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On the blast resistance of high performance tunnel segments

Matteo Colombo1, Paolo Martinelli2*, Marco di Prisco3

1 Assistant Professor, Department of Civil and Environmental Engineering, Politecnico di Milano, P.za L.

da Vinci 32, 20133 Milan (Italy)

E-mail: matteo.colombo@polimi.it; Tel: 0039-0223998789; Fax: 0039-0223998771 2* Corresponding author, Assistant Professor, Department of Civil and Environmental Engineering,

Politecnico di Milano, P.za L. da Vinci 32, 20133 Milan (Italy)

E-mail: paolo.martinelli@polimi.it; Tel: 0039-0223998785; Fax: 0039-0223998771 3 Full Professor, Department of Civil and Environmental Engineering, Politecnico di Milano, P.za L. da

Vinci 32, 20133 Milan (Italy)

E-mail: marco.diprisco@polimi.it; Tel: 0039-0223998794; Fax: 0039-0223998771

ABSTRACT

This paper presents the main findings of an experimental study that focuses on the response of

fibre reinforced concrete used in underground tunnel linings in case of internal explosion. Two

situations are explored: (a) the effectiveness of thin High Performance Fibre Reinforced

Cementitious Composite (HPFRCC) plates applied to the intrados of new or existing tunnels as

a protection panel and (b) the behaviour of a layered tunnel segment solution made of Steel

Fibre Reinforced Concrete (SFRC) and HPFRCC when a void is present in the mortar filling

layer injected between the lining and the excavated surface, thus amplifying the in–service

internal actions (bending moment and shear force).

Shock tube experiments are carried out to investigate the two situations. These conditions are

experimentally achieved by means of a proper arrangement of an existing shock tube designed

for soil–structure interaction at Politecnico di Milano. A small portion of a tunnel segment is

investigated by using circular layered specimens subjected to two different levels of reflected

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pressure. Simplified models are proposed for assessing the overall response of the two situations

explored under blast loading.

Keywords: internal tunnel explosion, protection panel, multi–layer tunnel structure, fibre

reinforced concrete, shock tube test

1 INTRODUCTION

Over the last few years, there has been an increasing interest in using steel fibre

reinforced concrete (SFRC) as a partial or total substitution of traditional reinforcement

made of steel bars in precast tunnel segments. SFRC presents several advantages

compared to the conventional reinforced concrete (RC): reduced segment rejection due

to wide cracking or corner chipping, improved durability, higher fatigue, and fire and

impact resistance mainly guaranteed by local toughness. This last performance is

important during handling operation and when the lining is pushed by hydraulic jackets

for tunnel boring machine (TBM) advance (Plizzari and Tiberti 2006). Segmental

circular tunnel linings are typically characterised, in serviceability loading condition, by

the dominance of compressive normal forces combined with relatively small bending

moments. This loading condition suggests the use of SFRC segments without

conventional steel bar reinforcement.

Several SFRC studies focusing on design methods and experimental investigations of

segment lining with reduced or without any conventional reinforcement have been

reported in the literature so far (de Waal 1999; Kooiman and Walraven 1999; Kooiman

2000; Schnütgen 2003; Dupont et al. 2003; Gettu et al. 2004; King 2005; Sorelli and

Toutlemonde 2005; Woods et al. 2005; Dobashi et al. 2006; Molins et al. 2006; Plizzari

and Tiberti 2006; Groeneweg 2007; Tiberti et al. 2008; Kasper et al. 2008; Tiberti 2009;

Cavalaro 2009; Caratelli et al. 2011; Molins and Arnau 2011; Caratelli et al. 2012).

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Nevertheless, none of these studies take into account the blast load situation in the

lining design.

Until now, blast has been considered as exceptional load only in the design of safety

systems aimed at reducing the structural collapse. Tunnels are particularly sensitive to

internal explosion due to the high degree of confinement that amplifies the explosive

energy density compared to that of an unconfined blast (Silvestrini et al. 2009).

The present study is part of a more comprehensive project called ACCIDENT

(Advanced Cementitious Composites In DEsign and coNstruction of safe Tunnel) aimed

at designing prefabricated tunnel segments, built by TBM technology, taking into

account exceptional loads like blast and fire. In case of blast, the soil–structure

interaction response and the inter–layer delamination were the main topics of a previous

study (Colombo et al. 2013). A design procedure based on a simplified FE model for

underground tunnels subjected to internal explosion preceded by fire accidents was

recently proposed by Colombo et al. (2014).

This work presents an experimental investigation of two important situations in case

of an internal tunnel explosion: (a) the response of panels made of high performance

fibre reinforced cementitious composite (HPFRCC) applied to the intrados of new or

existing tunnels and (b) the response of a tunnel portion when incomplete mortar filling

between the lining and the excavated surface takes place (Blom 2002; Gettu et al. 2004;

Sugimoto 2006).

