Bernard Lotz
email: bernard.lotz@ics-cnrs.unistra.fr

André André Kovacs

Kovacs

Frank Padden

The structural language of crystalline polymers

In sharp contrast with their amorphous counterparts, crystalline polymers provide a wealth of information on their chain conformation, the packing of the chains in unit-cells, the existence or not of mirror symmetric conformations, on the crystalline lamellae, on the folds linking the crystalline stems, etc. Three illustrations of these insights are presented here: (a) the orientation of polymer folds in crystalline lamellae, (b) the complete structural analysis of the alpha phase of isotactic polypropylene by a simple observation of the lamellar morphology and (c) the so-called lateral spread following secondary nucleation on the growth faces of a polymer crystal.

Introduction.

This special issue honoring the contributions of Greg McKenna to the understanding of polymer glasses and rheology gives me the opportunity to evoke the lasting friendly

polystyrene and polyethylene oxide (PS-PEO): glass transition of the PS sequences and crystallization/melting of the PEO ones. [START_REF] Lotz | 2Properties of copolymers composed of one poly-ethylene-oxide and one polystyrene block. II. Morphology of single crystals[END_REF] The PhD thesis was more centered on single crystals of these systems investigated by electron microscopy and electron diffraction: the crystalline part of the block copolymers had taken precedence. 2,3 These same techniques were used in my post-doc to investigate the crystal structure of silks and fibrous proteins. [START_REF] Lotz | Crystal structure of poly(L-ala-gly) II. A model for silk I[END_REF] They have been my favorite tools ever since.

Having had the opportunity to test and compare the level of information provided by crystalline and amorphous materials, it became clear that crystalline polymers "speak" to us -or at least to me -much more loudly than amorphous polymers. Their language needs of course to be translated, but the translation can reach an unusual level of insight -up to a detailed spelling of the words. This feast is hardly accessible to amorphous polymers since they have definitely a more limited language -which calls for a more elaborate design of experiments and a deeper evaluation of the data provided by these experiments.

In this contribution, three examples taken from our earlier work will illustrate the insights provided by crystalline polymers. They deal with (a) the orientation/structure of the folds in crystalline lamellae (b) the detailed analysis of the crystal structure of a lamellar branching observed for isotactic polypropylene in its most common alpha phase (aiPP). This analysis helps determine the helical hand (aiPP is made of right and of left-handed helices) and the orientation of each and every helix in these structures by a simple visual observation (c) the determination of the so-called "lateral spread" linked with the density of individual nucleation events on the growth faces of a crystal -a challenging issue in polymer crystallization.

I.

The structure and orientation of folds in lamellar crystals.

When crystallized from the bulk, crystalline polymers are made of thin lamellae organized in more complex three-dimensional spherulites. Similar lamellae are produced by crystallization from solution. In the lamellae, the crystalline stems are usually normal or nearly normal to the lamellar surface. The lamellar thickness is much less than the length of the polymer chains. As a result, the chains must fold in an accordion-type manner. This conclusion was first reached by Keith Storks back in 1938 when analyzing thin films of gutta-percha. [START_REF] Storks | An Electron Diffraction Examination of Some Linear Polymers[END_REF] It was later developed by Keller (1957) for single crystals of polyethylene and for spherulites. [START_REF] Keller | A note on single crystals in polymers: Evidence of a folded-chain configuration[END_REF][START_REF] Keller | Polymer crystals[END_REF] Chain folding in polymers is ubiquitous in polymer crystallization: the surface of polymer lamellae is covered with an amorphous layer of less organized, amorphous material made of segments of the chain that leave and reenter the crystalline core.

For many years, the exact nature and structure of these layers remained a matter of debate -for good reasons. [START_REF]Organization of macromolecules in the condensed phase[END_REF] We are dealing with a thin layer, one or two molecular cross-sections thick that can hardly be investigated by experimental techniques designed to investigate bulk materials.

Flory in particular advocated a highly disordered layer with "uncontrolled" orientations of folds as in the old-fashioned telephone switchboards. Crystallography-oriented colleagues considered more "organized" surfaces -if only to accommodate the density difference between the crystal core and the amorphous surface layer. [START_REF]Organization of macromolecules in the condensed phase[END_REF] This view had taken strength already when we introduced with Jean-Claude Wittmann the following elegant means to illustrate the folds orientation. 9

The structure of surfaces, including of thin layers, can be investigated by resorting to decoration techniques. The principle is simple. In polymer crystals, folds cannot be resolved individually.

If some material is deposited (actually vaporized) on the fold surface and if it interacts with the folds, it may generate a pattern that tells something about those folds -for example their orientation. This pattern must be at a larger scale to become visible, but it can reveal much smaller and hard to identify substrate features -after all, the deposit/substrate interactions involve mostly van der Waals forces (6-8Å range). The decoration technique was initially developed by Alan Bassett. [START_REF] Bassett | A new technique for decoration of cleavage and slip steps on ionic crystal surfaces[END_REF] Gold vaporized on cleaved sodium chloride single crystals moves on the surface and gathers in droplets that are aligned along cleavage steps. It was the first time a 3.5Å sized feature (the height of the cleavage steps) could be, if not "seen", at least located. Applying the same technique but vaporizing polyethylene on single crystals of polyethylene (and other crystalline polymers, e.g. polyoxymethylene) yields the result shown in Figure 1.

PE vapors condense and crystallize on the cold (room temperature) substrate. Crystals formed by the condensation of vapors on the glass surface are not oriented. Crystals formed on the PE fold surface are highly oriented by the substrate folds. The depositing small PE fragments end up lying flat on the surface and become oriented parallel to the folds (cf. inset of Figure 1).

Lateral accretion of these oriented fragments generates what is in essence piles of wood trunks

-in this case lamellae edge-on. The orientation of these lamellae is at right angle to the orientation of the folds. The evidence is compelling: the folds have different orientations in the different growth sectors. They are oriented parallel to the growth faces as would be expected when a random coil is deposited and "flattens" on a flat growth face. The method can be used for bulk crystallized materials, in spherulites. It reveals a similar orientation of the folds, essentially parallel to the local growth front. 9

This decoration technique has therefore a resolution of about 10nm (the length of the vaporized PE fragments). It cannot reach the very local, nanometer range, but it confirms that a significant fraction of the folds is indeed oriented in both solution and bulk crystallization, which invalidates the switchboard model.

II.

The local structure in alpha phase iPP lamellar branching.

The crystallographic insight to be described now can be reached only in the alpha phase of isotactic polypropylene (aiPP) thanks to a unique combination of crystal structure features and growth processes.

The crystal structure of aiPP) was determined by Natta and Corradini in 1955, soon after the first synthesis of this polymer using a catalyst developed by Ziegler. 11 The chain conformation is helical, with three motifs per turn (Figure 2, top left). Since iPP is not a chiral polymer, righthanded and left-handed helices can exist. In aiPP, these helices are organized in layers: layers of right-handed helices alternate with layers of left-handed helices along the b axis of the unitcell. Furthermore, in chain axis projection, the helices pack "face-to-face" and "tip-to-tip":

along the b axis: the structure is actually an alternation of bilayers. The "tip" faces of the bilayers have an interesting structure: they are a perfect lozenge pattern of methyl groups.

Indeed, the cell is monoclinic: the a axis is at ≈100° from the c axis and the a and c axes of the unit-cell have the same length: ≈6.5Å.

The tip-to-tip interaction of layers made of helices of opposite hand is simple: the lozenge patterns are shifted such that the "tip" methyl groups of one layer are located at the center of the lozenge of the facing layer. The chain axes remain parallel. An original situation is created when the facing layers are made of helices of the same hand. [START_REF] Wittmann | The molecular origin of lamellar branching in the a (monoclinic) form of isotactic polypropylene[END_REF][START_REF] Lotz | Structure and morphology of poly(propylenes): a molecular analysis[END_REF] The depositing layer must rotate around the b axis in order to bring its c axis parallel to the substrate a axis in order to recreate an interaction similar to the crystallographic one (Figure 2, bottom left). This is a case of homo-epitaxy. [START_REF] Wittmann | Epitaxial crystallization of polymers on organic and polymeric substrates[END_REF] Growth of lamellae with this different helix axis orientation generates a unique, profuse lamellar branching with branches at an 80° or 100° angle. This lamellar branching is also an original morphological marker. The orientation of the c axis in the lamellae is known: it is normal to the lamella. In addition, in the present case, the c axis orientation of one set of lamellae indicates the orientation of the a axis in the other set of lamellae -an information that would be accessible only by diffraction but is reached thanks to this lamellar branching.

This information turns out to be crucial. The symmetry of the unit-cell and this monoclinic structure make it possible to determine if the cell is seen from the "front" or from the "back" of the b axis, i.e. from the b or the -b axis. From the front, the a axis appears to be oriented at 4

o'clock to the c axis; from the back, it appears to be oriented at 8 o'clock to the c axis (imagine a transparent clock with the long arm (the chain axis) at noon and the short arm at 4 o'clock looked at from the front or from the rear). In turn (case 1 in Figure 2) when seen from the front (or more exactly from the +b side), the layers of helices with a single methyl group oriented towards the observer is made of left-handed helices, the layer showing the "back" of the helices with two methyl groups are made of right-handed helices. When (case 2 in Figure 2) the cell is seen from the -b side, the helix senses are reversed: the right-handed helices have their single methyl facing the observer. Figure 2 illustrates these analyses as applied to a thin film of aiPP crystallized on benzoic acid.

iPP crystallizes epitaxially on this nucleating agent, with the ac face as the contact plane -the exact orientation needed to illustrate the above features. [START_REF] Wittmann | Epitaxial crystallization of polymers on organic and polymeric substrates[END_REF] The film is made of two sets of lamellae with different orientations, as also observed in solution or bulk crystallization of aiPP as a result of the homoepitaxy. The electron diffraction pattern indicates that the unit-cell is oriented as shown in the insets, with in each set the c axes normal to the lamellas. In the set of lamellae oriented from bottom left to top right, the a axis is at 8 o'clock to the c (or helix) axis of the unit-cell: the single methyl group of left-handed helices faces the observer (case 2). In the set of lamellae oriented from the bottom left to the upper right, the a axis is at 4 o'clock to the c axis: the single methyl group of right-handed helices faces the observer, and left-handed helices show their back, with two methyl groups (case 1).

