INTRODUCTION

Structural health monitoring and the detection of damages in structures have gained increasing importance in recent times. Successful detection of damage can be directly related to the epistemic uncertainty related to the deterioration of a structure and recommend appropriate proactive maintenance, rehabilitation strategies and optimized decision making policies as required by the engineers, owners, managers and the users from safety and serviceability aspects. Accurate non-destructive damage detection techniques help recommending proactive measures in terms of assessment and performance at any given condition of a structure. This paper considers a four level hierarchical framework proposed by [START_REF] Rytter | Vibration Based Inspection of Civil Engineer ing Structures[END_REF] comprising of the detection of the presence, location and extent of damage and the prediction of remaining service life of a structure. The paper proceeds to illustrate an image processing based damage detection technology including the first three levels of such a framework since the problem of predicting service life is dissociated from the remaining three levels both in scope and extent [START_REF] Carneiro | Model-Based Vibration Diagnostic of Cracked Beams in the Time Domain[END_REF].

The problem of marine environment induced damage on steel piles has been considered and the harbour in St. Nazaire, located on the Atlantic coast of France has been considered to be the structure under consideration. The photographs of chloride induced corroded plates have been analysed using image processing techniques and the damage has been successfully described from both qualitative and quantitative aspects. The statistical properties of the spatial variation of the damage have been found. The probability of detection and the receiver operating characteristics (ROC) have been constructed. The method is observed to have a definite potential for use as an unmanned structural health monitoring tool.

DESCRIPTION OF THE PROBLEM

The Benchmark Structure

The benchmark structure is a wharf located at St. Nazaire, France and the general arrangement of the wharf is provided in Figure 1. This wharf belongs to the category of on piles wharfs. It is located in the

F. Schoefs

Institute in Civil and mechanical Engineering, Nantes Atlantic University, Nantes, France ABSTRACT: Measurement of the extent of damage in a real structure is extremely important in terms of any maintenance strategy. However, this measurement often turns out to be difficult, time consuming and error -prone. The necessity of a simple, fast and relatively inexpensive damage monitoring system with reliable measurements is growing for quite sometime. The paper proposes a camera based image analysis technique to quantify and classify damage in structures at various levels of scale. The general method has been applied to corroded plate specimens in the laboratory with the aim to identify the affected areas on a steel pile due to pitting corrosion. The method depends on the contrast of the corroded region with respect to its surroundings, performs intelligent edge detection through image processing techniques and computes each affected and closed region to predict the total area of the affected part along with its spatial distribution on a two dimensional plane. Moreover the performance of the camera allows defining a detection threshold and the so-called probability of detection (PoD) and probability of false alarms (PFA). PoD are suggested as functions of the area of the pitting for the construction of Receiver-Operating-Characteristic (ROC) curves. The methodology can be used as a tool for the owners/managers of the structure for objectively quantifying and localising the extent of pitting corrosion, rather than providing information through a subjective visual assessment. Moreover, it allows introducing the probability of detection and probability of false alarms in the decision chain and in risk analysis. The method is shown to be robust, reliable, simple and inexpensive. estuary of Loire river near between Nantes and Saint Nazaire towns and is a very important harbour on the Atlantic side of Franc. Being in the marine environment, the steel piles are susceptible to corrosion and hence the assessment of the structural health of such a structure is considered to be of great practical importance. In fact steel piles play two major roles -the first being a mechanical function and the second being a protection of reinforced concrete inside against corrosion, which is generally uniform. Submarine inspections and investigations of localized corrosion have been observed by divers in this regard. These damage conditions have been recorded on video tapes and reported as pictures on inspection report. The damages look like pitting in white metals, which is usually why the corrosion is referred to as 'pitting corrosion'. This type of corrosion is often a consequence of the defects in the metals that the structure is comprised of. In fact, these piles come sometimes from the rebus of the pipe-lines (nonconforming pieces).

The presence, the location and the distribution of the corroded regions are regarded to be vital information for the assessment of structural health at a certain condition. From standard inspection it is very hard to quantify these properties due to the harsh conditions and it brings about a considerable and unwanted increase of inspection time. An automatic video pictures processing after appropriate preprocessing of the material seems to be a good alternative once the errors on measurement have been quantified.

Image Dependant Information

Being an underwater structure, the measurement of the quantitative aspects of the corrosion is extremely difficult. However, information based on the photographs of the corroded regions are available. These photographs can be directly obtained from the piles or can be from the experimental plates attached to the piles or those corroded in a similar environment within the laboratory. The corroded plates can be untreated or chemically treated to accentuate the corroded region. A successful identification of the presence, location and the extent of damage using such photographs is required by any structural health monitoring scheme. Figure 2 shows an example of one of the treated plates. The corroded regions are observed to be in contrast with the background and this fact is considered to be the starting point behind damage detection from photographic information.

Even when the damage samples are available, both from the laboratory and from the structure, the quantification of the damage is manual and hence difficult and time consuming task. As a result such assessments are usually limited to accurate identification of the presence of damage. The information of the geometric properties of the damage is less reliable due to the presence of human factor and the time involved with such analyses increase greatly even when the number of observations is moderate in size. All these problems necessitate the development of an image processing based damage detection technique that is easy to handle, more accurate and less time consuming.

IMAGE PROCESSING BASED DAMAGE DETECTION

Theoretical Background and Detection Scheme

Applications of image processing have gained popularity very recently in the field of structural health monitoring. [START_REF] Patsias | Damage Detection us ing Optical Measurements and Wavelets[END_REF] have illustrated the use of video camera based dynamic shape identification in conjunction with wavelet analysis. Similar image processing based damage descriptor for asphalt mix has been proposed by [START_REF] Hartman | Evaluating Four-Point Bend Fatigue of Asphalt Mix Using Image Analysis[END_REF]. Application of such video camera based work has also been seen to track the motion of a cable [START_REF] Gehle | Tracking the Multi Com ponent Motion of a Cable using a Television Camera[END_REF]).

Multiple cameras have been used to identify damages by using photogrammetric software by Benning et.al (2004). Open cracks in beams have been identified using wavelet analysis in conjunction with image processing by both static [START_REF] Rucka | Crack Identification using Wavelets on Experimental Static Deflection Profiles[END_REF]) and dynamic (Pakrashi et.al, (2007)) deflected shapes.

The detection method in this paper is dependent on the fact that the damages present in the photograph are optically different from its surroundings in terms of colour, brightness and geometry. The object is to convert the coloured image to a binary image and identify the edges of the damaged regions successfully. A successful detection ensures that the coordinates of all the points lying at the edge of the closed geometry of the damages are available. By calibrating the pixel length of the photographs in the horizontal and the vertical direction against some pre-existing benchmark of distance in the real specimen or structure, the entire spatial geometry of the damaged regions are retrieved along with the possibility of post-processing to obtain the statistical measures of such geometry.

The MATLAB 7.0 image processing toolbox (MATLAB, 2006) has been employed for the proposed detection scheme. The saved image of the corroded plate is essentially a rectangular grid of pixels and the centre of a pixel occupies the integer co-ordinates in the grid so produced. The interior of each pixel can be further subdivided into a continuous spatial coordinate system by considering that the local origin for each pixel lies at the top left hand corner of the pixel, and not at the centre. Each pixel is associated with a vector of number describing its hue-saturation value.

The gray-level threshold of the image is computed by minimizing the interclass variances of the black and white pixels using Otsu's method using MATLAB 7.0 image processing toolbox. Pixels below the threshold assume a value zero and turn black, while the other pixels turn white. This enables to convert a complex matrix from the original image to a simpler binary black and white image.