In case (a) the panels are conceived as a countermeasure for tunnels under blast

events; they also improve the tunnel performance under fire conditions. In this situation,

there is an air interspace between the lining and the applied panels (Fig. 1). The panels

have limited sizes (0.5–1 m × 0.5–1 m) in order to allow easy handling; moreover they

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have a limited thickness (20 mm) for cost and space reasons.

In the second case (Fig. 2), the blast event amplifies the internal actions (bending

moment and shear force) due to the incomplete filling (which is often the critical

situation in serviceability condition). In fact, incomplete filling involves the lack of soil

reaction in a limited tunnel portion. A scale factor of 1:2 is applied to the dimensions of

the tunnel segment to fit the sizes of the shock tube used to carry out the experimental

tests.

2 MATERIALS

In this work, four circular slabs are tested on the shock tube facility described in Section

3.1. The first specimen consists of a circular slab entirely made of HPFRCC (named 1L

in the following to indicate just one layer) and prepared for studying the situation

illustrated in Figure 1. The second and third specimens are composed of an internal

massive layer of SFRC embedded in two external thin layers of HPFRCC, resulting in a

three layered specimens (indicated 3L in the following). The last specimen (indicated

2L in the following) is composed of two layers, where the extrados HPFRCC layer is

removed. The multi–layer specimens are aimed at studying the problem shown in

Figure 2.

The specimens’ preparation and their geometry are presented in Section 3.2. A

description of the materials composing the specimens is given in the following sections.

2.1 SFRC

The characteristic cubic compressive strength of the SFRC, measured on 150 mm–sided

cubic specimens, is equal to 70 MPa. The material has a density equal to 2300 kg/m3,

and the mix design is reported in Table 1. Low–carbon hooked–end steel fibres, 30 mm

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long with an aspect ratio (lf/df) equal to 45, are used in the mix. A fibre content equal to

50 kg/m3 (0.64% by volume) is adopted. Siliceous aggregates are used. The material is

classified as “1a” with reference to the characteristic values according to Model Code

2010 specifications (fib Bulletin No. 65 2010). Nine notched beam specimens

150×150×550 mm with mid–span notch depth equal to 25 mm (EN 14651 2004) were

cast and tested together with the plates obtaining the following values (fctm,fl = 5.06

MPa, Std = 0.70 MPa, fct,fl,min = 3.86 MPa; fR1m = 2.53 MPa, Std = 0.77 MPa, fR1,min =

1.42 MPa; fR3m = 1.86 MPa, Std = 0.65 MPa, fR3,min = 1.00 MPa). All the specimens

were prepared in the precast factory Magnetti Building.

2.2 HPFRCC

The characteristic cylindrical compressive strength of the HPFRCC material is equal to

110 MPa. Table 1 reports the mix design of high performance cementitious composite

optimised with steel fibres. The density of the composite material is equal to 2380

kg/m3. High–carbon straight steel fibres that are 13 mm long with a diameter of 0.16

mm (aspect ratio lf/df equal to 80) are used in the mix. The fibre content in the mix is

equal to 100 kg/m3, which corresponds to a volume fraction Vf equal to 1.27%.

The mixing procedure consists of several phases: initially, cement, slag and sand are

mixed for 3 minutes at dry condition, and then water and superplasticizer are added and

the cement paste is mixed for other 14 minutes. Finally, the fibres are added to the

cement paste and mixed for another 4 minutes. Six circular slabs with a thickness of 20

mm and a diameter of 560 mm are manufactured: four used for specimens 3L, one for

specimen 2L and one for specimen 1L. The fibre dispersion inside the specimens is

favoured by the self–compacting characteristic of the material. The circular slabs were

cast from the centre and the fibres tend to align perpendicular to the flow of the concrete

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as pointed out by Ferrara et al. (2008) and Barnett et al. (2010) for similar materials,

geometry and casting procedure. The material is denoted as “15b” according to Model

Code 2010 (fib Bulletin No. 65 2010), and the results of three notched beam specimens

(EN 14651 2004) are: fctm,fl = 8.80 MPa, Std = 2.03 MPa, fct,fl,min = 6.85 MPa; fR1m =

15.69 MPa, Std = 0.43 MPa, fR1,min = 15.42 MPa; fR3m = 13.05 MPa, Std = 1.41 MPa,

fR3,min = 11.95 MPa.

