 2.49 2.18 2.72 2.91 2.67

27.27 32.14 31.29 10.80 4.79 8.76 17.70 16.45 23.08

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blast and fragments should be done for a cracked cross-section (in cases where the fragments are expected to reach the structure before or together with the blast wave), at least for damage level and penetration depths that are similar to those that were caused in the field tests. The slopes of the initial cracked phase of the load-deflection curves were taken from the measured plots (refer to Fig. 9). For the damaged specimens, the initial slope was considered because they had no uncracked phase, and for the control specimens and specimen ‘140 , the slope that was considered was right after the first drop of the load, which indicated cracking (points that are marked ‘Cr’ in Fig. 9). The results are shown in Table 4 and Fig. 11. It can be seen that the control specimens have the highest post crack stiffness (27–32 kN/mm). In addition, the damaged specimens showed stiffness values that decreased as their standoff distance from the charge was smaller (i.e., 16 to 23 kN/mm and 5 to 11 kN/mm at standoff distances of 4 and 2 m, Table 3). Fig. 11. Measured post crack stiffnesses.

Fig. 12. Mid-span deflection capacity at the (a) maximum load (dU) and (b) the first rupture of one of the reinforcement bars (dR).

) Fig. 13. Ductility ratios determined by the deflections at (a) rupture of the rebars and (b) maximum load capacity.

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3.3. Ductility The deflection capacity of a flexural member is denoted by its ultimate deflection. Examination of the deflection capacity according to the mid-span deflections at the maximum load (dU) and midspan deflections at the first rupture of one of the reinforcement bars (dR) is given in Table 4 and in Fig. 12. The damaged, and thus reduced cross-section heights have led to increased ultimate deflections, as can be seen in Fig. 12. However, they also caused increased deflections under the yield moment. Consequently, when the ductility ratios are considered, an opposite trend is observed, where the ductility ratio is calculated here, based on two criteria. The first is the ratio between the mid-span deflections at the first rupture of one of the reinforcement bars (dR) and at the yield point (dY). The second is the ratio between the mid-span deflection at the maximum load (dU) and dY. These ductility ratios are presented in Table 4 and in a graphical form in Fig. 13. The figure shows that by both methods, for the damaged specimens from tests 3 and 4 there is a trend of decreasing ductility ratio as the specimen was closer to the charge. However, for the ratio, which is determined by the deflection at the rebar rupture (dR/dY, Fig. 13a), the control specimens have a ductility ratio, which is in between the damaged specimen results, except for the specimens that were located 2 m from the charge. Note that the ductility ratio dR/dY of the bare charge is relatively low because, as explained above, one of the steel rebars was ruptured in a relatively early stage of the test. The deviation of this point, as shown by the red mark in Fig. 13a, conforms to the above reasoning that one of the rebars in this specimen had lower rupture strain than the others. Thus, no clear conclusions can be drawn regarding the difference in the ductility ratio dR/dY between the undamaged and damaged specimens, yet it is clear that a protective wall that suffers considerable damage due to fragmentation impact loses not only its capacity but also its ductility (see specimens at a standoff distance of 2 m in Fig. 13). The ratio dU/dY shows a clearer trend of decrease in the ductility ratio as the specimen was closer to the charge (Fig. 13b). The specimens that were located 4 m from the charge had similar ductility ratios to those of the control specimens and of specimen ‘140 , which was subjected to a bare charge detonation. The similarity of the ductility ratio (according to dU) of specimen ‘140 to those of the control specimens further shows that this specimen had residual mechanical properties that were similar to those of the control specimens. Furthermore, this result supports the deduction