This analysis therefore helps determine the helical hand and the orientation of each and every stem in the whole film based on a simple observation of the branched lamellae morphology. It also confirms the structural origin of the homo-epitaxy leading to this unique lamellar branching in aiPP: the interaction of the two sets of lamellae takes place between layers made of helices with the same chirality. Indeed, in the two sets of lamellae, the "tip" layers made of helices with the same hand are oriented in opposite directions (+b and -b) and with c axis orientations ≈100° away in the ac plane, which is the exact requisite needed to generate the homo-epitaxy when they interact (bottom left diagram in the figure).

Needless to say, this level of insight questions and challenges some of the very diverse views expressed about crystallization processes. One line of thought considers that polymer crystallization is a multistep process. In an initial step the macromolecular chains (pre)organize in smectic-type "bundles" that deposit on a loosely, still ill-defined growth front and reorganize to reach their final, crystallographic structure. [START_REF] Strobl | Crystallization and melting of bulk polymers: New observations, conclusions and a thermodynamic scheme[END_REF] This scheme has the merit of being "generic" but does not take in account the very detailed analyses provided by a more "crystallographic" approach. [START_REF] Lotz | What can polymer crystal structure tell about polymer crystallization processes?[END_REF] The aiPP crystals and lamellar branching indicates that the depositing stems "read" the surface topography and only helices with the correct hand are attached to the growth front.

The selection process is even able to generate/select different stem orientations 100° apart depending on the helical hands of the depositing chains and substrate layer. Such a major reorientation is definitely not accessible to an initial "smectic"-type structure in which the helical hand is not defined and the helices are (must be) parallel. In other words, this crystallographic analysis tends to support a step-by step (stem by stem) crystal growth process in polymers that is very similar to the classical picture of the small molecules-type crystal growth. [START_REF] Lotz | What can polymer crystal structure tell about polymer crystallization processes?[END_REF][START_REF] Lotz | Polymer crystallization processes as seen from the growth front's perspective[END_REF] III. Crystallization processes: the buildup of a new layer via lateral spread/growth.

The diffraction patterns of single crystals are made of a number of spots that correspond to the diffraction from specific planes. In so-called electron microscopy dark field imaging, it is possible to select individual spots and enlarge them to produce a picture of the crystal made only of the electrons diffracted by the selected diffracting planes. The crystal thus appears in "dark field" since the main electron beam is blocked by the selection aperture. This feature makes it possible to "see" the crystal interior and investigate local features such as defects, etc.

In the case developed now, it helped reach a "hidden" feature of the crystal growth process.

Crystal growth amounts to building a wall with identical bricks. This is a layer by layer process: a first brick is used to start a new layer -the secondary nucleation process. Other bricks are lined up on both sides next to it -the so-called lateral spread. The lateral spread is limited by the density of secondary nucleation events taking place on the new layer -by the number of workers who build the wall and start the new layer. Since only the overall crystal growth rate can be measured, there is no means to determine whether a given growth rate results from limited nucleation and large spread or from dense nucleation and limited spread: there is a priori no means to access such fundamental variables in crystal growth since, once deposited on the growth face, the individual constituents -the bricks or crystalline stems -are all alike.

One means to measure lateral spread does exist: it is to give to only one of the workers bricks of a different color at some stage during the building process. In crystallography, such a difference may be observed in growth twins -i.e. a sudden change in the lattice orientation.

For the present purpose however, twinning must be a mild perturbance and affect the growth process in a minimal way. Such a system was found with a crystal structure of isotactic poly(vinylcyclohexane) (iPVCH) (PVCH is polystyrene with fully hydrogenated benzene rings). [START_REF] Alcazar | Polysynthetic twinning in poly(vinylcyclohexane) single crystals and "fractional" secondary nucleation in polymer crystal growth[END_REF] The crystal structure of interest is tetragonal, the chain conformation has a four-fold symmetry and (but!) in c axis projection the chains are not parallel to the a and b axes (cf. As shown in Figure 3 (bottom left), the solution grown single crystals are square and virtually featureless when examined in conventional transmission electron microscopy. When examined in dark field however (by selecting a diffraction spot that differentiates the stems "color") the crystal is clearly made of multiple narrow domains oriented normal to the growth fronts. [START_REF] Alcazar | Determination of the extent of lateral spread and secondary nucleation density in polymer single crystal growth[END_REF] The breadth corresponds to the contributions of individual twinned secondary nucleation events and their associated lateral spreads (the twinned orientation is maintained during further growth since the incoming stems reproduce the substrate stems orientation, which explains that the domains remain twinned in later growth). Similar pictures can be taken for different Tcs. Quite expectedly, the secondary nucleation events increase with decreasing crystallization temperature: the average breadth of the twinned domains decreases, from ≈70 stems at 200°C to≈30 stems at 120°C.

It should be emphasized that such insights cannot be reached for many (or more exactly, up to the present time, for any) other crystalline polymer. Very frequently, twinning induces more important crystallographic differences/disturbances that perturb the growth process. The iPVCH polymer, and only in this particular crystal structure, has the right combination of cell symmetry and limited disturbance to help reach this otherwise inaccessible feature of the crystallization process.

Conclusion.

The present contribution is of course far removed from the major interests of the community of colleagues working on polymer processing (only structures "at rest" are considered) or on glasses and rheology -the major themes of this special issue. It has attempted to show, in simple words, that crystalline polymers are indeed complex, but at the same time very friendly materials. They let us reach their intimacy at levels that are hardly accessible to other systems.

Their structure at different length scales, from the unit-cell to the morphology (a field not covered in the present account) "speaks" to us -provided of course that we are able to decipher their language. Most useful in this respect is the use of electron microscopy and diffraction, techniques well adapted to the length scales of polymer morphologies, and even more so to polymer single crystals. The variety of chemical and crystal structures, of cell geometries, etc.

is also a considerable advantage. It allows selecting the proper polymer to investigate specific problems such as the impact of folds on the lamellar shape (twisted, scrolled, etc.) [START_REF] Lotz | A critical assessment of unbalanced surface stresses as the mechanical origin of twisting and scrolling of polymer crystals[END_REF][START_REF] Lotz | Structure of Negative Spherulites of Even-Even polyamides. Introducing a Complex Multicomponent Spherulite Architecture Macromolecules[END_REF] or, as illustrated here, the extent of lateral spread during crystallization. In short, as indicated in the title of this contribution, crystalline polymers are very talkative about their structure, crystallization behavior, etc.

By contrast, amorphous polymers are, to me at least, almost mute. This is why this short contribution cannot end without conveying my sincere admiration for the work performed on polymer glasses and rheology. The challenges are considerable because the information provided by these systems remains very global, which makes it difficult to reach the intimate knowledge we all aim for. As illustrated by the contributions of André Kovacs, Greg and many others, clever instrumental designs and experimental protocols had to be, and have been,

developed to understand, also, their language.

Figure 1 .

 1 Figure 1. A solution grown single crystal of polyethylene (lateral size: 5-6 m, thickness ≈12 nm) decorated with polyethylene vapors. The decoration orientation indicates the orientation

Figure 2 .

 2 Figure 2. The crystal structure of isotactic polypropylene, alpha phase (top left) and the origin of the lamellar branching: interaction of facing layers made of helices of the same hand (bottom left). The resulting lamellar branching (right) helps determine the two unit-cell a axis orientations, parallel to the c axis of the other set of lamellae. (at 4 o'clock to the c axis orientation for case 1, at 8 o'clock for case 2) and the viewpoint: 1 or 2 (arrows, top left).

Figure 3 ,

 3 Figure 3, top left). The two slight rotations of the stems (clock and anti-clock) in an otherwise identical unit-cell are the two different "colors" needed to identify them by dark field imaging.

Figure 3 .

 3 Figure 3. The crystal structure of isotactic poly(vinylcyclohexane) (iPVCH) (top left). Note the rotation (here anticlockwise) of the helices relative to the tetragonal unit cell edges. Clockwise rotation corresponds to the twinned structure. A single crystal of isotactic poly(vinylcyclohexane) as seen by electron microscopy in bright field (lower left)) and darkfield through a 240 reflection. This reflection is sensitive to the azimuthal setting of helices in the unit-cell and is therefore well suited to reveal twinned domains. Note that such domains appear randomly during crystal growth (their relative distance from the crystal center is variable) but once formed, they continue to grow as twinned domains. This crystal was produced in a squalene solution at 180°C.


Zahid Yousif
email: engr.zahid.yousif@gmail.com

Intesab Hussain
email: intesab@quest.edu.pk

Soufiene Djahel
email: s.djahel@mmu.ac.uk

Yassine Hadjadj-Aoul
email: yassine.hadjadj-aoul@irisa.fr

A Novel Energy-efficient Clustering Algorithm for more Sustainable Wireless Sensor Networks enabled Smart Cities Applications

Keywords: Wireless Sensor Networks, Energy-efficiency, Smart Cities, LEACH

Wireless Sensor Networks (WSNs) is a major sensing technology that has revolutionized the way information is collected, processed, and used in many smart cities' applications that rely on sensing technologies for events detection and monitoring. Despite the multiple benefits that such technology offers, the quick depletion of sensors' battery power represents a major concern, mainly due to the extensive computational tasks and communication operations performed by individual sensors. Indeed, the cost of replacing batteries can be prohibitively expensive, especially when sensors are deployed in areas where access is difficult, in urbanized cities. To extend sensors' lifetime, this paper proposes a new variant of LEACH protocol named LEACH enhanced with PRObabilistic Cluster Head Selection (LEACH-PRO). LEACH-PRO introduces several measures to extend WSNs nodes' lifetime such as cluster head nodes selection using a probabilistic function based on maximum residual energy and minimum distance to the sink. The obtained simulation results have proven the supremacy of LEACH-PRO over LEACH and Direct Transmission protocol in terms of the achieved network lifetime and the generated traffic overhead. Most importantly, LEACH-PRO will significantly extend the sensors' lifetime, which would make this type of deployment more viable in smart city scenarios.