3 EXPERIMENTAL SET–UP

3.1 Shock tube equipment

The shock wave tests are carried out in the Shock Tube Laboratory of Politecnico di

Milano. The double diaphragm shock tube facility was developed to investigate

underground tunnel linings under blast and fire conditions. The shock tube is able to

produce a high pressure loading range, with a maximum reflected target pressure of

about 3 MPa. It can be distinguished by other shock tubes for a suitable end chamber

designed to investigate soil–structure interaction and for an appropriate burner

equipment to heat concrete specimen intrados according to a defined fire curve. The

influence of thermal damage on the structural response of the specimens under blast

loads is the main focus of further studies, and therefore, no details are given herein on

the burner equipment. A detailed description of all other shock tube components can be

found in Colombo et al. (2011); only the main points of interest are summarised below.

A schematic layout of the shock tube device in the assembled configuration is shown

in Figure 3a. It consists of four chambers that can move on a linear guide system: the

driver chamber, the buffer or diaphragm chamber, the driven chamber and the

specimen/soil chamber. The total shock tube length is 14.9 m. The tests are carried out

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using pressurized helium inside the driver and buffer chambers, and air at ambient

condition in the driven chamber.

Driver, buffer and driven chambers have a length of 2.35 m, 0.26 m and 10.5 m,

respectively, with an internal diameter of 481 mm. The driver and driven chambers have

a 13.5 mm thick wall, while the buffer chamber has an external diameter of 857 mm that

corresponds to the maximum diameter of the flange welded on the driver and driven

ends.

When the two scored steel diaphragms that separate the buffer chamber from the

driver and driven chambers fail and form 4 petals, the rapid propagation of the

pressurized gas into the driven chamber occurs and leads to the creation of a shock

wave. It is worth noting that no breaking devices are used to force the opening of the

diaphragms, but the diaphragms’ failure is obtained by a differential pressure created

between the driver/buffer and buffer/driven chambers. A numerical investigation

corroborated by experimental tests helped to correctly design the diaphragms’ thickness

and score depth (Colombo et al. 2014).

As mentioned before, the specimen/soil chamber represents a peculiar characteristic

of the present shock tube: it is 1.8 m long, 13.5 mm thick and has an inner diameter of

583 mm. The chamber contains both the circular slab specimen and the soil; the

classical load scheme reproduced is that of a circular slab resting on soil and subjected

to a predefined uniform pressure (Fig. 3b). This load scheme was adopted in a previous

study mainly directed to investigate the impulsive soil–structure interaction and the

delamination between HPFRCC and SFRC layers (Colombo et al. 2013).

The load scheme in Figure 3c is adopted in this study in order to reproduce the

possible local lack of supporting soil at the extrados of the segment. The load scheme in

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Figure 3c differs from that illustrated in Figure 3b for the introduction of a steel cylinder

closed at one end between the rear side of the specimen and the soil. In this way, a

unilateral simply supported condition is reproduced for the loaded specimen. It is worth

noting that the orthoradial compression of the ring is not taken into account in favour of

safety because generally, according to the M–N interaction diagram, tunnel segments

work in the diagram region where the axial force has a positive effect on the bending

strength and stiffness. The same load scheme is used for studying the situation shown in

Figure 1, where discrete panel supports are substituted with a continuous linear support

along the perimeter (dashed line in Fig. 4b).

In the 1L specimen case, the soil in contact with the concrete plate cannot support a

significant reaction due to the stiffness of both the steel cylinder and steel flange, which

prevents the rotation of the plate at the support. In the multi–layer cases, the main

movement is a longitudinal translation. This kinematic condition pushes both the soil

and the steel cylinder, thus creating a situation that is realistic for the specimen but not

for the soil. In fact, it induces a reaction under the steel cylinder that does not represent

the situation with a void.

3.2 Specimen preparation

The specimen sizes are detailed in Figure 4. The layered specimens (3L and 2L) were

produced in several steps: initially, the HPFRCC layers were cast and two connectors

were placed across the layers to ensure mechanical anchorage between HPFRCC and

SFRC layers during the handling operations. These connectors are not present in the

full–size tunnel segments where the bond between the two materials is guaranteed by

the chemical adhesion and by the curved geometry that is able to ensure a multi–layer

composite behaviour (Colombo et al. 2013). In order to reduce as much as possible the

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influence of connectors on the specimen response, they are placed at 25 mm from the

specimen edge on opposite points located on the same diameter and avoiding the

connectors to be inside the loaded area (see Fig. 4). One layer of HPFRCC was placed,

once hardened, at the bottom of a steel formwork, and then the SFRC layer was cast

and, in the case of 3L specimens, the second HPFRCC layer was placed at the top of the

SFRC, thus completing the specimen preparation.

It is worth noting that steel connectors are never activated. In fact, in the 2L case, the

shock wave pressure insists on the HPFRCC side and therefore no dowel action arises

since the stretched portion is located on the opposite side where no connectors are

present. In the 3L case, a previous experimental investigation (Colombo et al. 2013)

showed that no delamination between external layers and core occurred: therefore, steel

connectors are not activated thanks to the large stiffness of the bond interlayer surface.