This transformation is important when the feature of interest is in contrast with its surroundings in the image whereby the corroded regions in contrast to the background can be identified as closed geometries within the binary matrix so produced. The black and white binary images are converted by thresholding and the edges of the images are found using the Sobel method [START_REF] Sarfraz | Computer Aided Intelligent Recognition Techniques and Applications[END_REF]) incorporating the MATLAB 7.0 signal processing toolbox. The Sobel method scans a binary image and returns the approximation to the derivative of the two-dimensional data. The edges are returned as the points where the gradient of the image are locally maximum.

The efficiency of the detection lies in the contrast of the damage region with respect to its surroundings and the ability of the analyzing system to identify such contrasts within a closed geometry. Since ferric ions, in the presence of water, oxygen and/or organic and inorganic acids in the marine environment tend to form coloured products, the discolouration due to corrosion is usually common. This fact has been observed by Tsushima et.al (1997) in conjunction with basic image processing methodology.

Although the depth of the damage region and hence the extent of damage cannot be identified using such image processing methodology directly for certain limit states, the localisation and the spatial statistical information yielded from the analysis immediately enables the end user to minimize the maintenance region and prioritize the regions according to the importance within the framework of an existing maintenance plan. This has a direct and a positive effect in terms of efficient investment of the maintenance budget and the decision making policy of the structure in the long run.

An example of a successful image processing based damage region detection as proposed in the paper is given in Figure 3, where Figure 2 has been successfully analyzed to isolate eight major closed damaged areas of irregular geometry with precision. Some spurious features are also identified due to the environmental noise but are insignificant with respect to the damaged regions. Sometimes, a visual idea about the spurious features can be helpful to preprocess the picture to make the computational effort of the pattern recognition scheme easier and the scanning region comparatively smaller.

Statistical Information

Once the closed geometries and their co-ordinates are identified within the photograph, various statistical properties of the geometries can be found. The centroids, the areas within each identified object and the major and minor axes of each of the objects have been computed in this study as an example using the MATLAB image processing toolbox. The summary of the information is provided in Table 1 where the spatial variability and the extent of the damage regions have been quantified. Any other photograph produces such results and can be related to the actual length scale by choosing a pre-existing benchmark.

It is also important to note that the objects labeled 2 and 3 in Figure 3 are considered to be a single object while processing and hence the combined geometric property of the system has been rendered instead of their individual statistics. This is due to the fact that in the real specimen the damages are in fact physically connected. However, by a proper control on preprocessing, lighting and camera resolution these two geometric regions can be separate incorporating some additional effort.

The information provided by Table 3 can also act as a tool for the relative ranking of the damaged locations within the structure. For this particular case the total area of damage has been found to be approximately 5.7% of the total area under consideration. The unit of length in Table 1 is in pixels and that of area is in square pixels. The terms Xbar and Ybar represent the coordinates of the centroid of each labeled damaged region in horizontal and vertical direction respectively. With the information on the successful detections and false alarms available, the receiver operating characteristics can be constructed. Inspection by video processing is not perfect when considering on site video recording: luminosity, distinctness and contrast are not known and are neither uniform on a given picture and from a picture to another. Moreover, for the quality of image the most difficult part is the decision on the actual existence of what seems to be a defect. It has thus become a common practice to model the detection reliability in terms of the probability of detection (PoD), the probability of false alarms (PFA) and the Receiver Operating Characteristic (ROC) curves. The most common concept which characterizes inspection tool performance is the probability of detection. The PoD and the PFA depends on the following quantities of interest -the maximum size of the defect and the area of the defect. Here for simplicity, let us consider the area of the pitting. Let A d be the minimal pitting area, under which it is assumed that no detection is done. Parameter A d is called detection threshold in the following. Thus, the probability of detection is defined as:

d PoD(A) P(A A ) = ≥ (1)
where A is the measured area. A d is a deterministic parameter or a random variable. This definition implies that PoD is a monotonic increasing function.

To complete this concept, the probability of false alarm has been introduced. It is the probability to defect a non-existing defect. For a given range of defects A i , the curve that joints the points of coordinates (PFA, PoD(A i )) is called Receiver Operating Characteristic (ROC) curves [START_REF] Arques | Decisions en traitement du signal[END_REF], [START_REF] Fücsök | Human factors: the NDE reliability of routine radiographic film evaluation[END_REF]). Such a curve is plotted on figure 4. In view to introduce these concepts into practicable decision schemes, recent works have been carried out (Faber & Sorensen (1999), [START_REF] Rouhan | On the use of inspections results, in IMR plans[END_REF] and ( 2003)).

Statistical modelling of inspection results.

Knowing the probability density functions (pdf) of the signal and noise and that of the noise alone, the computation of PoD and PFA comes easily. It is reminded in [START_REF] Rouhan | Probabilistic modelling of inspect tion results for offshore structures[END_REF]. There is actually no way to obtain the pdf of the signal and the signal and noise together for image processing in harsh conditions where many factors affect the inspection results. One way of modelling such parameters is to analyse the probabilistic structure of the inspection results and to provide a model consequently. The I.C.O.N project has been dedicated to the inter-calibration of the N.D.T tools with the appropriate checks done on-the-spot in recent times for this purpose. A statistical analysis had been made there from a set of tests which consider • Various node typologies • Several inspection conditions (basin, sea)

• Several inspector teams coming from several countries. These considerations are reminded in [START_REF] Rouhan | Probabilistic modelling of inspect tion results for offshore structures[END_REF] and allow distinguishing between whether a crack or a group of cracks has been detected.

Here the problem is similar and conforms to such probabilistic information structure, especially in the case where two pitting areas are very close. We assume in the following that every detecting defect has a proper and identifiable shape. As the number of detected pitting areas can exceed number of existing pitting areas, the corresponding ratio is not a probability. Two sets of probabilities (eq. ( 2) and ( 3)) are defined. The first one concerns correct detections:

(2)

The second one deals with false detections:

(3) According to these definitions, f P (c) can be considered as PFA and b P (c) as PoD. This leads to obtain discrete PoD values according to the range defined and construct a whole ROC curve by modifying the image processing for a given range of defects.

An application of such a case is provided in the current problem and the results are provided in Figure 5. The ROC of the current detection condition is constructed. With the increase of resolution, the PoD detection increases, but so does the PFA. On the other hand with poor resolution characteristics within the image, both PoD and PFA are considerably low. It is only at some intermediate level of resolution is the optimized value obtained where a high PoD corresponds to a minimum of PFA. The effects of high and low resolutions are earmarked within the figure. Two alternative hypothetical curves in dotted lines are employed to emphasize the effects of the presence of other factors within the same methodology like lighting, nature of damage, etc.

The hypothetical ROC curves illustrate the uncertainties associated with the measuring conditions (which are variable) like luminosity, contrast, noise etc. and emphasize the shift of the efficiency achieved using the proposed NDT tool due to such uncertainties. It can be observed from Figure 5 that there may be possible cases where the ROC can be unsatisfactory due to the quality of the measured data itself and such situations can be identified by considering an envelope of ROC due to various conditions through existing data or simulations close to the chief governing conditions due to the change of the major affecting parameters. The efficiency and the robustness of the methodology are thus illustrated within the structural health monitoring framework in this regard.

CONCLUSIONS

An image analysis based damage detection and calibration scheme has been introduced in this paper along with an investigation on the uncertainties related to such detection process. A study on the identification of corrosion in an experimental plate has been performed and the existence, location and the extent of the damage locations have been successfully identified. The damage classification methodology is seen to be independent of the damage process and the material affected. The ROC of the damage classification methodology in obtained. This general detection scheme is simple, computationally inexpensive and shows a definite potential to be used as an unmanned structural health monitoring system.

Figure 1 .

 1 Figure 1. Steel piles with Corrosion.

Figure 2 .

 2 Figure 2. A Treated Specimen with Corrosion.

Figure 3 .

 3 Figure 3. Detected Damage Regions in a Specimen.

Figure 4 .