Introduction

The concept of smart cities continues to attract a lot of interest from industry, academia and policy makers to enable better quality of life for cities' inhabitants. At the forefront of these cities, sensors and actuators are the main driver for many value-added services and the expected automation, which not only targets the improvement of the urban life, but also the reduction of the management costs of these cities [START_REF] Ala' Khalifeh | Wireless sensor networks for smart cities: Network design, implementation and performance evaluation[END_REF]. In order to support the provision of these new services, Wireless Sensor Networks (WSNs) and other similar sensing technologies should be deployed all over the cities [START_REF] Bensaleh | Wireless sensor network design methodologies: A survey[END_REF]. Once deployed, these different sensors automatically organize themselves, forming an ad hoc network, in order to ensure global connectivity, regardless of their ranges which are sometimes very limited. Once deployed and configured, such sensors will allow the monitoring of multiple metrics such as motion, temperature or humidity level; they could be responsible of generating certain events, such as the detection of a fire to take safety measures in real-time [START_REF] Fauzi | Wireless sensor network applications: A study in environment monitoring system[END_REF]; they could even trigger actions, directly or indirectly, such as turning on the light when detecting movements.

WSNs are composed of tiny, low powered, low cost and light weighted sensor nodes. These nodes are capable of sensing, processing, aggregating and transmitting data on the wireless channel directly to the base station (BS) or via neighbor nodes to BS [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF]. Usually, WSNs are deployed in remote sensing fields where each node is equipped with a non-replaceable battery and consumes an amount of energy while sensing, aggregating and transmitting data [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF]. Hence, communication among sensor nodes must be efficient for faster relief operations in emergencies. In some situations, like areas where accessibility is difficult, it is almost impossible or too costly to replace the exhausted batteries [START_REF] Chandrakant | Middleware service oriented rescue and crime information system (rcis) using heterogeneous fixed nodes in wsns[END_REF]. Since the lifetime of a sensor node depends on its battery or power source capacity, which is consumed through communication and sensing activities, it is necessary to design energy-aware solutions to increase the lifetime of WSNs [START_REF] Fanian | Clusterbased routing protocols in wireless sensor networks: A survey based on methodology[END_REF]. The design of energy-efficient routing techniques for WSNs is very challenging task due to the limited computational and storage capacities in such tiny and energy-constrained sensors [START_REF] Rault | Energy efficiency in wireless sensor networks: A top-down survey[END_REF], [START_REF] Singh | Energy aware cluster based multi-hop energy efficient routing protocol using multiple mobile nodes (meacbm) in wireless sensor networks[END_REF]. In this paper, we propose a new protocol called LEACH-PRO (LEACH enhanced with Probabilistic Cluster Head Selection), which represents an enhanced version of LEACH (low energy adaptive clustering hierarchy), in order to maximize WSNs' lifetime.

The remainder of this paper is organized as follows. In Section 2, we provide a brief overview of the importance of wireless sensor networks in smart cities. In Section 3, we present an overview of LEACH routing protocol followed by the literature review in Section 4. Afterwards, we introduce our proposed scheme, named LEACH-PRO, and discuss its operation in detail in Section 5. In Section 6, we present and analyze the obtained simulation results. Finally, we conclude the paper in Section 7.

WSNs enabled smart cities applications

To deal with the expanding demography of urban centers, the development of smart cities is becoming more and more critical. These cities will indeed improve the quality of life of citizens by optimizing their daily lives (e.g., urban transportation planning), their safety (e.g., rapid response in emergency situations), while offering them value-added services (e.g., remote monitoring and control of their homes). On the other hand, these cities are expected to integrate intelligence, in order to automate their operation, and should foster energetic sobriety, for a more sustainable and resilient world [START_REF] Kamyab | Transition to sustainable energy system for smart cities and industries[END_REF].

The deployment of heterogeneous wireless network technologies will be necessary to enable these advances. Longrange wireless networks, such as 5G or Beyond 5G (B5G) networks, will definitely be needed to serve bandwidthintensive or low-latency applications. These cities will also require sensor networks, whether short-range, such as WSNs, or long-range, such as Low Power Wide Area Networks (LPWANs), which could serve as a base station (or sink) to aggregate and report sensors readings.

Without being exhaustive, WSNs can be considered in several use cases in smart cities. Their use within smart road infrastructure and integration with Connected Autonomous Vehicles (CAVs) will help preventing accidents while improving traffic flow fluidity. Their use in buildings can reduce energy consumption when combined with actuators. They can trigger alerts, faster, during fires, and allow to adapt, for example, the frequency of the means of transportation according to the needs, enabling a significant reduction in carbon footprint. The number of applications and practical use cases are extremely numerous and are only limited by the boundaries of the human imagination [START_REF] Lim | Smart cities with big data: Reference models, challenges, and considerations[END_REF].

By organizing themselves in networks, WSNs potentially cover large areas, even inside buildings [START_REF] Metallidou | Energy efficiency in smart buildings: Iot approaches[END_REF]. However, the viability of these sensors is very much linked to their lifetime which should be of several years. To maximize the operating lifetime of these wireless sensors, several strategies have been proposed in the literature. These techniques can be broadly divided into three categories: (i) strategies based on energy harvesting from the environment (stemming from different sources such as solar, mechanical, or electromagnetic energy) [START_REF] Sarpong Adu-Manu | Energy-Harvesting Wireless Sensor Networks (EH-WSNs)[END_REF], (ii) strategies optimizing the idle time of the devices [START_REF] Tchuani Tchakonté | Lifetime optimization of wireless sensor networks with sleep mode energy consumption of sensor nodes[END_REF], and (iii) techniques aiming to optimize the wireless devices' operation [START_REF] Halil Yetgin | A Survey of Network Lifetime Maximization Techniques in Wireless Sensor Networks[END_REF]. These different strategies can be found in different scenarios for smart cities. They are in no way contradictory, and can even be leveraged by the same wireless sensors.

In this paper, we focus on the operational optimization of sensors, and particularly on clustering techniques. Thus, our contribution may concern the various introduced use cases, in which clustering strategies are central for enhanced energy savings. In WSNs, recharging the batteries of sensor nodes is an infeasible task [START_REF] Fauzi | Wireless sensor network applications: A study in environment monitoring system[END_REF]. Hence, the network lifetime is a primary concern in WSNs. In order to prolong the network lifetime, several routing protocols exist and could be classified into two types depending on the network topology: Flat routing protocols and Hierarchical routing protocols.

Background and overview of LEACH

Since flat routing protocols require maintaining routing table data and cannot aggregate the sensed data, they are not applicable for large scale WSNs. However, hierarchical routing protocols can solve this issue to some extent. Direct Transmission (DT) [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF] is the basic hierarchical routing protocol used for transferring data from source node to the destination directly without any intermediate node. Due to this, DT consumes more power for sending information towards the BS, especially when this latter is located far away from the sensing field. This will quickly degrade nodes' battery and reduce the overall lifetime of the network [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF].

First order radio model

Low energy radio model is considered as an important factor to communicate effectively over a network. In our work, simple energy consumption first order radio model is presumed. However, energy consumption in transmitter and receiver modes will affect and compensate the performance of routing protocols. In transmitter and receiver mode electronic circuitry dissipate E T x-elec = E Rx-elec =E elec = 50 nJ/bit to run different operations of a given radio model. At the transmitter end the signal is amplified to ∈= 100pJ/bit/m 2 for achieving acceptable bit to noise ratio E b /N 0 at the receiver end, as shown in Fig. 1 and Table 2. Generally, this model describes the energy consumption while transmitting and receiving a packet to neighbor node or to an end station. Equations. 1 and 2 show the mathematical model for energy dissipation when transmitting a (l) bit packet to remote distance (d).

E Tx (l, d) = E Tx-elec (l) + E Tx-emp (l, d) (1) E Tx (l, d) = E elec ×l+ ∈ amp ×l×d 2 (2)
Equations 3 and 4 describe the energy dissipation induced by the reception of (l) bits packet. In this model, the receiver consumes less energy than the transmitter [START_REF] Adler | Design and deployment of industrial sensor networks: Experiences from the north sea and a semiconductor plant[END_REF] because it does not need to further amplify the signal for forwarding the received information, but instead will only process it.

E Rx (l) = E Rx-elec (l) (3)
E Rx (l) = E elec ×(l) (4)
Symmetric radio channel is assumed in this model, in which the energy required to transfer information from a nodeX to a node Y is similar to that needed to transmit the same information from node Y to node X. Alternatively, the clustering protocols are designed in such a way that consumes minimum amount of energy for each transition. Additionally, transmit distance should also be reduced for improving the energy consumption for transmission and receiving operation, especially in this model [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF], [START_REF] Geetha | Clustering in wireless sensor networks: Performance comparison of leach & leach-c protocols using ns2[END_REF], [START_REF] Shi | An energyefficiency optimized leach-c for wireless sensor networks[END_REF] and [START_REF] Akyildiz | Wireless sensor networks: a survey[END_REF]. DT is the basic routing protocol used in WSNs to route the data from the sensing field directly, without any intermediate node or AP (Access Point), towards the base station. The deployed nodes in the field transmit the sensed data directly to the BS without any intermediate or neighbor node intervention. The nodes located far away from the BS will consume more energy, as opposed to the closer ones, because the energy consumption is directly proportional to the distance separating the sender node from the BS. Such transmission operation will rapidly deplete the nodes' battery, which in turn leads to degradation of overall network lifetime. The BS is considered as a remote monitoring station equipped with sufficient power for processing the received data from the sensing filed.