3.3 Specimen instrumentation

The behaviour of the testing slab is investigated through an appropriate set of

instruments described herein. The surrounding soil is also monitored in two sections

through accelerometers.

Three ICP (Integrate Circuit Piezoelectric) dynamic pressure transducers are placed

along the driven chamber axis at 300 mm, 1250 mm and 2250 mm from its flange end.

The transducers have a quartz sensing element with a full scale pressure of 6.9 MPa, a

sensitivity of 0.7 mV/kPa, a rise time lower than 1µs and a resonant frequency higher

than 500 kHz.

The specimen acceleration on the surface facing the steel cylinder is measured by

means of seven ICP accelerometers: one (A1) placed at the specimen centre and the

other six placed at 120° relative to each other respectively at 70 mm (A2–A4) and at

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180 mm (A5–A7) from the specimen edge (Fig. 4b). Two accelerometers (A8–A9) are

embedded in the soil at the centre of the specimen/soil chamber cross–section,

according to the scheme indicated in Figure 3c; they measure the soil acceleration along

the tube axis. The accelerometer characteristics are: a quartz sensing element with a

measuring range of ±500g pk (peak acceleration), a band width larger than 10 kHz, a

broadband resolution of 0.005g rms (root mean square) and a resonant frequency higher

than 70 kHz.

The relative central displacement between the specimen and the steel cylinder is

measured by a displacement transducer. It has a frequency response of 800 Hz, a

resolution of 1.0 µm and a linear stroke length of 4 mm.

The signal conditioning for both accelerometers and pressure transducers is

performed with an ICP signal conditioner with gain equal to one, a bandwidth equal to

10 kHz and a broadband electrical noise equal to 3.5 µV rms.

All channels are acquired by means of the same data acquisition system with 56

parallel channels with the maximum sampling rate of 3 MS/s per channel and a 14–bit

resolution. The data acquisition for all the channels is triggered by the signal of the

pressure transducer placed at a distance of 2250 mm from the driven end flange: when

the shock wave goes through its position, the system starts acquiring data with a

sampling rate of 1 MS/s.

3.4 Test programme

The experimental tests differ for the blast load history applied to the specimens. Two

tests, hereafter indicated as the low pressure tests, are characterised by an average peak

pressure of 0.36 MPa and an average specific impulse of 3.32 MPa ms. The other two

tests, hereafter indicated as the high pressure experiments, are characterised by an

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average peak pressure of 1.07 MPa and an average specific impulse of 6.09 MPa ms. A

total of four tests are carried out: two low and two high pressure tests. An abbreviation

is used to indicate different tests that correspond to different specimens (for example

3L–H): 1L, 2L and 3L stand for single, double and triple layer specimen, respectively,

while the final L or H stand for low and high pressure test.

4 SIMPLIFIED METHODS FOR DESIGN ANALYSIS

4.1 Single degree of freedom model

The experimental results of the thin HPFRCC plate (1L specimen) are compared with a

simplified model often used in design applications. This model consists of an equivalent

elasto–perfectly plastic Single Degree of Freedom (SDOF), where the mass, the

stiffness and the applied load of the structural element are replaced in the equation of

motion with the equivalent values of a lumped mass–spring system. The transformation

coefficients that relate the equivalent mass, stiffness and load in the SDOF system to

their respective quantities in the actual plate are obtained by using the principle of

virtual displacement. This approach allows for obtaining an equivalent system with

kinetic energy, strain energy and external work equal to the distributed system (Biggs

1964). The transformation factors necessary to develop the equivalent SDOF model for

the elastic and plastic stages are given in Colombo and Martinelli (2012) and refer to a

simply supported plate. The plate considered has a diameter equal to the steel cylinder

one (φ = 480 mm), is supported on its external circumference and is uniformly loaded

on the whole surface.

The procedure followed for the calculation of the ultimate bending moment

resistance necessary to calculate the ultimate resistance force was proposed by di Prisco

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et al. (2004; 2009) for FRC elements. A linear softening constitutive law for the tensile

behaviour as specified in Colombo and Martinelli (2012) is considered. The material

parameters necessary to describe the model are the average values indicated in

Section 2.

4.2 Linear elastic FE models

Linear elastic FE analysis is a common tool in engineering design and is herein adopted

with the double purpose of checking the reliability of the SDOF model in the elastic

range for the single layer specimen response and to provide additional insight into the

layered specimen response where the specimens remain in the elastic domain at both

low and high pressure conditions.