 4 Figure 4. Receiver Operating Characteristic curve.

  For the purpose of successful calibration, let us consider n(c) tests within a range c ( as the number of existing corroded regions which are detected. f n (c) as the number of non-existing pitting areas which are detected ; n n (c) number of existing corroded regions which are not detected. r n (c) as the number of healthy areas where no pitting areas have been detected.

Figure

  Figure 5ROC Curves for the Current Problem.

Table 1 .

 1 Spatial Variability of the Identified Locations of Damage.

	Damage	Xbar	Ybar	Major	Minor	Area %
	No.			Axis	Axis		Area
	1	273	56	51	36	1151 0.9
	2 &3	173	139	66	34	1597 1.25
	4	232	200	30	24	539	0.42
	5	311	186	56	24	985	0.77
	6	346	212	34.5 20.3	494	0.38
	7	178	280	44	39.4	1272 0.99
	8	298	295	54	31.2	1240 0.97
	4 PROBABILISTIC STUDY ON IMAGE
	PROCESSING BASED DAMAGE
	DETECTION AND CALIBRATION

4.1 Inspection results modeling: theoretical basic concepts.


D Marot

Y Sail

A Alexis
email: alain.alexis@univ-nantes.fr

Experimental Bench for Study of Internal Erosion in Cobesionless Soils

Under the internal flow, hydraulic earth structures (dikes, levees, or dams) can incur a migration of particles that can induce a modification of hydraulic and mechanic characteristics.

With the objective to characterize this phenomenon named internal erosion and its consequences on mechanical behaviour of granular materials, a large oedopermeameter device is developed. An axial load is applied on specimen and also a downward flow with a constant hydraulic gradient. During the testing time, the bench can measure the spatial variability of density and of interstitial pressure along the specimen. Axial deformation, injected flow and eroded mass are also measured during the testing time.

Erosion of fme particles on downstream specimen part is accompanied by flne particles migration in the specimen. This migration induces a settlement and an increasing of interstitial pressure. Afterwards a localized instability appears and triggers specimen deformation.

INTRODUCTION

Within earth structure such as dam, dike or levee, seepage can induce a detachment and a transport of fine particles from the structure or from its foundation. This process named intemal erosion can modify hydraulic properties of soil as permeability but internal erosion can also modify mechanical behaviour. Finally these modifications can induce instability of the earth structure. The occurrence of failures in new earth structures demonstrates the need of improving the knowledge of these phenomena and its consequences on mechanical behaviour of soil.

In uncracked soils, the two main phenomena of internal erosion are suffusion and backward erosion. Suffusion is the detachment and transport process of only fine particles whereas backward erosion concerns all grains. Initiation of internal erosion processes is influenced by geometric conditions as grain size distribution, porosity of soil [START_REF] Kenney | Internal stability of granular filters[END_REF] and grain shape [START_REF] Li | Seepage induced instability in widely graded soils[END_REF] and by loading conditions as effective stress [START_REF] Li | Seepage induced instability in widely graded soils[END_REF] and hydraulic gradient [START_REF] Skempton | Experiments on piping in sandy gravels[END_REF]. Depending on the process of internal erosion, confinement stress has a complex effect on internal erosion development [START_REF] Bendahmane | Parametric study of suffusion and backward erosion[END_REF].

A new experimental bench is developed in order to characterize initiation and development of internal erosion. This device is described and a test procedure is performing for a specimen composed by a gap gradation of glass beads. Hydraulic and mechanical response of the specimen to an increasing hydraulic gradient is presented.

OEDO-PERMEAMETER DEVICE

The main bench characteristics are summarized in Figure 1. Device is configured to enable specimen preparation which is saturated and consolidated in oedometric condition. Specimen is subjected to seepage flow under a hydraulic gradient that increases by stages. The bench is composed of an oedo-permeameter cell with a funnel-shaped draining system which is connected to a collection system. The bench comprises also an axial loading system, a hydraulic control system and a gammadensitometric system. The control and acquisition part is provided by two units connected to two computers. All these components are detailed below.

Oedo-permeameter cell

With the aim to observe specimen during testing time, the rigid wall cell is made of Plexiglas tube. Internal cell diameter is ((>cell = 275 mm and the specimen height can reach 600 mm. It can be noted that oedo-penneameter cell allows testing specimen with a maximum grain size Dmax = 9 mm (equivalent to a cell factor Dmaxi<I>cell = 30) and a slenderness ratio of 2. The two ends of Plexiglas tube are reinforced by stainless steel plate. Cell wall is equipped with twelve pressure ports (two arrays of six pressure ports on opposite cell sides, two by two pressure ports at the same elevation and vertical spacing of 100 mm between pressure ports), a pressure port is placed on piston base plate (see below axial loading system) and a fourteenth port is positioned below specimen on draining system. In order to avoid discrepancy between two pressure transducers, pressure ports are connected to a multiplex unit which is connected to a pressure sensor [START_REF] Alexis | Experimental bench for study of settlingconsolidation soil formation[END_REF].

Thanks to several specimen supports, specimen with different heights can be tested. A stainless steel mesh screen is placed on specimen support. This 15 mm thick mesh screen has 10 rnm pore opening size in order to allow the migration of all grains. With a rim, different wire meshes can be ftxed on the mesh screen in order to take into account the effe.ct of pore opening size on internal erosion [START_REF] Marot | Internal flow effects on isotropic confmed sand-clay mixtures[END_REF]. To eliminate any preferential flow between mesh screen and cell, a geotextile is placed between wire screen edge and rigid wall of cell.

Top plate has two inlet ports 10 mm in diameter and the base plat has a vertical funnel-shaped draining system which is specially designed to avoid clogging. The opening of draining system is controlled by a pneumatic gate. Outlet pipe is in glass in order to permit the measurement of effluent transparency by means of an optical sensor (Bendalunane et al., 2008).

Collection system

The collection system is composed of an effluent tank which has an overflow outlet with a 0.08 mm mesh in order to catch the fine eroded particles. Effluent tank can be continuously weighing or can contain several beakers for the effluent sampling.

Axial loading system

A piston, a pneumatic cylinder and a reaction frame compose the axial loading system. Piston comprises two perforated plates which are made of 15 mm thick stainless steel. A 61 mm thick layer of gravel separates the two plates in order to diffuse the injected fluid on the specimen contact interface uniformly. Two joints are bonded to the piston edge to avoid any parasitic particle displacements between piston and cell wall.

Axial effective stress on the top surface of specimen is generated by a pneumatic cylinder (capacity: 11.5 kN) which has a 200 mm stroke in order to maintain the axial stress even in the case of a great specimen settlement. A load cell measures the axial force on the loading rod. The piston displacements and thus the specimen settlements are measured by a Linear Variable Differential transducer (L VDT) (stroke: 200 mm).

The pneumatic cylinder is mounted on a framework. This framework supports also the oedo-permeameter cell which is mounted on a large ball bearing for the axial cell rotation.

Hydraulic control system

Hydraulic system is composed of two reservoirs and a pump. A 1500 litre storage reservoir is supplied by public water system and placed in a temperaturecontrolled chamber.

With a pump, this reservoir supplies a 200 L tank which is equipped with a pressure controller. A pressure transducer connected to the pressure port on the piston base plate allows controlling the water head applied on specimen top face. The connexion between controlled pressure tank and eodo-permeameter cell includes two electromagnetic flowmeters (120 L/min and 480 L/min of capacity) for the measurement of seepage flow.

Gamma-densitometric system

The gammadensitometric bench was developed by [START_REF] Alexis | Experimental bench for study of settlingconsolidation soil formation[END_REF]. It comprises a radioactive gamma-ray source and a scintillation counter on the opposite cell side. These components are bonded on a carriage which can move in vertical direction thanks to an endless screw and a controlled electric motor. The position of the carriage is measured by a position transducer. According to a previous gauging data, a density calculator counts the scintillometer impulses and calculates the density.