To better understand the energy consumption in DT, consider a linear simple network model composed of n sensor nodes separated by uniformly distributed distance r. Equations 5, 6 and 7 describe the energy consumption needed for transmitting l bits long message from the sensing field to the BS in this network. For communication and data transmission, DT uses first order radio model explained in Section 3.1 [START_REF] Akyildiz | Wireless sensor networks: a survey[END_REF], [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF].

E direct = E Tx-elec (l, d = n×r) (5) E direct = E elec ×l+ ∈ amp ×l×(n×r) 2 (6) E direct = l×(E elec + ∈ amp n 2 r 2 ) (7)
3.3. LEACH overview Due to their tiny size, WSNs' nodes have limited energy resources, meaning that energy-efficient routing is compulsory to maximize the network lifetime. As discussed in Section II, several energy-efficient routing protocols have been proposed for WSNs in the literature, each of them has its advantages and limitations. However, hierarchical and cluster based routing techniques are the most prominent ones as they foster more energy efficient operations than other alternative schemes. Low Energy Adaptive Clustering Hierarchy (LEACH) is considered as one of the most important basic cluster-based routing protocols used for efficient communication in WSNs. A clustering algorithm ensures optimal energy utilization as compared with nonclustering routing algorithms [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF]. LEACH is a basic energy efficient routing protocol that minimizes the power consumption in all aspects of communication, thus improving the network lifetime. In LEACH, the network is divided into a number of clusters, each cluster comprises a cluster head (CH) and a set of cluster members (CMs) as shown in Fig. 2. CMs sense and aggregate data from the sensing field and transfer it to the CH. CHs are then responsible for transmitting this data to the BS. LEACH uses randomized selection of CHs to give equal chance to all participating nodes for competing in CHs selection process rather than using a pre-determined selection of CHs. In static clustering, CHs usually transmit data continuously, consume more power, and die quickly. LEACH operates in rounds; each round consists in two phases, setup phase and steady state phase. In setup phase, a CH is selected based on the generated random number R(N i ) between zero and one. If the random number R(N i ) is lower than the threshold function T (N i ), a CH node is elected as shown in Equation 8 [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF].

T (N i ) = { p 1-p×(rmod 1 p ) if N i ∈ G 0 Otherwise ( 8
)
Where p denotes the probability of selecting a node as CH in r rounds, and G represents a set of nodes that have not been selected as CHs in 1/p rounds. The nodes selected as CHs generate an advertisement message and broadcast it to CMs; the CMs will then join one of the clusters depending on the maximum received signal strength (RSS). The CH creates a Time Division Multiple Access (TDMA) slot for each CM for collision free intra cluster communication. In steady state phase, CHs compress, aggregate and transmit data to the BS. In LEACH, the number of transmissions is reduced by introducing the clustering. Efficient

Setup Phase

LEACH completes its operation in rounds, each round starts with a setup phase followed by a steady state phase. Initially, a cluster organizes itself in the setup phase and completes its advertisement operation. Then, in the steady state phase the CMs transmit data to the CH and this latter transfers the aggregated data to the BS [START_REF] Akyildiz | Wireless sensor networks: a survey[END_REF] and [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF].

When the clusters are created, each node individually decides whether to participate in CH selection operation in the current round or not. Equation [START_REF] Singh | Energy aware cluster based multi-hop energy efficient routing protocol using multiple mobile nodes (meacbm) in wireless sensor networks[END_REF] shows the formula for calculating T (N i ) threshold value where N i is a node and p is the probability of node N i to become the CH in round r. G is a set of nodes that are not selected as CH in previous 1/p rounds. Based on these parameters the threshold value is calculated for further setup operations [START_REF] Rault | Energy efficiency in wireless sensor networks: A top-down survey[END_REF].

Regardless of the network density, the decision is made up on the initial probability (i.e., the probability p used in Equation ( 8) of the nodes that will become the CH. Afterwards, those nodes get a chance to become the CH for the current 1/p rounds. CHs broadcast an advertisement (ADV) message to all nodes. Upon receiving an ADV message, CMs send a response message to their chosen CH individually based on the measured RSSI. Each CH creates a TDMA schedule and sends it to its CMs to avoid the collision while transmitting data to CH. Each CM receives the TDMA schedule and accordingly switches to sleep state until its scheduled time slot is reached. At this instant only, this CM can send the data. The operation of TDMA schedule creation is illustrated in Fig. 10(b), where T S i refers to Time Slot i.

Steady State Phase

At the end of the setup phase operation, every CM can start the data transmission towards its CH during its own assigned time slot. We assume that each CM has always data to transmit. Regardless of the communication in each cluster, the CH must keep its radio receiver on for receiving all data from its CMs. In addition, when TDMA time slot is over or a round time has ended the CH performs data compression over the received data from its CMs and sends the resulting data to the BS. As the distance from the BS to the CH is significantly larger than the distance separating this latter and its CMs, this transmission requires high-energy consumption compared to other data transmission operations. This whole process represents the steady state phase operation of LEACH. Subsequently, the sensor nodes which have not been elected as CH in previous rounds will participate to become CH in next rounds.

Related Work

In this section, we will provide a brief overview of the most important works that have proposed extensions or improvements to the basic LEACH protocol discussed in the previous section.

In [START_REF] Li | A differential evolution-based routing algorithm for environmental monitoring wireless sensor networks[END_REF], the authors proposed an effective differential evolution (DE) based routing algorithm, named DE-LEACH, to improve the performance of LEACH. DE-LEACH's CHs selection process is similar to LEACH, i.e., random selection based on threshold value shown in Eq. [START_REF] Singh | Energy aware cluster based multi-hop energy efficient routing protocol using multiple mobile nodes (meacbm) in wireless sensor networks[END_REF]. DE-LEACH is designed by leveraging two of the most important factors of WSNs, which are energy consumption and the distance separating neighboring nodes inside a cluster, to overcome the early death of CHs issue. DE-LEACH features a fast search mechanism based on optimum level while selecting CHs in the setup phase. Performance evaluation results, using simulation, show that DE-LEACH can successfully prevent random selection of nodes during the clustering process while improving largescale WSNs lifetime. However, the exclusion of random selection of CHs using optimal level based on residual energy increases the complexity of the algorithm and the overhead in the network [START_REF] Li | A differential evolution-based routing algorithm for environmental monitoring wireless sensor networks[END_REF].

In Energy-Efficient LEACH (EE-LEACH) protocol, proposed in [START_REF] Saminathan | Ee-leach: development of energy-efficient leach protocol for data gathering in wsn[END_REF], the CH selection is based on the residual energy where a sorting algorithm extracts the residual energy of each sensor node and the one which has the maximum residual will be chosen as a CH. Gaussian distribution is used for computing the coverage probability. The collection of data can save substantial energy despite the fact that one cluster formed in a small area can consume less energy than the cluster formed in a larger one. The experimental evaluation of EE-LEACH highlights that it has higher packet delivery ratio, lower end-to-end delay and lower energy consumption, but It achieves this at the cost of more traffic on the network. In Intra Cluster Balanced Cluster LEACH (IB-LEACH Protocol) [START_REF] Goyal | Inter cluster balanced leach algorithm for energy efficient wireless sensor network[END_REF], the clustering process is divided into two phases, i.e., intra cluster and inter cluster, which will further help to increase the energy efficiency of the system. The evaluation results reveal that the use of IB-LEACH protocol increases the network lifetime. On the other hand, due to the extra computing required it increases the traffic load to some extent.

Assisted LEACH (A-LEACH) [START_REF] Sunkara | Assisted-leach (aleach) energy efficient routing protocol for wireless sensor networks[END_REF] is an amplified form of LEACH aiming to minimize the power dissipation of CHs by introducing a helper node, called assistant node, to the cluster head. In A-LEACH, when a cluster is formed and the CH is selected this latter selects a helper node located near the base station. Then, the cluster head aggregates the received data from the cluster members and sends it, through the selected helper node, to the BS. The evaluation results has shown that A-LEACH performs better than LEACH .

Balanced-LEACH (LEACH-B) uses de-centralized approach for cluster formation in which each node knows the final destination to transmit data to and its own position but has no information about other nodes [START_REF] Li | Energy optimization algorithm of wireless sensor networks based on leachb[END_REF]. LEACH-B operation consists of three steps, cluster formation, CH selection and data transmission. A sensor node sends data to destination node using the best path characterized by the low power dissipation and based on that it selects the CH. Firstly, the great convergence and global optimization capability of the proposed algorithm can reasonably divide the entire network area into a number of subregions. Then, in each sub-region a CH is elected taking the residual energy factor into account. The conducted experiments results have shown that, compared to LEACH, LEACH-B can effectively balance the network load and improve the energy usage, so as to extend the network lifetime. However, the division of the entire network into subregions increases the communication overhead in WSNs [START_REF] Li | Energy optimization algorithm of wireless sensor networks based on leachb[END_REF].

In Round Robin Cluster Head (RRCH) [START_REF] Nam | An energy-efficient clustering using a round-robin method in a wireless sensor network[END_REF], clusters are created one time only, using similar method to LEACH, in order to minimize the energy usage during the clustering phase. Once the clusters are formed, RRCH keeps the clusters fixed and uses the round-robin scheme to select the CH within each cluster. All nodes have equal chance to be CH during each frame. Upon detection of an abnormal node, the CH modifies the scheduling information and broadcasts it to the entire cluster during the frame modification. Afterwards, its cluster members delete this abnormal node based on the received updated schedule information. Similar to LEACH, RRCH suffers from the incapability of guaranteeing a good quality of the formed clusters. Without the periodic re-clustering (i.e., regeneration of clusters), RRCH cannot manage clusters with varying sizes (e.g., overlay of clusters, very small or very large clusters).