Different finite element models for each specimen typology are built to simulate the

behaviour of the circular plates. The finite element program ABAQUS/Explicit 6.12

(ABAQUS Analysis User’s Manual 2012) is used for all numerical simulations. The FE

models are three–dimensional.

Ten–node modified quadratic and hourglass control tetrahedron elements (C3D10M)

are employed to discretize the specimens. The element has three degrees of freedom per

node plus three additional displacement variables to reduce volumetric and shear

locking (ABAQUS Analysis User’s Manual 2012). Due to symmetry, a slice of the

specimen (a quarter) is modelled for efficiency purposes. Symmetrical boundaries are

imposed on the x–z and y–z planes (Fig. 5a). According to the experimental set–up

used, the specimens investigated behave as simply supported along a circumference that

has a diameter equal to the diameter of the steel cylinder (see Fig. 5b). The driven end

flange acts as a “hard contact” point when significant flexure is experienced by the

specimen, especially in the one layer specimen case. In order to evaluate the effect of

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this situation, another limit boundary condition is considered by introducing an

additional bilateral support on the external circumference (Fig. 5c). In specimens with

two and three layers, where the soil deformability is larger than the specimen one, it is

not necessary to introduce such additional condition in the model for the load cases

investigated.

The main finite element mesh characteristics of the models are reported below. The

elements along the thickness for specimens with one, two and three layers are

respectively equal to 10 (1L), 8+28 (the number of elements refers to HPFRCC and

SFRC layers; 2L), and 8+30+8 (the number of elements refers to HPFRCC, SFRC and

HPFRCC layers; 3L); following the same order, the total number of nodes is equal to

207714, 110493 and 135065, while the total number of elements is equal to 141415,

77829 and 95508. The average aspect ratio (ratio between the longest and shortest edge

of an element) is lower than 2 in all the models. The Young’s modulus E and the

Poisson’s ratio ν are equal to E = 37000 MPa ν = 0.2 and E = 47500 MPa ν = 0.2,

respectively for SFRC and HPFRCC materials.

5 TEST RESULTS AND DISCUSSION

A summary of the experimental tests is reported in Table 2, which indicates, for each of

them, the peak pressure, positive load duration and specific impulse values. The

pressure history recorded by the transducer closest to the specimen for the low and high

pressure tests is shown in Figures 6a and 6b, respectively. Figure 6a shows how

specimens with very different stiffness lead to a reduced difference on the peak pressure

of about 15%. For this reason, it seems reasonable, as a first step, to uncouple the fluid

response from the structure response.

In the following, the single layer specimen response, referring to the structural

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application depicted in Figure 1, is presented first; the response of multi–layer

specimens referring to the problem shown in Figure 2 are then described. A comparison

between the two situations in terms of energy absorbed is finally reported.

5.1 Single layer specimen response

The results of accelerometers A2–A4 and of A5–A7 are shown in Figure 7: both the

triad of accelerometers are placed at 120° to each other on the specimen with the

difference that accelerometers A5–A7 are closer to the specimen centre compared to

A2–A4. For all axial accelerations (A1–A7), positive values indicate accelerations

directed from the specimen towards the steel cylinder. The figure shows a response

moderately symmetrical for nominally identical instruments. As shown in the following,

the lack of a perfect symmetry in the accelerometer response for times greater than

1.5 ms is due to the not perfectly symmetrical final crack pattern.

The flexural behaviour of the specimen is summarized in Figure 8 by comparing the

response of accelerometers placed along two radii at different distances from the centre.

In particular, Figures 8a and 8b refer to the radii R1 and R2 on which A1, A2 and A5

and A1, A3, A6 are placed, respectively (see Fig. 4b for the instruments position). In

Figure 8, A1 (central), A5, A6 (middle) and A2, A3 (external) indicate the position of

the accelerometers. The central and middle accelerometers are characterised by a similar

response immediately after the application of the blast pressure. The external

accelerometers, closer to the support, show reduced accelerations. It is also interesting

to note how the accelerometers closer to the steel cylinder embedded in the soil, that

acts as support for the plate, record a negative peak related to the reflection wave that

originated at the steel cylinder–soil interface.

A computation of the fundamental frequency of the simply supported slab

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corresponding to the first flexural mode gives a value of about 350 Hz for both the

SDOF and FE models (348.8 Hz for SDOF model and 352.2 Hz for the FE model).

Although the peak fundamental frequency of the specimen is visible in the experimental

frequency domain (342 Hz), it is not easily detectable in the time domain response (Figs

7 and 8) that is the result of the superposition of many frequencies. Lower peak

experimental frequencies, compared to the specimen fundamental one with infinitely

rigid supports, are observable in the frequency domain due to the complexity of the

whole system; in fact, the system deformability considers the specimen, the steel

cylinder, the soil and the shock tube chamber, where the soil plays the key role.