Monitoring and data acquisition system

The control and acquisition part is provided by two data units. One principally controls the gammadensitometric bench motor and the multiplex unit. It is also in charge of the acquisition of: density measurements, position carriage and water head. Two velocities of travelling motion are used, a cruising speed and an approach speed to limit both travelling duration and position discrepancy. This unit drives the run of the second data acquisition unit.

The second data unit carries out the measurements from load sensor, settlement sensor, mass balance and seepage flowmeters.

TEST PROCEDURE AND TESTED MIXTURE PROPERTIES

The tested material is a mixture of glass beads. This cohesionless material allows to compare our results with an experimental campaign performed by [START_REF] Moffat | A large permeameter for study of internal stability in cohesionless soils[END_REF] with a large permameter.

Grain size distribution of mixture

Figure 2 plots the grain size distribution of tested mixture (named G4-C by [START_REF] Moffat | A large permeameter for study of internal stability in cohesionless soils[END_REF] and the grain size distributions of the mixture components (coarse fraction C and fine fraction F). According to [START_REF] Moffat | A large permeameter for study of internal stability in cohesionless soils[END_REF], fine fraction F is equivalent to fine sand with a coefficient of uniformity Cu = 1.4 and d 85 = 0.19 mrn (where d 85 : sieve size for which 85% of the weighed soil is finer). Fraction C is equivalent to coarse sand with Cu = 1.7 and dto = 1.4 mm. Gradation 04-C is composed of 40% by weight ofF and 60% of C and it is characterized by a gap. The Illixture preparation phase is divided in four steps: positioning alternatively a series of coarse and fine fractions layers in mixing machine with I 0% of water content, mixing during 3 minutes and homogeneity verification by size distribution measurements.

Test procedure

A wire mesh with a 1.25 mm pore opening size is fixed on wire mesh screen in order to allow only the migration of particles F.

The cell is filled with water to saturate by gravity flow: the pressure connexions, the multiplex unit and the pressure sensor.

In conformity with specimen reconstitution technique used by [START_REF] Moffat | A large permeameter for study of internal stability in cohesionless soils[END_REF], specimen is prepared in several layers by slurry deposition. The total dry mass of glass beads in specimen is 51.64 kg and the initial specimen height is 45 em. An upper wire mesh of 0.08 nun is placed on specimen face to avoid fme particles migration in the piston. Specimen consolidation occurs under 25 kPa axial loading and with double drainage condition (dissipation of excess interstitial pressure in upward and downward direction).

Data acquisition is started afterwards specimen is submitted to a downward seepage under a first value of hydraulic gradient. Hydraulic gradient is increased by increments about unity until specimen failure. Each stage of hydraulic gradient is applied during 60 minutes. During testing duration, data are recorded with a periodicity of 1 second and the effluent sampling is performed with a 6 minutes period.

For this specimen height, Figure 3 shows the position of used pressure ports (number 1 to 11) and the distance from the specimen bottom of density measurement stations (section 1 to section 6).

At the end of each hydraulic gradient stage, the specimen is isolated by simultaneous closing of upstream and downstream gates and the controlled pressure tank is filled. TEST RESULTS AND DISCUSSION [START_REF] Moffat | A large permeameter for study of internal stability in cohesionless soils[END_REF] detected the onset of failure for a value of hydraulic gradient i = 8.3. About half of this value was chosen for the first stage of hydraulic gradient (i = 3.6) and two other stages could be applied on specimen before failure: 4.6 and 5.6 respectively.

Initial state of specimen

At the end of specimen preparation, a loss of fme particles is measured which represents around 2.7% of total fme mass. The upward and downward profiles of density measurement (cf. Figure 4) show a density which decreases in downward direction from 2 g/cm 3 to 1.95 g/cm 3 . The low discrepancy between these two density proftles shows that repeatability of density measurement is fairly good as the two profiles are very close.

Injected flow and permeability

During the first hydraulic gradient stage (i 1 = 3.6), the seepage flow is 1.3 L/min. For the second stage (iz = 4. 6), the flow reaches 1. 7 L/min and its value is 2 L/min during 20 minutes of third stage (b = 5.6). For these three stages, the specimen hydraulic conductivity is k = 1.1 0 4 m/s. At t = 20 min for the third stage, flow suddenly increases and fmally it exceeds the flowmeter capacity(> 8 L/min). So the specimen hydraulic conductivity is higher than 4.1 0 4 m/s. An instability characterized by no particle F can be observed along the cell (see Figures 5(a The initiation of this instability is observed at the specimen top interface and it progresses in downstream direction along the positions of pressure ports number 11, 10, 9, 8 and fmally 7.

Eroded mass and settlement

Application of the two first stages of hydraulic gradient induces a small erosion of fine particles (for it= 3.6, eroded mass mF eroded= 140 g, that represents a relative erosion mF eroded/mFinitial = 0. 7%; for h = 4.6, mF eroded = 250 g, ffiF eroded/IDFinitial = 1.2% ).

The measured settlements are similar for the two stages: for each stage around 2.4 mm (that corresponds to a 0.5% axial deformation).

During the first twenty minutes of the third stage (i 3 = 5.6) (which corresponds to the first fifteen minutes of effluent sampling) the increasing of settlement is quite similar to the settlement increasing in the course of previous stages and eroded mass is mF eroded= 200 g (mF crodediiDFinitial = 0.9%). At t = 20 min, settlement suddenly increases to reach 13 mm (axial deformation of 3%) and the cumulative eroded mass increases by 2.4 kg (mF eroded/ffiFinitial = 11%).

Figure 6 represents the instantaneous variations of eroded mass and settlement during the three stages. ---------i :: It can be noted the similar kinetics of increasing for eroded mass and settlement. Two hypotheses about the process can be considered:

:mlO -•-••••••••--•••-••-•••----•••••-•••••••------ ;; 2500 +---- 0 -
ii 2000 + ------------i ; 1~0+--------------i Ill ~-fCOO + -------------i 'i ~ ~0+--------------------
-fme particles erosion at specimen bottom induces a migration of fme particles which concerns the whole specimen and causes the settlement -fme particles erosion at specimen bottom induces an instability located on downstream part and which causes a specimen translation without any migration of fme particle in the specimen centre.

Density variations

Two types of density variations are measured during the two first stages of hydraulic gradient:

-decrease of density in the downstream part of specimen (sections 1, 2 and 3) with a relative variation in comparison to initial density between -0.5% and -1.5% -increase of density in the upstream part (sections 5 and 6) with a relative variation between +0.25% and +2.4%.

During the third stage, only the density values on downstream part evolve ( -1% for sections 1, 2 and 3). It must be noted that the localized instability was developed outside of the measurement zone of gammadensitometer (see Figure S(a)).

Local hydraulic head variations

Spatial and time evolutions of local hydraulic head during hydraulic gradient stages 1 and 2 don't evolve significantly.

Figure 7 represents profiles of hydraulic head during the third stage. At t = 5 min hydraulic head decreases because of the downstream gate opening. At t = 1 Omin, the hydraulic head on pressure port number 11 slightly increases. 5 minutes later, a fast increasing ofhydraulic head on pressure port number 10 of about ~h10 = 35 em is detected (that corresponds to an overpressure of 3.5 kPa).

At t = 17 min the hydraulic head on point 9 increases about Llh 9 = 55 em and one minute later on point 8: ~hs = 20 em. This increasing of interstitial pressure which appears in the specimen centre and progresses in downstream direction may be due to clogging. At t = 20 min, hydraulic head profiles decrease suddenly and this evolution appears at the same time as increasing of: seepage flow, settlement and eroded mass. Thus a clogging which induces an interstitial overpressure appears (at point 10) 5 minutes before the initiation oflocalized instability. This observation confirms the first hypothesis of a fine particles migration in the whole specimen.