Fixed LEACH (LEACH-F) [START_REF] Azim | A dynamic round-time based fixed low energy adaptive clustering hierarchy for wireless sensor networks[END_REF] is centralized technique of cluster formation in which the clusters are formed permanently by the base station, only the CHs are changed within a cluster in rotation. In default LEACH, reclustering is performed in each round, whereas, LEACH-F removes re-clustering process in next rounds for the whole network lifetime. The steady state is similar to LEACH. LEACH-F is not flexible due to preemptive policy of clusters formation. Before the completion, in each round, energy and information are wasted due to fixed round time in the steady state. Because the CHs or CMs in each cluster cannot change their behavior, this results in an uncertainty in the whole network and degrades the overall performance. This problem can be minimized by introducing a relationship between residual energy of nodes and round time within a cluster.

When the size of WSNs exceeds certain level, the distance between the CH and base station increases significantly, creating problems for single hop communications in LEACH [START_REF] Alsalih | Placement of multiple mobile data collectors in wireless sensor networks[END_REF]. Multi-hop LEACH (M-LEACH) solved the above issue by using multi-hop communication between the CHs and the base station. In Table 3, we compare LEACH and its various extensions based on the communication pattern considered, the assumption made about the mobility of sensor nodes, the achieved level of scalability, the used clustering approach, in addition to the achieved energy-efficiency level and the generated overhead.

A very large number of approaches continue to be proposed in the literature. A recent study addresses a detailed taxonomy of such existing works [START_REF] Daanoune | A comprehensive survey on leach-based clustering routing protocols in wireless sensor networks[END_REF]. Among the aspects addressed are the determination of the number of clusters [START_REF] Saputra Kirsan | Efficient energy for cluster head selection using new leach-based routing protocol in wireless sensor network[END_REF] and the consideration of mobility [START_REF] Thandapani | An energy-efficient clustering and multipath routing for mobile wireless sensor network using game theory[END_REF] of the devices. Although these aspects are necessary and essential, they are not covered in this paper, which focuses more on the routing aspects through an efficient selection of cluster heads.

Our proposed scheme

Although LEACH is an interesting routing protocol for WSNs it suffers from a number of weaknesses that affect its performance. Such weaknesses are due to a number of factors related to its operation, as highlighted below.

• Ignoring the residual energy of sensor nodes when selecting the CH in next rounds. Therefore, if a sensor node with low residual energy is chosen as the CH, then it dies quickly. Hence, the robustness of the network is affected and its lifetime degrades.

• The CHs located at the boundary of the clusters would dissipate more energy and thus decrease the overall performance of the network.

• CHs located far away from the BS consume more energy for transmitting data compared to CHs closer to the BS. This can compromise the network life time.

To overcome these issues and improve the performance of LEACH, a new variant named LEACH enhanced with Probabilistic Cluster Head Selection (LEACH-PRO) is proposed. LEACH-PRO introduces a probabilistic mechanism in which CHs selection is made based on two metrics: the maximum residual energy and the minimum distance to BS. LEACH-PRO has similar design logic as LEACH since both protocols operate in rounds. Each round completes its operations in two phases; setup phase and steady state phase. The main difference lies in the CH selection process and the fact that sensors located at the border of the sensing field are excluded from participating in the CH selection process if they satisfy the conditions set in Equation ( 9). LEACH-PRO detailed operational steps are illustrated in Fig. 4. We assume a static deployment of sensor nodes in the sensing field with the coordinates of each node determined a priori as (x i , y i ) to easily identify borderline nodes. Each node generates a random number and saves it in its memory. However, nodes at the borderline must be selected as CM only and excluded from the CH selection process.

Role of a border sensor node

The node that resides in the borderline of the sensing field or closer to it is considered as a border node. The node selected as CH must operate and communicate with its neighbors efficiently. When clusters are formed, almost in circular fashion, each CH broadcasts its ADV message to its neighbors. Such message is transmitted to all members of each cluster. A border node can cover its communication range either side of the sensing field, therefore, if it is selected as CH, it cannot communicate with its CMs effectively. To avoid such issue, LEACH-PRO excludes border nodes from participating in the CH selection process to improve the overall performance.

x f -1 ≥x i ≥x 0+1 y f -1 ≥y i ≥y 0+1 (9)
Let us assume that the coordinates of each node (x i ,y i )

are predetermined when the nodes are distributed in the sensing field. Thus, any node that satisfies the conditions set in Equation ( 9) is eligible to participate in the CH selection process; otherwise, it is excluded. These conditions are defined based on Fig. 5 which illustrates the area in the sensing field where border nodes are located. Nodes in this area cannot be selected as CH in next rounds and are declared as CMs. Generally, for clusters formation a threshold number T (N i ) is calculated based on the probability function as given in Equation. 10. If the randomly generated R(N i ) number between 0 and 1 is less than T (N i ) then the node (N i ) will be selected as CH from the set G of nodes that have not been elected as CH in the previous 1/p rounds. The first round of LEACH-PRO is similar to that of LEACH but next rounds will follow the working principle of LEACH-PRO, as illustrated in Fig. 4. ADV PKT is a control packet with a size of 200 bits as set in our simulation, that contains the current energy level of the CH node, the distance separating it from the BS and its cluster Id denoted by E CH , D CH and C id respectively as shown in Fig. 6.

T (N i ) = { p×E CM ×D CM E AVG ×D AVG ×(1-p×(r mod 1 p )) if n ∈ G 0 Otherwise ( 10

Cluster head selection process

The primary metric for selecting CHs is the residual energy of a node, as it is considered an optimal parameter for achieving better performance, while the distance to the BS is considered a secondary metric in the selection process of the CHs. In this regards, the following three cases are inspected. When a node is elected as a CH in the second round, it generates an ADV message and broadcasts it towards its CMs, as shown in Fig. 7(a).

Case1: E CH > E CM

Suppose that every CM in a cluster has less residual energy than the CH. Hence, each CM directly responds to join that specific CH, as shown in Fig. 7(b).

Case2: E CM > E CH

In this case, a CM with a higher residual energy than the CH generates a new ADV message and broadcasts it to its neighbors as a dominant CM in a cluster. Upon receiving this new ADV message each CM including the previously declared CH, discards the first received ADV message based on the C id information and responds to the new CH, as illustrated in Fig. 8(b).

Case3: IF E CM = E CH

Finally, this case cannot be resolved without considering the distance separating both nodes from the BS. If a CM within a cluster has similar residual energy as that of the declared CH, then this CM will check the distance to the BS metric. If this CM is closer to the BS than the currently declared CH then, the CM declares itself as CH and generates a new ADV message and broadcasts it to its neighbors in similar way as in case 2. Otherwise, the operation will be the same as in case 1. The operation of case 3 is illustrated in Fig. 9.

Finally, after selecting the optimal nodes as CHs, each CH defines a TDMA schedule and sends it to its CMs. Upon reception of this TDMA frame each CM switches to sleep state until its time slot is reached. The remaining operations of LEACH-PRO are similar to that of LEACH.

Complexity analysis

The computational complexity of the proposed solution is very low and allows a fast convergence. The latter is of the same order of magnitude as the original LEACH protocol [START_REF] Dzaferagic | Relation between functional complexity, scalability and energy efficiency in wsns[END_REF]. Indeed, there is no combinatorial here that would make the execution time important, so the execution time is of the order of o [START_REF] Ala' Khalifeh | Wireless sensor networks for smart cities: Network design, implementation and performance evaluation[END_REF]. However, if one looks at the functional complexity, by counting the number of messages exchanged, the complexity of our protocol is reduced since the edge nodes do not participate as CHs. For more details about the functional complexity, one could refer to [START_REF] Dzaferagic | Relation between functional complexity, scalability and energy efficiency in wsns[END_REF].

Results and discussion

A simulation environment is created using MATLAB-2015A where DT, LEACH and LEACH-PRO are implemented to evaluate and compare their performance under different scenarios. The simulation parameters used are similar to those used in many state of the art works in this topic. The main performance evaluation metrics used are NDR (Nodes Death Rate), SRE (System Remaining Energy) and Packets to BS. NDR is calculated by measuring the First Node Death rate (FND), Half of Nodes Death rate (HND) and 90% of nodes death rate. Similarly, SRE is also calculated by measuring the remaining energy in percentage as 10% SRE, 50% SRE and 90% SRE to analyze the overall performance of the protocols. Packets to BS refers to the number of packets sent towards the base station. A summary of the simulation setting is presented in Table 4.

Analysis of network lifetime and NDR

The network lifetime is described as the time elapsed between initiating the network operation until the death of its last node. The scenario simulated in our experiments is similar to the topology shown in Fig. 2. In this scenario, nodes density is also varied from 50 to 500 nodes to analyze the scalability of the three protocols.