Figure 9a shows the comparison in terms of central displacement between

experimental and numerical (SDOF and FE models) response. The figure reports the

response immediately after the application of the load. Displacements larger than ± 2.0

mm cannot be recorded by the transducer since the gauge length is limited. The FE

models differ in the boundary conditions: the model “FEM – supp.” is simply supported

on the steel cylinder as indicated in Figure 5b, while the model “FEM – fixed” has an

additional constraint due to the chamber flange as illustrated in Figure 5c. The initial

elastic response of the “FEM – supp.” model is in good agreement with the

experimental one.

The equivalent elasto–plastic SDOF model shows an initial stiffness very close to

that of the model “FEM – supp.” although with a little time delay. This delay is due to

the different load – time function used for the FE models and for the SDOF model; in

the first case, the experimental load–time function is used, while in the second case an

exponential function with rising time (time interval required to reach the peak of the

reflected pressure in the pressure–time history diagram) equal to zero is adopted. Figure

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9b clearly shows that the lack of rising time in the load function of the SDOF model

causes the delay in the response; indeed, if an exponential load function without rising

time (model “FEM – expon. load” in Figure 9b) is used in the FE model, identical initial

responses are obtained.

The experimental crack pattern at the end of the test is shown in Figures 10a and 10b.

The figure points out the formation of a plastic hinge at the support location; radial and

circumferential cracks are also visible. The SDOF model is able to reproduce the

experimental load–displacement response up to 1.5 mm and shows the activation of the

plastic phase thus predicting the specimen failure. Nevertheless, the large displacement

observed experimentally at failure (about 100 mm) is not reproduced for its intrinsic

limitations by the simplified SDOF model that provides a residual displacement of

about 5 mm.

It is interesting to observe that the specimen failure is characterized by fibre pull–out

(Fig. 10b) rather than fibre rupture. The same failure mechanism (Fig. 10c) is found on

small notched specimens (HPFRCC cylinders 20 mm long) subjected to tension through

a Modified Hopkinson bar (Caverzan et al. 2012). The strain rates are similar for the

two situations, respectively 120 s-1 (Fig. 10b) and 150 s-1 (Fig. 10c). Although the

specimen sizes, the loading scheme and the wave propagation are very different in both

cases, they exhibit the same failure mechanism governed by fibre pull–out.

5.2 Multi–layer specimen response

The variation of the axial acceleration along the radius R1 is shown in Figure 11 for the

specimen 2L–H. A decrease of the first peak moving from the specimen centre to the

specimen edge is observable; note that the negative peaks associated with the middle

(A5) and external (A2) accelerations are greater than the central one (A1). The

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oscillations in the acceleration diagrams are associated with different load transfer

mechanisms characterized by different stiffnesses: bending of the squat plate and

concrete inclined struts.

Figures 12a compares experimental and numerical FE central displacement response

respectively for low pressure. In Figure 12b the experimental response is not reported

since the signals were lost. The maximum numerical peak response at low pressure is

about 0.01 mm, while at high pressure the peak response is about 0.025 mm and 0.032

mm for specimens with three and two layers, respectively. In spite of the high pressures

applied on the specimens, the maximum displacements are almost negligible. This is

due to the squat shape of the specimens where the flexural contribution does not prevail

on the shear one. The comparison between experimental and numerical results in the

low pressure case highlights a significant underestimation of the maximum

displacement as evaluated by the model. A possible reason could be related to non–

continuous support of the specimen due to the roughness of its surface. It is worth

noting that the period of oscillation of the specimen response is well fitted as

demonstrated by comparison (0.59 ms against 0.60 ms, respectively for experimental

and numerical results).

Numerical results point out that the behaviour of the layered specimens at both low

and high pressure remains in the elastic domain. In particular, at high pressure

conditions, the maximum principal stresses are lower than 3.0 MPa thus far from the

crack onset.

Another important point for the multi–layer specimens concerns the possibility to

develop inter–layer delamination as a consequence of a blast event. To this regard, the

computed in–plane shear stress at the SFRC–HPFRCC interface during the loading is

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lower than 0.45 MPa, thus indicating that the inter–layer delamination did not occur for

specimens where the differential shrinkage between the two different materials has not

favoured an initial detachment of the layers (Colombo et al. 2013).

5.3 Single and multi–layer specimens: energy dissipation

The difference between the energies stored by the specimens for the single and multi–

layer cases can be appreciated in Figure 13a. It reports the axial accelerations recorded

in the soil (accelerometer A8, see Fig. 3c) during the tests 1L–L and 3L–L. The

maximum acceleration transmitted to the soil for the single layer case is about half of

that recorded for the three layer specimens. This observation indicates that, for equal

input energy into the system, the single layer specimen stores more energy compared to

the multi–layer specimen. Most of this stored energy is then converted into plastic

energy while a certain quantity is transmitted to the soil. The energy transferred to the

soil is higher for the multi–layer specimens that remain elastic during the load

application.