CONCLUSION

An experimental bench is designed to study initiation and development of internal erosion and its consequences on the hydraulic and mechanical behaviour of cohesionless soils. The device and experimental procedure are detailed. Results of a test performed on gap graded glass beads specimen are reported. On the downstream specimen part, an erosion of fine particles is detected and causes a migration of fme particles in the whole specimen. This evolution induces specimen settlement and a localized interstitial overpressure. This overpressure may be due to clogging and may be the cause of a localized instability. Finally the hydraulic conductivity is four times higher and the axial deformation reaches 4%.

The experiment setup could be used on different soils with varying particle fractions, in order to improve our understanding of the internal erosion mechanism.

Figure 1 .

 1 Figure 1. Schematic diagram of oedo-permeameter device

Figure 2 .

 2 Figure 2. Grain size distribution of tested mixture.

  450mrn

Figure 3 .

 3 Figure 3. Position of interstitial pore pressure ports and stations of density measurement.

Figure 4 .

 4 Figure 4. Initial profiles of density.

  Localized instability: (a) general view, (b) detail near pore pressure ports number 11 and 10 (h = 5.6 m/m, t > 20 min).

Figure 6 .

 6 Figure 6. Instantaneous variations of: (a) eroded mass, (b) settlement during the three stages.

Figure 7 .

 7 Figure 7. Instantaneous variations of hydraulic head (during third stage).

ACKNOWLEDGEMENT

The authors wish to acknowledge the support of the French National Research Agency (project ANR-ERINOH) and the support of the French Institute for Applied Research and Experimentation in Civil Engineering (IREX) for this research.

BIBLIOGRAPHY


Zarina M Charlesworth

Cédric Baudet

MIND THE GAP: SECOND LANGUAGE ACQUISITION COMES OF AGE IN A DIGITAL WORLD

Keywords: Innovation, Technology, Second language acquisition, Virtual reality

This paper presents an in-depth case study of an English language provider, its specific in-context method of teaching English as foreign language, and the evolution that has occurred through advances in technology. The introduction of technological innovation and barriers to acceptance as well as influencing variables are examined in light of the past, present, and future. Initial findings suggest that a key factor to success is related to the timeliness of introduction of the new technology in combination with variables previously identified in the Unified Theory of Acceptance and Use of Technology (UTAUT). The paper closes with suggestions related to the introduction of innovative technologies.

INTRODUCTION

"Could you teach English?" A split second of hesitation later and Gordon replied "Yes, of course". A first experience in the Swiss public-school system in 1984 and the basis for what would later become English in Context started to take root as Gordon began to develop his own method for teaching English as a foreign language. Who has never felt the frustration of being in a foreign language situation, be it private or professional, and not understanding what is being saidand this frequently after months of language training? Countless hours are spent in the classroom preparing for language exams to little avail when it comes to using the language. Discouraged by the methods that he was asked to use, Gordon left the school system and set up shop on his own two years later. This paper provides an in-depth look at the past, present, and future practices of a specific English Language provider where the use of in-context learning has not only developed over time but also weathered the introduction of more than one technological innovation. An analysis of the diffusion of innovation in the realm of language learning with an emphasis on the barriers to acceptance follows. Lessons are taken from past experience to look towards the successful integration of future technological developments.

As the tsunami of the 4 th industrial revolution [START_REF] Schwab | The Fourth Industrial Revolution[END_REF] breaks on the shores of the 21 st century only those industries ready for its impact will survive and thrive. With unprecedented demand for their services, those involved in the teaching of English as a second language are at the front of this wave. Market estimates for the global, academic plus non-academic, English language learning sector put it at up to US$ 63.3 billion for 2013 within which the digital language learning segment accounts for 5% [2,[START_REF] Adkins | The 2013-2018 Worldwide Digital English Language Learning Market[END_REF]. Within this sector the highest demand is currently coming from China, Asia and, Africa, however, even Western Europe is expected to to show an estimated 5-year Compound Annual Growth Rate (CAGR) of 4.5% taking the 2013 digital English language market figures from US$ 343.8 million to US$ 428.6 million by 2018 [START_REF] Adkins | The 2013-2018 Worldwide Digital English Language Learning Market[END_REF]. English has not only reinforced its position as an international language with the advent of globalization and the use of the internet but is also now being taught from the primary school level on up and is increasingly the language of instruction in universities around the world. This project is concerned with how best to weather technological change resulting in the acceptation and further diffusion of technology when significant future technological change is on the horizon through the introduction of virtual reality as a tool for second language acquisition.

LITERATURE REVIEW

The literature referred to in this research draws on two streams, one being that of second language acquisition and the other that of the acceptance of technological innovation. Educational approaches and models are continually undergoing revision, but today's educational paradigms are evolving at an unprecedented speed coupled with technological developments. Accordingly, a review of the principle developments in second language acquisition over time followed by a brief review of models pertaining to the acceptance of technological innovation are presented in the subsections below.

Second language acquisition

The teaching of English as a foreign language grew into its own in the 20 th century when the debate about the theoretical foundations of language teaching methods were laid, drawing on the work of linguists and psychologists [START_REF] Richards | Methods in Language Teaching[END_REF][START_REF] Curran | Methodology in Language Learning: T-kit[END_REF].

Research in second language acquisition clearly shows that the 'drill and rote' learning of the 1970's followed by the communicative approach and then the later task-based orientation of the 1990's do not adequately address the needs of today's language learners and it is only in the past twenty years that the idea of in-context learning has even taken hold.

Historically, learning a second language has undergone various influences on the approaches and methods used [START_REF] Celce-Murcia | Language Teaching Approaches: An Overview, in Teaching English as a second or foreign language[END_REF]. From as far back as the Middle Ages and through the 1800's, two major approaches to language learning can be identified, that of grammar-translation which focused on analysing the language and, a less frequent approach based on language use. It was, however, the grammar-translation method that remained the dominant approach as it was the standard method used in schools and universities. Despite the introduction of other approaches that stressed language use, such as the Direct Method, the Reading Approach for example, the grammar-translation approach held its own until the 1940's when a need for language use, especially by those in the U.S. armed forces, changed the imperative. It was at this time that the theoretical foundations of language teaching methods were laid, drawing on the work of linguists and psychologists [START_REF] Richards | Methods in Language Teaching[END_REF][START_REF] Curran | Methodology in Language Learning: T-kit[END_REF]. This led to the development of the Audio-Lingual approach in the United States and concurrently to the Situational Approach in Great Britain, followed by a number of other approaches that emphasized comprehension and communication.

Language teachers today have any number of methods, approaches, and techniques to choose from. Their choice may be dictated by the context in which the instruction is given, the school, the learners, or simply due to individual preference. It is not the intention of this very brief review to suggest that any one approach is the best rather simply to make the reader aware of the multiplicity that language teachers today are faced with and to call to the reader's attention changes in society that have and still are having a real impact on the demand for language instruction. Changes that include the massification of travel, a continued rise in study abroad programs, the rise of multinationals, the use of internet and music platforms such as Spotify, just to name a few.

Adding to the complexity of the afore-mentioned is the advent of digital / mobile technologies which is what brings us to the second body of literature that we are drawing on, the acceptance of technological innovation.