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that the structural damage in the field tests was caused by the fragmentation impact and not by the blast load. 3.4. Load carrying capacity The maximum loads (Fmax) of each specimen are presented in Table 4. The control undamaged specimens had slightly different maximum load capacities, with an average Fmax = 105.2 kN, which is considered here as a reference load carrying capacity of the undamaged specimens. The specimen that was subjected to the bare charge detonation reached a maximum load of 102 kN, which is almost the same as the average reference force (105.2 kN). This difference may be explained by the variation of the steel material properties, as can be seen in Fig. 6, because in this case of straining the steel to its ultimate state, the actual stress in the steel will have a pronounced effect on the cross-sectional moment capacity. The ratio between the load capacity of the damaged specimens (from the cased charge detonations) and the reference maximum loads, as a function of their horizontal standoff distance from the charge, is shown in Fig. 14. It can be seen that the trend of the results shows an increasing load capacity as the distance increases, as expected. The maximum bending moment equals to 0.25Fmaxl (where l = 1.6 m is the span length) and it develops at the midspan. A quantitative meaning of the measured static capacities and its possible application in design procedures of protective barriers that do consider the fragmentation effect, is presented in the following chapter. 4. Effective height The results of the static tests clearly indicate that the fragmentation-induced damage has to be considered in the design of protective barriers and that the common local effect of an impact of a single fragment is not sufficient for the global consideration of this damage. Within the scope of this paper, this damage is considered given or assessed (e.g., by analyzing the detailed measurements that are given in [13]), and thus the motivation here is to find the equivalent height of the damaged element due to the fragment penetrations that corresponds to the measured maximum load. Observing the pictures of the front faces of the walls (Fig. 2), it is evident that the fragmentation effect has occurred mainly within a limited strip of each specimen (and not along its whole height). Because the damage is not uniform over the height of the wall, for load-deflection analysis, the equivalent height that should be considered is not constant over the whole span. However, the equivalent height around the mid-span is still an important parameter because the measured capacity is set by the (maximum) moment that develops at this part of the beam. Moreover, the equivalent-height model which is presented in this chapter, shows that the concept of such equivalent effective height can be used in design of a RC barrier, which may be subjected to fragmentation impact (e.g., protective structure), where for a conservative design this effective height may be taken as constant over the whole span. For a quantitative estimation of the equivalent mid-span section height, which corresponds to the measured moment capacity, the constitutive relation of the steel and concrete are required. 4.1. Reinforcing steel

Fig. 14. Load carrying capacity versus standoff distance.

A proposed curve for the steel constitutive model is plotted in Fig. 6 by a green dashed line, where for its analytical representation, the equation from [16] has been adopted as follows:

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rs ¼

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8 <

Es es


:fu þ fy  fu

 e

u es eu  ey

P

;

es < ey ;

ð1Þ

ey  es  eu

In Eq. (1), rs is the steel stress, es is the steel strain, Es = 200 GPa is the modulus of elasticity, fy = 580 MPa is the yield stress, ey = fy/Es = 0.29% is the yield strain, fu = 680 MPa is the ultimate stress, eu = 2% is the rupture strain and P*=4 is the strainhardening exponent (which is also given in [17]). It can be seen in Fig. 6 that the proposed curve represents well an average behavior of the measured results of specimens #1 and #2, which were similar (and therefore, the curve of specimen #3 was excluded, except for its indication of the rupture strain). It is noted that the 2% rupture strain is relatively small, and it refers - although it does not completely adhere - to ‘‘Class A” reinforcing steel [18]. This material quality was a ‘‘given input” in this study (where, as reported above, the specimens were supplied by a local contractor as ‘‘standard T-walls”). The constitutive relation given in Eq. (1) of the reinforcement steel is adopted, where the same behavior is assumed for tension and compression steel.

1. The damage inflicted by the fragmentation impact is represented by a reduction in the cross-section height. 2. The strain distribution over the section height is linear, based on the Euler-Bernoulli beam theory. 3. The strain at the tension reinforcement fiber is the rupture strain (eu = 2%; based on, and corresponding to the current test results). 4. The tension force in the concrete in negligible. 5. The distance between the section bottom and the tension steel fiber is ds = 34 mm (see Fig. 15). 6. The upper (compression) reinforcement fiber is located 166 mm above the bottom fiber of the section (see Fig. 15). 7. There is perfect bond between the concrete and the steel rebars. Note that in the following derivation the compression zone depth c0 and the equivalent eight heq are the unknowns that have to be solved and that they are different for each specimen. The tension stress at the bottom steel is known and it is equal to fu = 680 MPa (see assumption 3, Fig. 15 and Eq. (1)). The maximum compressive strain in the concrete ec,max is calculated as follows:

c0 eu d  c0

4.2. Concrete

ec;max ¼

The constitutive relations of the concrete in uniaxial compression is taken from Eurocode 2 [18], and it is given by the following equation:

where c0 is the distance between the most compressive fiber of the cross-section and the neutral axis, d = heq-ds is the effective height of the equivalent section, ds = 34 mm is the distance between the bottom face and the tension reinforcement bars (see Fig. 5), and heq is the cross-section equivalent height (see Fig. 15). In this case, the 0 distance ds between the top face and the upper reinforcement bars is 34 mm (see Fig. 5), whereas in the damaged specimens, where 0 the height of the cross-section is reduced, ds is calculated as follows:

rc ðec Þ ¼ f cm

kg  g2 1 þ ðk  2Þg

ð2Þ

where rc is the concrete stress, fcm is the mean compressive strength, g = ec/ec1 where ec is the concrete strain and ec1 is the strain at peak stress and k = 1.05Ecmec1/fcm, where Ecm is the secant modulus of elasticity. The expressions for ec1 and Ecm are given in [18] as a function of the concrete strength as follows:

 0:3 f Ecm ¼ 22 cm ; 10

ec1 ð%Þ ¼ 0:7f 0:31 cm  2:8%

ð3Þ

where fcm is given in MPa and it refers to the concrete strength obtained from standard 150-mm diameter cylinders. Therefore, a suitable conversion factor has been applied in order to convert the measured cube strengths (see Section 2.3 and Table 3) into a cylinder strength, where according to Eurocode2 [18], a cylinder concrete strength is 0.80–0.83 of its cube strength (referring to 150  150  150-mm3 cubes). In the current study, a conversion factor of 0.8 has been applied. The tension stresses in the concrete are ignored in the current analysis, because it is assumed that they hardly affect the moment capacity.

ð4Þ

0

ds ¼ heq  ðh0  34mmÞ

ð5Þ 0

Eq. (5) satisfies the conditions ds(heq = h0) = 34 mm and 0 ds(heq = 166 mm) = 0, where h0 = 200 mm is the height of the 0 reference undamaged specimen. If ds < 0 it means that the reduction of height from h0 = 200 mm is more than 34 mm. In this case, the fragmentation damage cause exposure of the upper steel, which is located in this case outside the concrete section and is likely to buckle under a relatively low compression force. Therefore, in this case the force in the compression steel is taken as zero (see following text). In the field test results the steel at the front face was uncovered due to the fragment damage only in specimen ‘32B’, as it can be seen in Fig. 2. Therefore, it is expected that the model will show zero force (or d’s < 0) only for this type of specimen (i.e., which was located 2 m from the charge in the field test). The strain at the upper steel fiber (e’s) is given by: 0

c d e0s ¼
0  s eu

ð6Þ

d heq  c0

The tension force (T) of the bottom steel is given by:

4.3. Model for the equivalent cross-section height Evaluation of the section bending moment capacity of the current test specimens is illustrated in Fig. 15 and it is based on the following assumptions and data:

T ¼ As f u

ð7Þ 2

where As = 351.9 mm is the tension steel cross-sectional area and fu = 680 MPa. Thus, the tension force at ULS equals T = 228.7 kN.

strain ds’

heq

’s

d h0

166

ds b=1000 Fig. 15. Model of sectional analysis (dimensions in mm).

z

stress Cs

c,max

c0

C

u

T

H.Y. Grisaro et al. / Construction and Building Materials 207 (2019) 463–476

475

The force in the upper steel reinforcement (Cs) is calculated as follows:

(

Cs ¼

A0s r0s


0
 es c0 ; heq ; ;

0

0

ds  0 0 ds

ð8Þ

<0

where r’s is the stress (positive in compression), which is a function of e’s (see Eq. (1)), and A’s = 351.9 mm2 is the upper reinforcement steel area. The compressive force in the concrete is calculated by the integration of the stress over the cross-section compression area:

Z Cc ¼ b

z¼c0

rc ðzÞdz

ð9Þ

z¼0

where b = 1000 mm is the cross-section width. The compressive strain of the concrete, ec, at a coordinate z along the cross-section height (see Fig. 15) is given by:






ec c0 ; heq ¼


 z ec;max c0 ; heq c0

ð10Þ

Using this relation, the compression force in the concrete can be written as follows:

Cc ¼ b

c0

ec;max

Z

ec ¼ec;max

ec ¼0







rc ec c0 ; heq dec

ð11Þ

For a given (measured) moment capacity, the two unknowns are c0 and heq. Thus, the two nonlinear equations to be solved are the equilibrium equation for a total zero cross-sectional axial force and the known maximum bending moment (Mmax):



 C c c0 ; heq þ C s c0 ; heq  T ¼ 0

M max ¼ C c Z C þ C s Z Cs ¼ 0:25F max l

ð12Þ

where ZC and ZCs = 166 – ds (in mm) are the lever arms of the forces Cc and Cs, respectively, relative to the tension reinforcement. ZC is calculated by finding the centroid of the concrete stress function:


 c0 Z C ¼ d heq  c0 þ

ec;max

R ec ¼ec;max

rc ðec Þec dec rc ðec Þdec

Rece¼0 c ¼ec;max ec ¼0

ð13Þ

The two nonlinear equations were solved numerically to find the unknowns c0 and heq and they are presented in Table 4, where it can be seen that the ratio c0/heq is less than 0.1 in all cases (which corresponds to the low, 0.2% tension reinforcement ratio; refer to Fig. 5). Note that the damage that was caused to each specimen in the field tests was different and therefore, their corresponding c0 and heq are also different (mainly due to the standoff distance of each specimen, as shown later in the text).