Figure 13b compares the axial soil accelerations at two different locations during the

test 3L–H. A great quantity of energy is dissipated in the soil in only 400 mm (distance

between axial accelerometers A8 and A9, see Fig. 3c), as can be observed by looking at

the acceleration peak reduction.

6 CONCLUSIONS

The paper reports the main findings of an experimental study focusing on the response

of fibre reinforced concrete used in an underground tunnel in case of internal explosion.

Two situations are explored: (a) the effectiveness of thin HPFRCC panels applied to the

intrados of new or existing tunnels as fire protection of tunnel linings in case of blast

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and (b) the behaviour of a new layered tunnel segment made of SFRC and HPFRCC

when incomplete mortar filling is inserted between the lining and the excavated surface

thus amplifying the in–service internal actions (bending moment and shear force).

The experimental tests carried out by means of shock tube on concrete specimens

confirm that thin HPFRCC panels could break even for blast pressures of 0.3 MPa, with

anchor spans of about 40 cm, if simple air space is used to reduce thermal effects in the

segment, while the behaviour of layered segments is not critical up to about 1 m of

unfilled zones and blast pressures in the order of 1 MPa, taking into account a scale

factor of 2 between the thickness of the specimen tested and the real thickness of the

segment considered as the reference. In the first case, a simple 1 degree of freedom

elasto–plastic model can predict the failure and load–displacement response up to a

displacement of 1.5 mm.

With reference to the layered structure, the main problem consists in the modelling

of the surface roughness of the support: the perfect constraint introduced in the

modelling does not allow the fitting of the measured displacement. When the single and

the three layer situations are compared in terms of axial acceleration into the soil, it is

interesting to observe how the panel failure (1L–L case) reduces about 50% of the

acceleration transmitted to the soil, which means a higher energy dissipation due to

plastic strain and cracking in the specimen. Moreover, when a pressure of about 1 MPa

is applied, the axial soil acceleration experiences a reduction of about 60% in only 400

mm, denoting an energy dissipation that occurs during the wave propagation into the

soil.

Finally, the failure exhibited by the thin HPFRCC panel showed the same pull–out

mechanism observed in previous uniaxial tension tests performed by means of a

20

modified Hopkinson bar on cylindrical specimens made of the same material, thus

confirming that the failure mechanism of HPFRCC is not at all affected by the wave

propagation path in dynamic failure.

ACKNOWLEDGMENTS

The research was financially supported by the European INTERREG IT/CH 2006_2013

project ACCIDENT ID 7629770, Measure 2.2.

The authors want to thank Lorenzo Corti and Luca Corti for their help in the

experimental tests as a part of their M.Sc. thesis in Civil Engineering at Politecnico di

Milano.

21

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24

LIST OF FIGURES

HPFRCC panel

Air

Lining

Explosion

Tunnelp(t)

Figure 1 Schematic layout of the HPFRCC panel applied to the intrados of the tunnel

Soil

Explosion

Tunnel

p(t)

Filling grout

Void in the

filling grout

Filling grout

Soil

Tunnel lining

Figure 2 Tunnel cross–section: the problem of a void in the mortar filling grout

25

Soil Driven

1Vertical section

SpecimenSpacer disk

Polyethylene

Soil DrivenSpecimenSpacer disk

Polyethylene Steel cylinder

(b)

(c)

900

500

A9 A8

Accelerometer

2.3m (φ = 481mm)1.8m (φ = 583mm) 0.26m10.5m (φ = 481mm)

Driver chamber

Specimen/soil

chamberDriven chamber

Diaphragms

chamber1

Support

(a)

Figure 3 Lateral view of the shock tube facility (a) and vertical section of the specimen/soil

chamber: (b) classical load scheme and (c) load scheme adopted in this study (units: mm)

26

SPECIMENS FRONT VIEW

20

20

14

02

01

40

SFRC HPFRCCHPFRCC

SFRC HPFRCC

Specimen type 3 (3L)

Specimen type 2 (2L)

20

HPFRCC

Specimen type 1 (1L)

SPECIMEN PLAN VIEW

(rear side)

Legend

A = accelerometer

δ = displacement transducer

A1,δ1

A2

A3A4

A6A7

A55

60

70

18

0

48

0

cylinder trace

R1

R2R3

(a) (b)

560

M8

L = 50 mm

25 25

Figure 4 Specimen dimensions and location of the instruments: (a) front view and (b) plan view

(units: mm)