Figures 10 and11 depict the achieved network lifetime and NDR by DT, LEACH and LEACH-PRO when applied to a WSN with sizes of 50, 100, 200 and 500 nodes respectively. The plotted results show that LEACH-PRO is outperforming the other two protocols. In DT, the source node directly transmits its data to the BS and thus consumes more transmit power, hence, the death rate of nodes in DT is much higher which makes the network lifetime much shorter as well. In LEACH, instead of direct transmission the data is transmitted via CHs, thus, LEACH achieves longer lifetime than DT, but the blind CHs selection leads to a fast degradation in its performance compared to LEACH-PRO. The supremacy of this latter, in 11(a), the first node dies after 263 rounds, in DT, after 759 rounds, in LEACH and after 1484 rounds in LEACH-PRO. For DT, 50% of nodes die after 502 rounds, and the entire network die after 584 rounds, whereas for LEACH 50% of nodes consume their entire power after 1114 rounds. These results highlight that the death of the first node in LEACH-PRO occurs after the death of 1005 of nodes in DT and 50% of nodes in LEACH. This trend continues when the network size is increased to 100 nodes. However, for a network with 200 nodes, the FND in LEACH-PRO occurs after the death of all nodes in DT but before HND occurrence in LEACH. This trend will hold with a network of 500 nodes. Such significant improvement of performance shown by LEACH-PRO is justified by the stability in finding a node with maximum residual energy to act as a CH. 50 and 500 nodes, we find that the death speed increases by a factor of 3.37, 1.36 and 1.67 in DT, LEACH and LEACH-PRO respectively. For HND, its occurrence speed has similar trend to FND where it increases by a factor of 5.52, 1.28 and 1.96 in DT, LEACH and LEACH-PRO respectively. The analysis of these results tell us that although LEACH-PRO is still outperforming DT and LEACH it has a slightly higher HND speed compared to LEACH.

Analysis of Energy Consumption

Each node in WSNs is equipped with a limited power source or battery. Therefore, the nodes energy should be utilized in an efficient manner for better sustainability of the network. The lifetime of a node is directly proportional to the speed at which its energy is being consumed. In this work, the initial energy of each node is set to 0.5 Joule. Figures 14 and15 represent the system residual energy (SRE) and energy consumption evaluation of DT, LEACH and LEACH-PRO for network size of 50, 100, 200 and 500 nodes respectively. As illustrated in the plotted results, LEACH-PRO is outperforming the other two protocols. DT has fast energy degradation rate as it does not use intermediate nodes for transmission towards the BS. LEACH uses its own probability function for selecting CHs, where each node has the same probability to become a CH, thus all nodes die quickly because of the blind CH selection strategy. LEACH-PRO, however, achieves the lowest degradation rate of energy due to its CH selection strategy that maximizes the energy efficiency of the network.

As shown in Figure 15, DT consumes more energy in less number of rounds and exhibits low performance as the size of the network increases. LEACH and LEACH-PRO both show comparable performance at the start of communication operation and do not have much difference up to 50% of SRE. However, beyond this limit and up to 10% of SRE LEACH-PRO performs significantly better than LEACH. This supremacy of LEACH-PRO is inversely proportional to the increase of WSNs size as the performance gap between it and LEACH shrinks as the network gets larger.

Analysis of Traffic Load in the Network

Traffic load is measured as the number of packets transmitted in the network. Higher packet transmissions directly affect the bandwidth and energy consumption, these resources are limited and thus their usage should be optimized. Therefore, it is necessary to reduce the frequent packets transmission in the network. Figure 16 illustrates the traffic load pattern generated by the three protocols. As we can see, DT generates high traffic load as compared to LEACH and LEACH-PRO due to the frequent transmissions towards the BS, and sensors die quickly after at most 500 rounds. The traffic load generated in LEACH increases gradually to stabilize after 1500 rounds, for networks of 200 and 500 nodes, and after 1000 rounds for smaller networks. LEACH-PRO has similar pattern to LEACH but the traffic load generated is almost 40% to 50% lower, especially after the first 500 rounds.

Conclusion

In this work, a novel energy-efficient routing protocol named LEACH-PRO was proposed to make WSNs more sustainable and optimize their operation in many smart cities use cases. This protocol was designed to overcome the limitations of LEACH by introducing the probabilistic cluster head selection based on the residual energy and the distance to the base station. Performance evaluation results highlighted that LEACH-PRO outperforms both LEACH and Direct Transmission protocol in terms of the achieved network lifetime, node death rate speed, residual energy depletion speed in addition to the generated traffic load on the network. However, the results show also that as the network size increases the performance of LEACH-PRO degrades to some extent. Future works will include implementing LEACH-PRO on a hardware platform and testing its performance at the campus of QUEST in Pakistan. The promising performance shown by LEACH-PRO suggests that it can efficiently support several application scenarios in future smart cities.

Figure 1 :

 1 Figure 1: First order radio model

Figure 2 :

 2 Figure 2: Example of a WSN composed of a number of clusters

Figure 3 :

 3 Figure 3: LEACH frame operation

Figure 4 :

 4 Figure 4: LEACH-PRO working principle

Figure 5 :

 5 Figure 5: Border sensor nodes distribution in a sensing field

  ) Where E AVG is the Average Energy of System, E CM refers to the Current Energy of CM, D CM is the Distance separating a CM from the BS, r represents the Number of Rounds, 1/p denotes the Number of Nodes in each Cluster, D AVG is the Average Distance to the BS, and G represents the set of nodes that have not been selected as CH in 1/p rounds.

Figure 6 :

 6 Figure 6: Advertisement message packet format

(a) Step 1 :Figure 7 :

 17 Figure 7: Selection of the energy-efficient node as CH

Figure 8 :

 8 Figure 8: Maximum Residual Energy Node Broadcast ADV Message

Figure 9 :

 9 Figure 9: Optimal node declaration as CH with nearest distance to BS

6. 2 .Figure 10 :Figure 11 :

 21011 Figures 12 and 13 show the evolution of FND and HND occurrence under the three protocols when the WSNs size increases. The plotted results reveal that the speed at which FND and HND occur in all protocols increases with the increase of the WSNs size but the speed increase varies. If we compare the FND occurrence between the WSNs of

Figure 12 :Figure 13 :

 1213 Figure 12: FND evolution under varying WSN densities

Figure 14 :Figure 15 :Figure 16 :

 141516 Figure 14: System residual energy under varying network densities

Table 1 :

 1 SUMMARY OF THE USED NOTATION

	Notation	Meaning
	CH	Cluster Head
	CM	Cluster Member
	BS	Base Station
	l	Length of Message in Bits
	p	Probability to Select a Node as CH
	N i	i th Node
	T (N i )	Threshold Function Value against i th Node
	R(N i )	Random Number against i th Node
	DT	Direct Transmission
	AP	Access Point
	G	Set of Nodes not selected as CH
	RSS	Received Signal Strength
	TDMA	Time Division Multiple Access
	r	Number of Rounds
	d	Remote Distance to BS
	E b /N 0	Bit to Noise Ratio
	E AVG	Average Energy of System
	E CH	Current Energy of CH
	E CM	Current Energy of CM
	D CM	Distance of CM to BS
	D AVG	Average Distance to BS
	E Tx-elec	Transmitter Electronics
	E Rx-elec	Receiver Electronics
	∈ amp	Transmitter Amplifier
	ADVPKT	Advertisement Message Packet
	CTRPKT	Control Packet
	DRN	Death Rate of Nodes
	FND	First Node Died
	HND	Half of the Nodes Died
	SRE	System Remaining Energy
	C id	Cluster ID

Table 2 :

 2 Radio characteristics

	Operation	Energy Dissipaton
	Transmitter Electronics || E Tx-elec
	Receiver Electronics || E Rx-elec	50nJ/bit
	(E Tx-elec = E Rx-elec =E elec )
	Transmitter Amplifier (∈ amp )	100pJ/bit/m 2
	3.2. Direct Transmission (DT)

Table 3 :

 3 Comparison of various extensions of LEACH protocol

	Protocol	Communication Mobility assumption Scalability Clustering Energy-efficiency Overhead
		Pattern			approach
	LEACH	Single-Hop	Nodes are Stationary	Low	Distributed	Moderate	High
	A-LEACH	Chain-Based	Nodes are Stationary	Low	Distributed	High	Low
	LEACH-EE	Multi-Hop	Nodes are stationary Very High Distributed	High	High
	LEACH-M	Multi-Hop	Nodes are Mobile	High	Distributed	Low	High
	LEACH-F	Single-Hop	Nodes are Stationary	Low	Centralized	High	High
	LEACH-DE	Single-Hope	Nodes are Stationary	Low	Distributed	High	High
	IB-LEACH	Single Hop	Nodes are Stationary	Low	Distributed	High	High
	LEACH-PRO	xx	xx	xx	x	x	x

Table 4 :

 4 Summary of simulation settings

	Parameters	Values
	MATLAB Version	2015/R
	Node Deployment Area	200 m x 300 m
	Network Sizes (Nodes Density) 50, 100, 200, 500
	Initial Energy (J) of each node	0.5 J]
	E T x-elec	50 nJ/bit
	E Rx-elec	50 nJ/bit
	∈ amp	100 pJ/bit/m2
	Control Packet Length	200 Bits
	Data Packet Length	4000 Bits
	Number of nodes in Cluster	10
	Probability	0.1
	Simulation Rounds	4000
	Position of BS	(100,300)


Nirina Miora

Amine Robson

Omar Lahouar

Nicolas Al-Mansouri

Roberto Pinoteau

Marco Piccinin

Sébastien Abate

Dashnor Rémond

Hoxha

Miora Nirina Robson
email: mioranirina.robson@cstb.fr

Amine Lahouar

Omar Al-Mansouri

Nicolas Pinoteau

Roberto Piccinin

Marco Abate

Sébastien Remond

Dashnor Hoxha

Simplified analytical fracture mechanics model for the evaluation of concrete cone capacity of a single headed stud and experimental validation on anchors with various embedment depths

Keywords: concrete cone, headed stud, fracture mechanics, energy balance, analytical model

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Anchoring systems are an engineering solution allowing to transfer load from external elements to concrete. In general, they can be classified as either cast-in-place anchors or post-installed anchors. The first category corresponds to anchors that are secured in the formwork prior to casting the concrete, whereas the second category consists of anchors installed in hardened concrete after casting [START_REF] Eligehausen | Anchorage in Concrete Construction[END_REF]). Among cast-in-place anchors, headed studs are commonly used. When loaded in tension, a headed stud experiences one of the following failure modes: steel failure, concrete cone failure, concrete splitting, pull out failure and lateral blow out failure (EN 1992(EN -4 2018) ) [START_REF] Eligehausen | Anchorage in Concrete Construction[END_REF]). The concrete cone failure is characterized by the formation of a cone-shaped fracture surface in concrete.