Fig. 16. Calculated equivalent heights with distance.

the main flexural crack at the mid-span propagated into the concrete above the upper steel reinforcement, indicating that the compression zone was located above it (see Fig. 10). The same observations were found for specimen ’140 , which was exposed to the bare charge detonation. Next, after the model validation, the equivalent heights of the other specimens were calculated, and they are presented in Table 4. Specimen ’140 had a maximum load capacity, which is very similar to that of the control specimens, and its calculated equivalent height is 195.7 mm, which is close to 200 mm. The calculated equivalent heights heq of the damaged specimens are lower, and they are given in Table 4, together with the ratio between them and the reference height h0 (200 mm). This ratio is plotted against the field-test standoff distance of the damaged specimens in Fig. 16, which shows a reduction of this ratio (i.e., of the equivalent height) with decreasing distances. Only in specimens ’32A’ and ‘32B’ (that were located 2 m from the charge), the model predicts heq < 166 mm, together with Cs = 0, as explained above, which is in good agreement with the experimental observation of exposed rebars within the damaged concrete zone (Fig. 2). It should be noted that in all cases, the calculated value of ec,max was lower than the concrete nominal ultimate strain (3.5‰, as suggested in the Eurocode2 model for the concrete strengths of the specimens). This result strengthens the experimental observation, which was implemented as assumption #3 of the model (see Section 4.3) that the failure is caused by rupture of the tension steel reinforcement.

4.4. Model validation 5. Summary and conclusions The height of the reference undamaged specimen is h0 = 200 mm. This height was used for the validation of the computational procedure described above, by verifying the expected result that for the reference specimens the model should predict heq = h0 = 200 mm. Indeed, for specimens ’Control10 and ’Control20 the calculations yield equivalent heights of 202.6 and 195.6 mm, respectively (see also Table 4). These results are in good agreement with the expected 200 mm value, and their deviations from this value can be related to the experimental scatter. Furthermore, the calculations yielded values of c0 that were lower than 34 mm, which means tensile strain of the upper steel reinforcement. A similar observation was denoted by the readings of the upper horizontal LVDTs of these specimens, where at the beginning of the tests these LVDTs indicated compression strains, but before the rupture of the first tension reinforcement bar, they measured extension, corresponding to tension strains. In addition,

This paper presents results from static tests that were conducted within the second part of a study that was aimed at investigating the effect of explosive-induced fragmentation on the structural properties of a reinforced concrete barrier. These tests followed the first part, in which field tests were conducted, of RC T-wall specimens that were subjected to fragmentation caused by detonations of steel-cased cylindrical charges [13]. The methodology of this research was to experimentally study the structural behavior of the damaged specimens in three-point bending static tests, and then examine the characteristics of the resulting load-deflection curves. In the static tests, all specimens exhibited a flexural failure mode, which was characterized by rupture of the tension reinforcement (due to the low steel class that was applied in the construction of the T-walls). The results and analysis consider the cracking, the ductility ratio, and the deflection and

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load carrying capacities. For the latter, a model has been presented to find an equivalent height that corresponds to the measured capacity. The test results show differences in the behavior of the undamaged and damaged specimens with the following conclusions.
Fragmentation effect on the global response and load bearing capacity of a protective barrier should be considered in its analysis (or design). The commonly local effect (penetration or perforation) of a single projectile or fragment alone, is not sufficient for representation of the fragmentation induced by extreme load generated from denotation of a cased charge.
A global structural design of a barrier, which is intended to withstand extreme explosive loads that generate fragmentation, should consider damaged structural members, which are already cracked (i.e., the response curve should start from the cracked phase).
For a given or assessed fragmentation damage, a model is proposed to evaluate an equivalent, reduced cross-section height for design purposes of a barrier, subjected to such damage.
For the current scope of the tests that were conducted, this reduced equivalent height can be up to 30% lower than the original cross-section height (corresponding to specimen ‘32B’).
For a global structural analysis of a barrier under blast and impact loads, this equivalent-height approach may be adopted. Yet it should be noted that applying this reduced, equivalent height along the whole span would lead to a conservative design, because the actual distribution of the damage over the element is not uniform. A more general non-uniform damage distribution may be more realistic to adopt.
Examination of the equivalent heights of the current specimens together with their positioning data in the field tests show a trend of decreasing equivalent heights for specimens that were closer to the charge in the field (Fig. 16).
The damaged specimens had lower ductility ratios as the specimen was closer to the charge, but higher absolute deflection values. The measured data that was obtained in this study emphasizes the fact that the damage due to the fragmentation impact should be considered and that it cannot be neglected (at least within a certain standoff distance). Although application of the procedure for evaluation of an equivalent cross-section (Chapter 4) along the whole span of the barrier is bound to yield conservative results, it is a first step towards such consideration of the fragmentation effect. It should be noted that in a realistic scenario of the combined blast and fragmentation loading, the response will be dynamic rather than static. However, although the dynamic response of RC elements to blast load has been studied extensively, the damage due to the fragmentation impact is commonly neglected, while the above findings show that it should indeed be taken into account.