Diffusion and acceptance of technological innovation

Two of the key issues related to innovation are its diffusion and long-term adoption. Drawing on wellestablished models Abernathy and Utterback [START_REF] Abernathy | Patterns of Industrial Innovation[END_REF] and Rogers [START_REF] Rogers | Diffusion of innovations[END_REF], the main objective of this project is the identification of strategies to prevent a fall into the chasm as described by Rogers [8] that exists between the early adopters of a new technology and the considerably larger market of early users. In order to better understand the variables involved in the acceptance of new technology we turn to Venkatesh et al. and their work on the Unified Theory of Acceptance and Use of Technology (UTAUT) [START_REF] Venkatesh | User Acceptance of Information Technology: Toward a Unified View[END_REF][START_REF] Venkatesh | Unified Theory of Acceptance and Use of Technology: A Synthesis and the Road Ahead[END_REF]. Although subsequent work has been done on the original model, we have chosen to use the original four variables identified, shown in Table 1, applying them to the acceptance of new technology Table 1. UTAUT Variables Based on Venkatesh et al. [START_REF] Venkatesh | User Acceptance of Information Technology: Toward a Unified View[END_REF] and cited in Dwivedi et al. [START_REF] Dwivedi | Re-examining the Unified Theory of Acceptance and Use of Technology (UTAUT): Towards a Revised Theoretical Model[END_REF] Performance Expectancy (PE)

The degree to which an individual believes that using the proposed technology will allow for gains in job performance

Effort Expectancy (EE)

The degree of ease associated with the use of the technology Social Influence (SI)

The degree to which an individual perceives that those of importance feel the technology should be adopted or used

Facilitating Conditions (FC)

The degree to which an individual believes that an organizational and technical infrastructure exists to support the use of the system and not just to information systems as was initially intended. In addition to the afore-mentioned variables, one other important element relating to the acceptance of technology can be illustrated with Gartner's Hype Cycle shown below in Figure 1.

Figure 1. Gartner's Hype Cycle [12]

The point of interest here is around the time of consolidation and failures combined with the second / third rounds of capital funding. It is at this time that relatively new technologies start to become available to a larger public. At this stage we are still looking at early adopters, but the early users are not far off. Our interest is looking at a specific market through the eyes of one English language provider and evaluating what has allowed for success upon success each time a new technology has been introduced.

With this in mind the following research questions were formulated to help contextualise the project.

How can the introduction of new and sometimes disruptive technologies be navigated?

How can barriers to the introduction of new technology be overcome?

How might the following variables: performance expectancy; effort expectancy; social influence; facilitating conditions; playing a role in the acceptance of new technology?

METHODOLOGY

A multiple-technique ethnographic case study approach was selected to provide an in depth look at the past, present and future practices of a selected English language provider, English in Context. As our questions were essentially "how" questions, the choice of the case study method became clear [START_REF] Yin | Case Study Research: Design and Methods[END_REF]. The rationale for using a single case for study was that due to the thirty-year plus experience of the person behind English in Context and the fact that one technological innovation after the other have been successfully integrated into the product offer we felt that this satisfied the critical case condition put forth by Yin [START_REF] Yin | Case Study Research: Design and Methods[END_REF]. A case study comprises several methods. This project draws on data collection techniques which include, semi-structured interviews with key informants, chains of conversations and participant observation.

At this time, only the initial interviews coupled with conversations and observation have been completed. An interview guide along the lines of the afore-mentioned research questions was used and the interviews were transcribed and coded for analysis. Additional information concerning English in Context has come from conversations with the language providers as well as with learners. One interview has also been carried out with an expert in a formal higher education setting where English is taught as a second language.

Initial findings are based on observation, chains of conversations and interviews. As mentioned previously, English in Context is a language provider that has moved from book-based in-class teaching and learning to the introduction of mobile applications followed by the development of a virtual campus for on-line teaching and is now preparing to supplement its product offer with the introduction of the Interactive Immersion Learning System 360° (IILS360°). The latter being 3-D virtual reality immersive videos. All technological introductions have been successfully weathered to date. As this is often not the case, the "how" behind strikes us as of utmost importance.

The question of timely introduction cannot be sufficiently emphasized. As with any technology, if it is proposed ahead of its time the chance of success is limited. At the same time, once the technology is sufficiently widespread, particularly true in a competitive market, its use is no longer seen as adding value but as run of the mill. In the case of English in Context its success seems intimately linked to having timed the introduction of each new technology at just the right time. This is best illustrated with the time-line shown below. It is of interest to note that every time English in Context has appropriated a new technology it has been just as the technology was going mainstream so whilst on an upward growth curve meaning that: it was accessible to both the company as a provider and to its students; the price of the technology would have decreased; it was still early enough so as to stake a claim before other, larger providers took over the market allowing English in Context to keep ahead of the game. In answer to our question of how best to navigate the introduction of new technologies, it would seem that timing is of the essence.

We also explored barriers to technology and this at the level of both the provider and also at the student level. From discussions and interviews, our initial reading is that of the four variables previously mentioned those of Performance Expectancy and Effort Expectancy seem to have more of an influence than do the others on the student. Whereas, the Social Influence variable seems to be of more importance for providers. These findings remain to be confirmed, however.

In terms of real barriers, it is not the technology itself that seems to come in question rather ease of access and use and, also that of cost. Here too, the importance of a well-timed introduction allows these barriers to be easily overcome.

DISCUSSION & CONCLUSIONS

Although only at the early stages of the research project we feel that there are important concepts that emerge from our preliminary analysis. In addition to what Abernathy and Utterback said some forty years ago "It is reasonable that the diversity and uncertainty of performance requirements for new products give as advantage in their innovation to small, adaptable organizations with flexible technical approaches and good external communications, and historical evidence supports that hypothesis" [START_REF] Abernathy | Patterns of Industrial Innovation[END_REF], and which still stands today, is the idea of timeliness. The introduction of a new technology to early on is often doomed to failure, waiting until the technology is just getting established and sufficient interest is shown by the market would seem to be ideal as it is at this time that a firm or an educational institute can differentiate in a way that learners and students can appreciate.

It is expected that the coupling of this idea of timeliness with the UTAUT variables will allow us, in the future, to propose a model that integrates a social element into the standard product or technology lifecycles and may give education providers, whether independents or schools, an even better way of gauging when best to introduce new technologies.

Table 2 .

 2 Introduction of new technologies over time by English in Context

	YEAR	TECHNOLOGY	MARKET MATURITY
	2000	MP3	Named coined in 1995, by 2000 a cultural phenomenon
			the world over and just beginning to go mainstream with
			early users
	2010	YouTube	2005 the first video was uploaded, end 2009 the 1
			billion daily world view mark was reached, and full HD
			launched. The market was going mainstream
	2012	Smartphone apps	The first smartphones were introduced in 2007, by 2010
			both Apple and Android had systems up and running on
			phones and tablets. Here to the market was going
			mainstream
	2017	Learning	Cloud-based LMS's first came into use in 2012 as a
		Management	follow-up to LMS platforms introduced in schools and
		System (LMS)	universities in the late 1990's. The market for
			independent users is still growing and really taking off.

ACKNOWLEDGEMENTS

Particular thanks go to English in Context for having opened their doors and their hearts to us as well as to Dr. Particia Pullin for her expertise.


E Cueto
email: ecueto@unizar.es

A Ma

F Chinesta

M R Mackley

Numerical simulation of spin coating processes with carbon nanotubes suspensions

Keywords: Spin coating, carbon nanotubes, numerical simulation, meshless methods

In this paper we address the problem of simulating the behaviour of Carbon nanotubes (CNTs) suspensions in spin coating processes. Spin coating is a procedure used to apply uniform thin films to flat substrates by means of a high rotating velocity and the subsequent centrifugal force.

In this work we assume a suspension of chemically treated CNTs, such that they do not aggregate. In such a suspension, CNTs can be treated as rigid fibres whose orientation is dictated by the flow of the solvent. In order to treat the associated free-surface problem and to avoid the numerical problems associated to their FE solution, we have implemented a Natural Element strategy in an updated Lagrangian framework.

The resulting model is thus composed by a description of the micro scale, related to the orientation of the carbon nanotubes and the assumption of a quadratic closure relation, together with the natural element approximation for the Navier-Stokes problem governing the macroscopic suspension kinematics.