Several investigations have been performed over the past few decades to explain and characterize the mechanism of a concrete cone failure and to determine the failure load [START_REF] Ottosen | Nonlinear Finite Element Analysis of Pull-Out Test[END_REF] [START_REF] Elfgren | Fatigue of Anchor Bolts in Reinforced Concrete Foundations[END_REF]) [START_REF] Krenchel | Fracture Analysis of the Pullout Test[END_REF] (Eligehausen and Sawade 1989) [START_REF] Elfgren | Anchor bolts in concrete structures: Summary of round robin tests and analysis arranged by RILEM TC 90-FMA "Fracture Mechanics of Concrete -Applications[END_REF]. It can be deduced from these studies that when a headed stud is loaded in tension, high circumferential tensile stresses develop around the point where load is introduced in the concrete. Subsequently, microcracks and circumferential tensile cracks are initiating at the head of the anchor. As the load increases, these cracks propagate towards the concrete surface. This propagation is stable during a first step but becomes unstable when the ultimate load is reached. At the ultimate load, the circumferential cracks reach only 40% to 50% of the full apothem of the final cone (Eligehausen and Sawade 1989). Moreover, the slope of the cone envelope varies between 30° to 40° with respect to the surface of the concrete component. On average it is about 35°, however, it has the tendency to increase with embedment depth [START_REF] Zhao | Tragverhalten von randfernen Kopfbolzen-verankerungen bei Betonbruch[END_REF]). In addition, recent investigations showed that the failure angle also increases with anchor head size [START_REF] Nilforoush | Experimental Evaluation of Tensile Behaviour of Single Cast-in-Place Anchor Bolts in Plain and Steel Fibre-Reinforced Normal-and High-Strength Concrete[END_REF] (Nilforoush et al. 2018).

At the present, most of the design-oriented documents at international level (EN 1992(EN -4-2018) ) (fib Model Code for Concrete Structures 2010) are derived from the well known CCD method [START_REF] Fuchs | Concrete capacity design (CCD) approach for fastening to concrete[END_REF] for the evaluation of the concrete cone capacity of anchors. According to this method, the mean concrete cone capacity of a headed stud unaffected by neighboring anchors or nearby concrete edges is given by (1):

𝐹 𝐶𝐶𝐷 = 15.5 √𝑓 𝑐𝑐 ℎ 𝑒𝑓 1.5 (1)
In (1), fcc [MPa] is the compressive strength of concrete based on 150 mm cubes and hef [mm] is the effective embedment depth measured between concrete surface and top corner of the anchor head. Therefore, the 15.5 factor takes dimensional units of [N 0.5 /mm 0.5 ]. According to [START_REF] Fuchs | Concrete capacity design (CCD) approach for fastening to concrete[END_REF], the term √fcc indicates that the concrete tensile strength is proportional to the square root of the concrete compressive strength. Besides, the term hef 1.5 signifies that the ultimate load is proportional to the total failure area and affected by a size effect. Indeed, at ultimate load, if the embedment is increased, the stress obtained by dividing the ultimate load to the idealized concrete cone surface is decreasing. As for the coefficient 15.5 in (1), it was derived empirically from regression analyses of 318 individual tests carried on headed studs of different embedment depths cast in specimens of varying strength [START_REF] Rehm | Befestigungstechnik RILEM[END_REF]) [START_REF] Fuchs | Concrete capacity design (CCD) approach for fastening to concrete[END_REF]. However, no clear relationship can be established between compressive strength and fracture energy of concrete [START_REF] Kozul | Effects of Aggregate Type, Size, and Content on Concrete Strength and Fracture Energy[END_REF]. Therefore, it may be said that despite its user-friendly aspect, (1) does not indicate explicitly the dependence of the concrete cone capacity on the failure mechanism.

To study the effect of fracture properties on the concrete cone ultimate load-bearing capacity, a numerical study on the influence of the concrete tensile strength ft and the concrete fracture energy GF was performed [START_REF] Eligehausen | Use of the Tensile Strength in Anchorage to Concrete[END_REF]. The results indicated that for a given fracture energy, the ultimate load increases slightly with the concrete tensile strength. However, for a given concrete tensile strength, the concrete cone failure load increases considerably with the fracture energy. Moreover, this increase is roughly proportional to GF 0.5 . This is coherent with Sawade's energy-based equation (2), which suggest the dependence of the failure load on the fracture energy GF and Young's modulus E of concrete. This energy model was based on Linear Elastic Fracture Mechanics and used numerical simulations to identify the dimensionless coefficient 2.1 [START_REF] Sawade | Ein energetisches Materialmodell zur Berechnung des Tragverhaltens von zugbeanspruchtem Beton[END_REF].

𝐹 𝑆𝑎𝑤𝑎𝑑𝑒 = 2.1 √𝐸𝐺 𝐹 ℎ 𝑒𝑓 1.5 (2)
The present investigation consists in evaluating analytically the concrete cone capacity of a single headed stud using a simple representation of the failure mechanism. An experimental investigation to assess the validity of this simplified model is presented. The test results are also compared to the predictions of CCD method and Sawade's model to assess their practical validity.

Description of the analytical model

Fracture mechanics theory studies the mechanical behaviour of cracked bodies subjected to an applied load, and allows to determine the maximum admissible stress for a given crack size, or to determine the maximum admissible crack size given an applied load. For the application to the concrete cone capacity, the goal is to predict the failure load. For a concrete-like loaded cracked body, the sum of the potential energy, Wpot , and the surface energy from macro crack growth, Wcrack , could be written as a difference between the work of internal forces, Wint , and external forces, Wext , (3)(4):

𝑊 𝑝𝑜𝑡 + 𝑊 𝑐𝑟𝑎𝑐𝑘 = 𝑊 𝑖𝑛𝑡 -𝑊 𝑒𝑥𝑡 = 𝑊 𝑒𝑙 + 𝑊 𝐹𝑃𝑍 -𝑊 𝑒𝑥𝑡 (3) 𝑊 𝑝𝑜𝑡 = 𝑊 𝑒𝑙 -𝑊 𝑐𝑟𝑎𝑐𝑘 + 𝑊 𝐹𝑃𝑍 -𝑊 𝑒𝑥𝑡 (4)
where, Wel is the elastic strain energy, WFPZ is the fracture process zone (FPZ) energy where any other dissipative phenomena such as matrix microcracking, debonding of matrix-aggregate interface and eventual plastic yielding can be observed. Therefore, the minimum of potential energy principle in cracking process reads (5):

𝜕𝑊 𝑝𝑜𝑡 𝜕𝐴 = - 𝜕W ext 𝜕𝐴 + 𝜕𝑊 𝑒𝑙 𝜕𝐴 - 𝜕𝑊 𝑐𝑟𝑎𝑐𝑘 𝜕𝐴 + 𝜕𝑊 𝐹𝑃𝑍 𝜕𝐴 = 0 (5)
To obtain a simple expression for the strength, without a description of the stable crack propagation nor of the FPZ developing, the analysis can be focused on a hypothetical situation when the pull-out test is conducted up to the critical crack length and is immediately unloaded to avoid the failure. If the precracked sample is reloaded, the full reloading process up to critical crack length becomes elastic. Therefore, for the reloading elastic process, the area under load-displacement curve is exactly the half of the work of external load i.e. the work of external load is the double of the elastic energy. In addition, after stable crack propagation in concrete, the FPZ energy becomes negligible compared to crack energy due to a drop of FPZ size [START_REF] Kim | Determining the Fracture Process Zone Length and Mode I Stress Intensity Factor in Concrete Structures via Mechanoluminescent Technology[END_REF]. Finally, the classical energy release rate equation is obtained (6):

𝜕𝑊 𝑒𝑙 𝜕𝐴 = - 𝜕𝑊 𝑐𝑟𝑎𝑐𝑘 𝜕𝐴 (6)
To evaluate Wel and Wcrack at this stage, the fundamental idea consists in applying brittle materials theory, as the concrete shows a pure brittle material behaviour from the instability point. In one hand, Wcrack is evaluated with considering an invariant surface energy equal to the so-called fracture energy GF of concrete, giving Wcrack = GF(πa²cosβ). In the other hand, Wel is evaluated using a simplification for brittle materials. For a crack of length 2a in an infinite plate remotely loaded by stress σ, Perez (2017), showed that energy released is equal to that of a uniform density energy stored in two cylinders of radii equal to half of the crack length. Similar results, implying however a corrective factor close to 4/π² could be obtained for a penny-shaped crack with cylinders replaced by a torus of section radius equal to that of the penny shaped crack and enveloping the crack edge. Therefore, transposition to the case of a coneshaped crack suggests that the energy release zone would have the equivalent size of a torus shaped volume element surrounding the crack tip (Fig. 1). Therefore, the released energy reads Wel = (∫σdε) (4π²a 3 cosβ). Hence, with a cone shaped crack surface proportional to the crack length a, the conservation of energy variation due to the displacements arising from the crack length change ∂a can be defined as (7):

𝜕(𝜎𝑑𝜀) (4𝜋 2 𝑎 3 𝑐𝑜𝑠𝛽) 𝜕𝑎 = - 𝜕𝐺 𝐹 (𝜋𝑎²𝑐𝑜𝑠𝛽) 𝜕𝑎 (7)
Moreover, the strain energy density can be expressed using Hook's law, with a normal stress σ assumed to act over the crack region as σ = Fcosβ/πa²cosβ. Therefore, the expression of the load is obtained after derivations as ( 8):

𝐹 = √𝜋𝑎 3 𝐸𝐺 𝐹 (8)
At failure, the crack length has its critical value acr which is presumed to be approximately 45% of the slant height of the final cone (Eligehausen and Sawade 1989), hence acr ≈ 0.45l ≈ 0.45hef /sinβ. Therefore, the ultimate load can be expressed as a function of the embedment depth and the failure angle as ( 9):