27

(a)

(b)

p(t)

x

y

240

280

p(t)

v=θx=θz=0

(y symmetric condition)

(c)

u=θy=θz=0

(x symmetric

condition)

Figure 5 Boundary condition for the quarter model of the specimen: (a) plane view, (b) front

view in the simply supported case and (c) front view in the simply supported – hard contact case

(units: mm)

28

0 10 20 30 40−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4(a) Low

Time [ms]

Pre

ssur

e [M

Pa]

3L−L1L−L

−5 0 5 10 15 20 25 30 35−0.2

0

0.2

0.4

0.6

0.8

1

1.2

(b) High

Time [ms]

Pre

ssur

e [M

Pa]

3L−H2L−H

Figure 6 Shock wave pressure in proximity of the specimen face: (a) low and (b) high pressure

tests

0 1 2 3 4 5−6000

−4000

−2000

0

2000

4000

6000

(a) 1L−L

Time [ms]

Acc

el. [

m/s

2 ]

A2A3A4Av.

0 1 2 3 4 5−6000

−4000

−2000

0

2000

4000

6000

(b) 1L−L

Time [ms]

Acc

el. [

m/s

2 ]

A5A6A7Av.

Figure 7 Axial specimen accelerations for specimen 1L–L: (a) accelerometers A2–A4 and (b)

A5–A7

29

0 1 2 3 4 5

−4000

−2000

0

2000

4000

6000(a)

Time [ms]

Acc

el. [

m/s

2 ]

A1A5A2

0 1 2 3 4 5−3000

−2000

−1000

0

1000

2000

3000

4000

5000

6000(b)

Time [ms]

Acc

el. [

m/s

2 ]

A1A6A3

Figure 8 Axial specimen accelerations for specimen 1L–L (a) along radius R1 and (b) along

radius R2

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

(a)

Time [ms]

Dis

pl. [

mm

]

Exp.SDOFFEM − supp.FEM − fixed

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

Time [ms]

Dis

pl. [

mm

]

(b)

SDOFFEM − experim. loadFEM − expon. load

Figure 9 (a) Experimental vs. numerical central displacement response for specimen 1L–L and

(b) influence of the applied load time history shape on the specimen’s central displacement

30

Figure 10 (a–b) Crack pattern and fibre pull–out failure mechanism for the specimen 1L–L; (c)

HPFRCC fibre pull–out failure mechanism for a specimen after uniaxial tension test (Caverzan

et al. 2012)

0 1 2 3 4 5−5000

−4000

−3000

−2000

−1000

0

1000

2000

3000

4000

Time [ms]

Acc

el. [

m/s

2 ]

A1A5A2

Figure 11 Axial specimen accelerations for specimen 2L–H along the radius R1

31

0 0.5 1 1.5 2 2.50

0.02

0.04

0.06

0.08

0.1

(a) 3L−L

Time [ms]

Dis

pl. [

mm

]

Exp.FEM

0 1 2 3 4 50

0.005

0.01

0.015

0.02

0.025

0.03

0.035

(b)

Time [ms]

Dis

pl. [

mm

]

3L−H FEM2L−H FEM

Figure 12 Central displacement responses for layered specimens at (a) low and (b) high

pressure levels

0 5 10 15 20

−600

−400

−200

0

200

400

(a) A8

Time [ms]

Acc

el. [

m/s

2 ]

1L−L3L−L

0 5 10 15 20 25−3000

−2500

−2000

−1500

−1000

−500

0

500

1000(b) 3L−H

Time [ms]

Acc

el. [

m/s

2 ]

A8A9

Figure 13 (a) Soil acceleration A8 during tests 1L–L and 3L–L and (b) soil accelerations A8

and A9 during test 3L–H

32

LIST OF TABLES

Table 1 SFRC and HPFRCC mix design (* = hooked end fibres lf = 30 mm, df = 0.67 mm; † = straight fibres lf = 13 mm, df = 0.16 mm)

Component Dosage (kg/m3)

SFRC HPFRCC

Cement type I 52.5 480 600

Slag - 500

Aggregate 1 620 (0 to 3 mm) 977 (0 to 2 mm)

Aggregate 2 440 (0 to 12 mm) -

Aggregate 3 710 (8 to 16 mm) -

Water 192 200

Steel fibres 50* 100†

Superplasticizer 6.5 33

Table 2 Experimental test: shock wave characteristics

Specimen

name Test type

Peak

Pressure

Positive load

duration

Specific

Impulse

(MPa) (ms) (MPa ms)

1L-L Low pressure 0.33 31.33 2.76

3L-L Low pressure 0.39 32.29 3.88

2L-H High pressure 1.08 15.56 6.14

3L-H High pressure 1.06 15.44 6.05