INTRODUCTION

Carbon nanotubes have generated a tremendous interest in the scientific community after their discovering by Iijima in 1991 [START_REF] Iijima | Single-shell carbon nanotubes of 1-nm diameter[END_REF]. A single-walled carbon nanotube (SWNT) is a one-atom thick sheet of graphite (called graphene) rolled up into a seamless cylinder with diameter on the order of a nanometer. They posses impressive mechanical and electrical properties:

• Young's modulus: 1 to 5 TPa

• Tensile Strength: 13-53 GPa

• Elastic strain up to 5%.

• Density 2160 kg/m 3 . This, together with their low price (in the order of 50$/kg) suggest their use as reinforcements in composites. In addition, nanotube based transistors have been made that operate at room temperature and that are capable of digital switching using a single electron. To this end, it is extremely important to know their behaviour in suspension. Although several studies have focused on producing polymer nanotube composites, many practical challenges remain before their potential can be fully realized. Dispersing the nanotubes individually and uniformly into the matrix seems to be fundamental in producing composites with reproducible and optimal properties.

In this work we establish a method for the numerical simulation of carbon nanotubes suspensions forming processes. We focus our attention to spin coating processes, although we believe that the tech-nique is general enough to be applied to other forming processes as well.

SPIN COATING PROCESSES

Spin coating is a procedure used to apply uniform thin films to flat substrates. In essence, an excess amount of a solution is placed on the substrate, which is then rotated at high speed in order to spread the fluid by centrifugal force, see Fig. 1. The difficulties in the numerical simulation of spin coating processes arise from the tremendous deformation of the domain, on one side (note that films of around 30 -50µm are produced after a drop of liquid) and to the multiscale nature of the problem on the other.

The numerical strategy employed is composed by two main ingredient in order to cope with these difficulties. First, meshless methods (in particular, the natural element method, NEM) were employed to avoid the remeshing efforts characteristic of FE simulations, which are linked, as is well known, with numerical diffusion on the results and subsequent loss of accuracy.

In order to cope with the second difficulty mentioned before, we have implemented a kinetic theory model to simulate the behaviour of the carbon nanotubes in suspension. This model considers the carbon nanotubes as rigid fibers and allows for the tracking of their orientation during the process.

BASICS OF THE NATURAL ELEMENT METHOD

Consider a model composed by a cloud of points N = {n 1 , n 2 , . . . , n m } ⊂ R d , for which there is a unique decomposition of the space into regions such that each point within these regions is closer to the node to which the region is associated than to any other in the cloud. This kind of space decomposition is called a Voronoi diagram (also Dirichlet tessellation) of the cloud of points and each Voronoi cell is formally defined as (see figure 2):

T I = {x ∈ R d : d(x, x I ) < d(x, x J ) ∀ J = I}, (1)
where d(•, •) is the Euclidean distance function. The dual structure of the Voronoi diagram is the Delaunay triangulation, obtained by connecting nodes that share a common (d-1)-dimensional facet. While the Voronoi structure is unique, the Delaunay triangulation is not, there being some so-called degenerate cases in which there are two or more possible Delaunay triangulations (consider, for example, the case of triangulating a square in 2D, as depicted in Fig. 2 (right)). Another way to define the Delaunay triangulation of a set of nodes is by invoking the empty circumcircle property, which means that no node of the cloud lies within the circle covering a Delaunay triangle. Two nodes sharing a facet of their Voronoi cell are called natural neighbours and hence the name of the technique.

Equivalently, the second-order Voronoi diagram of the cloud is defined as

T IJ = {x ∈ R d : d(x, x I ) < d(x, x J ) < d(x, x K ) ∀ J = I = K}. (2)
The most extended natural neighbour interpolation method is the Sibson interpolant [7] [START_REF] Sibson | A brief description of natural neighbour interpolation[END_REF]. Consider the introduction of the point x in the cloud of nodes. Due to this introduction, the Voronoi diagram will be altered, affecting the Voronoi cells of the natural neighbours of x. Sibson [START_REF] Sibson | A Vector Identity for the Dirichlet Tesselation[END_REF] defined the natural neighbour coordinates of a point x with respect to one of its neighbours I as the ratio of the cell T I that is transferred to T x when adding x to the initial cloud of points to the total volume of T x . In other words, if κ(x) and κ I (x) are the Lebesgue measures of T x and T xI respectively, the natural neighbour coordinates of x with respect to the node I is defined as

φ I (x) = κ I (x) κ(x) . ( 3
)
x 1 In Fig. 3 the shape function associated to node 1 at point x may be expressed as

φ 1 (x) = A abf e A abcd . (4)
Sibson's interpolation scheme possesses the usual reproducing properties for this class of problems, i.e., verifies the partition of unity property (constant consistency), linear consistency (and therefore are suitable for the solution of second-order PDE). Other interesting properties such as the Kronecker delta property [START_REF] Sukumar | The Natural Element Method in Solid Mechanics[END_REF] and linear interpolation on the boundary [START_REF] Cueto | Imposing essential boundary conditions in the Natural Element Method by means of density-scaled α-shapes[END_REF] are also verified by the NEM. This is especially important for problems involving friction or, in general, in which the compatibility along the boundary is important.

This kind of interpolation scheme is then used in a Galerkin framework, exactly like in the finite element method. The advantages that this method provides, if compared to the Finite Element Method, is that no lack of accuracy is obtained due to mesh distortion [START_REF] Alfaro | A study on the performance of Natural Neighbour-based Galerkin Methods[END_REF]. This allows us to employ an updated Lagrangian strategy for simulating the free surface flows arising in the problem, which notably simplifies the formulation and practical implementation of the code. For more details on the method, the interested reader can consult [START_REF] Martinez | Updated Lagrangian free surface flow simulations with Natural Neighbour Galerkin methods[END_REF].

CONSTITUTIVE MODELLING

The flow model of carbon nanotubes (CNT) considered as short fibers suspensions is defined by the following equations (see [START_REF] Martínez | Fixed mesh and meshfree techniques in the numerical simulation of injection processes involving short fiber suspensions[END_REF] and references therein)

• The balance of momentum equations, where we only consider, following [START_REF] Emslie | Flow of a viscous liquid on a rotating shell[END_REF], the centrifugal forces Divσ = -ω × (ω × r)

where σ is the stress tensor and ω the rotating speed of the machine.

• The incompressibility condition

Divv = 0 (6)
where v represents the velocity field.

• The constitutive equation, with a quadratic closure relation for the fourth order orientation tensor and other simplifying assumptions, results σ = -pI + 2µ{D + N p Tr(a D) a} [START_REF] Sibson | A Vector Identity for the Dirichlet Tesselation[END_REF] where p denotes the pressure, I the unit tensor, µ the equivalent suspension viscosity, D the strain rate tensor, N p a scalar parameter depending on both the tube concentration and its aspect ratio, and a the second order orientation tensor defined by

a = ρ ⊗ ρ Ψ(ρ) dρ ( 8
)
where ρ is the unit vector defining the CNT axis direction, and Ψ(ρ) is the orientation distribution function.

From a physical point of view, we can consider that the eigenvalues of the second order orientation tensor (a) represent the probability of finding the CNT in the direction of the corresponding eigenvectors.

• With a quadratic closure relation the orientation equation is expressed as

da dt = Ω a -a Ω + + k (D a + a D -2 Tr(a D) a) (9)
D and Ω are the symmetric and skewsymmetric components of Gradv, k is a constant that depends on the nanotube aspect ratio r (fiber length to fiber diameter ratio): k = (r 2 -1)/(r 2 + 1).

This model is solved on the domain defined by the nodes as they evolve. More details on a similar formulations can be found at [START_REF] Martínez | Fixed mesh and meshfree techniques in the numerical simulation of injection processes involving short fiber suspensions[END_REF] and references therein.