Conflict of interest None. Acknowledgements The first author is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities. The Adams Program support is gratefully acknowledged. The authors would like to thank the National Building Research Institute (NBRI), and especially Mr. Elhanan Itzhak and Mr. Eduard Gershengoren for their valuable technical support. References [1] E.M. Fisher, The Effect of the Steel Case on the Air Blast Report 2753, Naval Ordnance Laboratory, White, Oak, MD, USA, 1953. [2] H. Grisaro, A.N. Dancygier, On the problem of bare-to-cased charge equivalency, Int. J. Impact Eng. 94 (2016) 13–22, https://doi.org/10.1016/j. ijimpeng.2016.03.004. [3] M.D. Hutchinson, The escape of blast from fragmenting munitions casings, Int. J. Impact Eng. 36 (2009) 185–192, https://doi.org/10.1016/j. ijimpeng.2008.05.002. [4] H. Hader, Effects of Bare and Cased Explosives Charges on Reinforced Concrete Walls, Interact. Non-Nuclear Munitions with Struct., U.S. Air force Academy, CO, USA, 1983, pp. 221–226. [5] R. Forsen, M. Nordstrom, Damage to reinforced concrete slabs due to fragment loading with different fragment velocities, fragment areal densities and sizes of fragments, Trans. Built Environ. 8 (1994) 131–138. [6] U. Nyström, K. Gylltoft, Numerical studies of the combined effects of blast and fragment loading, Int. J. Impact Eng. 36 (2009) 995–1005, https://doi.org/ 10.1016/j.ijimpeng.2009.02.008. [7] K. Ek, P. Mattsson, Design with regard to blast and fragment loading MSc Thesis, Chalmers University of Technology, Gothenburg, Sweden, 2009. [8] R. Forsén, Response to RC slabs subjected to combined blast and fragment loading, 5th Int. Conf. Des. Anal. Prot. Struct. (DAPS5), Liang Seah Place, Singapore, 2015. [9] J. Leppänen, Concrete structures subjected to fragment impacts Doctoral Thesis, Chalmers University of Technology, Gothenburg, Sweden, 2004. [10] H.Y. Grisaro, A.N. Dancygier, Characteristics of combined blast and fragments loading, Int. J. Impact Eng. 116 (2018) 51–64, https://doi.org/10.1016/j. ijimpeng.2018.02.004. [11] M. Nordstrom Fragment loading of concrete slabs 1, Swedish Defense Research Agency (FOA) Report D Sundbyberg, Sweden, 1992. [12] J.E. Crawford, J.. Magallanes, Y. Zhang, Determining the effects of cased explosvies on the response of RC columns, in: 22th Int. Symp. Mil. Asp. Blast Shock (MABS 22), Jerusalem, Israel, 2012. [13] H.Y. Grisaro, D. Benamou, A.N. Dancygier, Investigation of blast and fragmentation loading characteristics – Field tests, Eng. Struct. 167 (2018) 363–375, https://doi.org/10.1016/j.engstruct.2018.04.013. [14] The Standards Institution of Israel (SII), SI 26 part 1: testing concrete: Sampling of fresh concrete, 2011. [15] E.C. for S. (CEN), BS EN 206-1:2000 - Concrete - Part 1: Specification, performance, production and conformity, 2016. [16] Z. Tao, X.-Q. Wang, B. Uy, Stress-strain curves of structural and reinforcing steels after exposure to elevated temperatures, J. Mater. Civ. Eng. 25 (2013) 1306–1316, https://doi.org/10.1061/(ASCE)MT.1943-5533.0000676. [17] P. Wong, F. Vecchio, H. Trommels VecTor 2 &, FormWorks user’s manual second 2013 edition [18] Eurocode, 2: Design of concrete strucutres - Part 1–1: General rules and rules for buildings 2004