𝐹 = √ 0.45 3 𝜋 (𝑠𝑖𝑛β) 3 √𝐸𝐺 𝐹 ℎ 𝑒𝑓 1.5 (9)
If the failure angle is assumed to have an average value β=35° as suggested in past investigations [START_REF] Zhao | Tragverhalten von randfernen Kopfbolzen-verankerungen bei Betonbruch[END_REF]) [START_REF] Fuchs | Concrete capacity design (CCD) approach for fastening to concrete[END_REF], the ultimate load Fmax at failure would finally read (10):

𝐹 𝑚𝑎𝑥 ≈ 1.23 √𝐸𝐺 𝐹 ℎ 𝑒𝑓 1.5
(10)

Description of the tests

Test specimens

The type of headed stud considered in this experimental campaign consisted of M16 threaded rods with 2 mm threads, welded to a nut and a washer whose characteristics are shown in Figure 2. For each component, carbon steel of grade 10.9 has been used (ISO 898-1-2009) and the mean ultimate tensile strength of the threaded rod was fu = 1280 MPa. The concrete material used to construct the slab was a ready-mix concrete of class C25/30 with a maximum aggregate size of 13.5 mm. Table 2 presents the composition of the concrete and the average values of its mechanical properties. The pull-out tests and the characterization of concrete mechanical properties were performed after a minimum of 35 days from casting. The compressive strength of concrete was measured on additional concrete cubes (side: 150 mm) in accordance with EN 12390-3. Likewise, the tensile strength was measured on cylinders (diameter: 160 mm; height: 320 mm) in accordance with EN 12390-6. In addition, Young's modulus of concrete was characterized following EN 12390-13 and the concrete fracture energy was measured by means of a three-point bending test on standard concrete notched prisms (length: 600 mm, width: 150 mm, height: 150 mm), in accordance with RILEM TC 162-TDF 2002(RILEM 2002). A displacement-controlled system was chosen to capture the post-peak behaviour of the anchor. The loading was applied to the anchor using a hydraulic jack with a maximum capacity of 200 kN. The jack transferred the load through a high-strength steel rod, which was connected to a hollow cylinder cage, connected to the free end of the anchor by two coupling nuts. To prevent the vertical movement of the slab, the jack was supported by a steel support which rested directly on the slab. The dimension of the support was chosen sufficiently large, i.e. a diameter larger than 4hef to allow the formation of an unrestricted cone. The applied load was measured by a load cell placed on the top of the load cylinder.

For measuring the anchor displacement, a linear variable differential transformer (LVDT) was installed on the top of the anchor, in such a way that its axis and that of the anchor coincide.

Test results and discussions

Load displacement curves

For all performed tests, the evolutions of the measured tensile load F with the measured displacement of the anchor are summarized in Figure 4. It may be observed from the load-displacement curves that before the ultimate load, each curve consists on a short first part slightly linear and then a second part non-linear until the ultimate load. The first part corresponds to low loads not sufficient to create a crack.

The passage to the non-linear phase may suggest the beginning of a stable crack growth and the development of the Fracture Process Zone. It can also be seen on the curves that the stiffness is decreasing during the non-linear phase, which may indicate an additional displacement resulting from microcracking. Moreover, the load decreases suddenly after ultimate load, which is coherent with the consideration of a post-peak quasi-brittle failure. Besides, the displacement at ultimate load seems to be greater for the two deepest embedment depths, suggesting a higher degradation of the stiffness at failure, i.e. a greater damage linked to a larger crack surface and/or a larger Fracture Process Zone. This seems to confirm that the critical crack length is proportional to the embedment depth of the anchor.

Failure mechanism and crack patterns

During the loading and until the ultimate load was reached, no crack was observed on the surface of the slab. As expected, all anchors underwent concrete cone failure. However, the extracted cones were sometimes split into separated pieces, which may indicate the formation of radial cracks. The failure angle of the extracted cones varied between 25° and 40°. In addition to a variation from one test to another, the variation of the failure angle was also observed within the same failure cone whether it was along the failure crack or depending on the viewing angle. Photos of a failure cone taken from two different sides of the same failure cone with one of the shallowest anchors hef = 57 mm are shown on Figure 5. Moreover, measurements seemed to show that the failure angle slightly increase with embedment depth.

Ultimate loads and comparison with prediction models

Table 3 gives the summary of ultimate load Fu,i obtained with each individual test as well as the mean ultimate load Fu,m per embedment depth. The coefficient of variations (COV) associated to the mean ultimate loads Fu,m are also given to have indication on the scatter of the tests results. 1) and (2) as well as the proposed analytical equation ( 10). In addition, the predictions of the analytical equation ( 9) using the minimum measured failure angle of 25° and the maximum measured angle of 40° are presented. It may be observed in Figure 6 that the CCD method and Sawade's equations give predictions close to the experimental results, despite a slight overestimation as could be observed in past studies [START_REF] Eligehausen | Anchorage in Concrete Construction[END_REF] (Eligehausen and Sawade 1989). It can also be seen that the prediction of the analytical equation ( 10) provides a good agreement with the data, except for hef = 108 mm, for which the larger scatter shown in Table 3 does not allow a conclusive statement. Moreover, the test results as well as the prediction of CCD method lie between the boundary values predicted by the analytical equation ( 9) using the minimum and the maximum measured failure angles. The upper limit obtained with the minimum failure angle β = 25° is close to the prediction of the existing equations ( 1) and ( 2). These results seem to suggest that the use of the concrete fracture parameters is suitable for the evaluation of the concrete cone capacity. In this study, a failure angle β = 35° seems to give a good fit of the test data. However, the cracking of concrete may depend on the arrangement and the characteristics of aggregates and the cement matrix. Therefore, further investigation would be necessary to assess if the analytical equation is still appropriate with other concrete formulations.

Concluding remarks

This paper presents an investigation of the concrete cone capacity of a single headed stud at room temperature with consideration of the failure mechanism. A simplified theoretical development using energy-based Linear Elastic Fracture Mechanics was established to evaluate the concrete cone ultimate capacity. The analysis was done considering a hypothetical moment at the end of the stable crack growth, and relies on the following main assumptions:  At the onset of unstable crack growth, concrete behaves similarly to an elastic pure brittle material with an invariant fracture energy GF.  As a generalisation of Perez's suggestions, the energy release is represented by the uniform strain energy stored into a torus of radius equal to the crack length.  The failure angle is around 35° and the stable crack growth ends when the crack length is approximately 45% of the total failure cone apothem. An experimental program to assess the validity of the prediction of the proposed model with regard to four values of embedment depths was then presented. Moreover, test results were confronted to the main existing models in literature. The results may call for the following observations:  The load-displacement curves transcribe the failure mechanism by showing the three main steps of a concrete cone failure: a first elastic short part, a second nonlinear part corresponding to stable crack growth with FPZ development and a progressive decrease of stiffness, and an unstable crack propagation phase with rapid decrease of the capacity after the ultimate load.  The failure angle varies from 25° to 40° depending on the test, on the angle of view around a failure cone, and on the measurement point along the crack path. Moreover, the angle seemed to increase with embedment depth.  The proposed model seems to be in good agreement with the tests results in almost all cases compared to existing equations. This may highlight that the concrete cone capacity is better represented with the fracture parameters of concrete. However, as the experimental program investigated only one type of concrete formulation, further investigation will follow to assess the accuracy of the model with different concrete formulations.

Figure 1 :

 1 Figure 1: Equivalent torus-shaped energy release zone

Figure 2 :

 2 Figure 2: Characteristics of the headed studFour values of the embedment depth hef have been considered (Tab. 1). For each embedment depth, three tests have been carried out to ensure a good reproducibility. The total of 12 headed studs were cast in a common large reinforced concrete slab 2.5 m long, 1.4 m wide and 0.4 m thick. Their positions have been chosen to avoid overlap of each individual concrete cone, based on the design method in(EN 1992-4).

Figure 3

 3 Figure3shows the test setup adopted for the pull-out tests following the recommendations of corresponding assessment document (EAD 330232-01-0601).

Figure 3 :

 3 Figure 3: Concrete breakout test setup/unconfined tension test acc. EAD 330232, 2016

Figure 4 :

 4 Figure 4: Load-displacement curves

Figure 5 :

 5 Figure 5: Typical failure cone

Figure 6 :

 6 Figure 6: Comparison between experimental ultimate loads and models predictions

Table 1 .

 1 Embedment depths and number of tested headed studs

	hef	Number
	57 mm ±5.3%	3
	81 mm ±1.6%	3
	108 mm ±2.2%	3
	136 mm ±1%	3

Table 2 :

 2 Properties of concrete

	Cement proportion	286 kg/m 3
	Water/Cement ratio	0.54
	Aggregate/Sand ratio	1.06
	Compressive strength fcc	33.1 MPa
	Tensile strength ft	3.2 MPa
	Young's modulus E	27.6 GPa
	Fracture energy GF	96.5 J/m²
	3.2

. Test setup and test process at room temperature

Table 3 .

 3 Ultimate loads

	hef (mm)	Number of tests	Fu,i (kN)	Fu,m (kN) (COV)
	57	3	30.85 31.03 30.43	30.77 (1.00 %)
	81	3	43.81 46.2 43.84	44.62 (2.04 %)
	108	3	91.68 69.68 93.84	85.07 (15.72%)
	136	3	98.79 97.75 104.61	100.38 (3.68%)

Acknowledgements

The authors want to thank the technical team of the CSTB: Etienne Bruchet, Killian Regnier, Julie Skorupka, Jean Christophe Caillot and Hubert Auster for their contribution to the preparation of the specimens and the execution of the tests.

Copyright

The authors confirm their consent to be published by fib Symposium 2021.