NUMERICAL RESULTS

The before presented model was applied to the simulation of spinning a drop of CNT suspension, with initial Gaussian geometry. The model was composed of 977 nodes under axisymmetric assumptions for the flow (but not for the orientation field, assumed 3-d). The results on the orientation field for the carbon nanotubes are shown in Fig. 4. Bottom: rθ plane).

CONCLUSIONS

A model has been presented for the numerical simulation of spin coating of carbon nanotubes suspensions. The model is composed of a meshless (natural element) strategy for the flow that allows for a proper description of the free-surface flow and a micro-macro description of the nanotube scale that allows for a suitable description of their orientation field. Other possibilities, such as the kinetic description derived from the Fokker-Planck equation or its equivalent stochastic (Itô) counterpart could also be applied in this same framework. They constitute our current effort of research.

Figure 1 :

 1 Figure 1: An example of a spinning machine (Cf.wikipedia.org)

Figure 2 :

 2 Figure 2: Delaunay triangulation and Voronoi diagram of a cloud of points.

Figure 3 :

 3 Figure 3: Definition of the Natural Neighbour coordinates of a point x.

Figure 4 :

 4 Figure 4: Orientation field for the CNT suspension at an intermediate step of the simulation (top: rz orientation field.Bottom: rθ plane).


Keywords: Damage Detection, Image Processing, Texture Analysis, Grey Level Co-occurrence Matrix (GLCM), k-means Clustering, Bridge Management Systems (BMS). 1

This paper presents a texture analysis based approach for the detection of damaged regions on the surface of infrastructural elements. A k-means clustering algorithm was used to partition regions with similar textural properties. Four texture measures were derived from a Grey Level Cooccurrence Matrix (GLCM) namely; contrast, homogeneity, entropy and Angular Second Moment (ASM). The approach is validated successfully on an image of a damaged concrete bridge beam. The performance of this Non-Destructive Testing (NDT) technique is evaluated for various values of k through the use of performance points in the Receiver Operating Characteristic (ROC) space. The technique may be deployed as a Structural Health Monitoring (SHM) tool to track the extent of surface damage, and can used in a Bridge Management System (BMS) to aid structured decision making and scheduling of repair work.

INTRODUCTION

Bridges may be subjected to numerous forms of damage during their service life. The damage may include cracking, corrosion of reinforcement bars, leaching, rust spotting, spalling, honeycombing, collision damage, efflorescence, wear etc. [1].With this in mind, regular inspections of the integrity of structures are vital to ensure they remain safe and fit for purpose. Currently, many structures are assessed under a regime of visual inspections of varying scope; from a cursory check for gross defects, to a close examination of all surfaces, including the use of special equipment if necessary. The quality of data collected often depends on the ability of the inspectors to observe and objectively record details of damage. The damage is usually described and archived qualitatively by the inspector, with appropriate photographs attached as evidence behind the qualitative comments. An attempt to quantify the severity of the damage is generally made at this stage through the use of a numerical scale. The scales typically range over a limited number of categories (e.g. 5 levels), leading to some degree of uncertainty and vagueness. The use of numerical scales, though helpful for relative ranking and prioritising, does not lend itself to be integrated with future quantitative analyses or experiments and repair options as this level are usually based on qualitative comments based on personal expertise. The output from visual inspections can markedly vary and can have a lower level of accuracy and repeatability of detection compared to other inspection methods [2]. An image processing based detection approach acts as a relatively inexpensive tool to facilitate maintenance management and can offer a greater reproducible and measurable performance over visual inspection techniques [3]. Image processing based techniques have received significant attention in many other fields. However, they are yet to be explored to their full potential in the area of Structural Health Monitoring (SHM).

Image based analysis is a form of Non-destructive testing (NDT), which can provide useful information on the state of the structure [4]. This in turn may be fed into a Bridge Management System (BMS). The output from the BMS can help in the planning of long-term repair strategies and enable informed decisions to be made when prioritising resources towards the correction of deficiencies. Furthermore, information acquired from NDT techniques increase understanding of defect initiation and propagation and provide a solid foundation for improving ageing laws for real structures or for updating existing models to predict the behaviour of a particular structure and thus achieve a more reliable and suitable management strategy. This aspect has attracted a growing interest in recent years as the importance of life cycle optimisation and the related financial benefits continue to be recognised [5,6]. An important aspect of managing a bridge is having a means to determine the current health of bridge elements based on past inspection data. An image processing approach caters for this as captured images can be archived for assessment of degradation over time, thereby enabling the rate of propagation of damage to be estimated. Image processing techniques are particularly relevant to bridge monitoring as there are typically large sections that are largely inaccessible to close-up visual inspections and other NDT techniques. From an image processing perspective, the images can be acquired from a relatively far distance from the surface under consideration thereby minimising road user delay costs, minimising inspection time and cost related to access equipment, improving safety aspects of the inspection process, and keeping the structure in operation. There exists a broad range of NDT techniques used to asses structural integrity such as ultrasonic scanning [7], acoustic emission techniques and eddy current testing [8]. The most suitable choice of NDT for a given application will largely depend on the damage to be detected and will require an in-depth knowledge of the advantages and limitations associated with each option. The measure of the on-site performance of a NDT tool is still an 92208 44322 Nantes Cedex 3, France email: obyrnemj@tcd.ie, bghosh@tcd.ie, v.pakrashi@ucc.ie, franck.schoefs@univ-nantes.fr pertinent question in many cases [9]. Image processing based techniques, in conjunction with powerful detection algorithms, can be considered as an accessible, inexpensive, and easily deployable technique for visual inspection. The primary limitations of this approach are the lack of penetration below the surface of the material and the requirement of good visibility and lighting conditions. Previous image processing based methods have relied on colour information [10,[START_REF] Tarighat | Fuzzy concrete bridge deck condition rating method for practical bridge management system[END_REF], textural information [12], or a combination of the two (Wu and Tsai, 2006) to segment and extract regions of interest in images.

Texture and colour based segmentation approaches are the primary modes of segmentation employed for image analysis. While both approaches have important applications in image processing methods, the colour based methods have been researched to a much greater extent. Texture may be considered as an innate property of surfaces. It may be qualified by terms such as fine, coarse, smooth, rippled, molled, irregular, or lineated [13]. Texture segmentation finds particular relevance in cases where the regions of interest are more separable from the background based on their texture than colour. There are numerous texture based image segmentation techniques. Such techniques include wavelet analysis [14], Laws' texture energy [15] and Grey Level Cooccurrence Matrix (GLCM) [16]. This paper presents an enhanced texture based detection technique involving GLCM. GLCM is a well established texture analysis method and offers a highly accurate approach for quantifying the perceived texture in an image. k-means clustering is subsequently used to partition regions of similar texture features together. GLCM had been used previously in conjunction with k-means classification on magnetic resonance images [17], however their algorithm used a different set of statistics. It is felt that the four statistics used in the proposed technique provide a well-rounded description of the texture in the image whilst offsetting unnecessary computational time that would result from the inclusion of additional statistics that would only contribute to a minimal increase in accuracy of detection.

The methodology of the proposed technique is detailed in the following section. The technique is applied to an image of a concrete bridge beam featuring cracking to concrete and exposed reinforcement. The successful application of the method is presented and the performance of the technique is evaluated.

METHODOLOGY

A semi-automatic image based damage detection algorithm is proposed in this paper. The algorithm involves two steps; the first step is using a GLCM to develop to a texture characteristics map of an image of a damaged surface. The image is in a greyscale form which is represented by a single numerical array, or plane, that is populated by pixel intensity values. Typical ranges for intensity values are 0 to 255, or 0 to 1. Black is represented by 0 in both cases while white is denoted by 255 and 1 respectively. Values within this range represent intermediate shades of grey. The second step in the algorithm is to partition the damaged regions in the image using k-means clustering. These two steps are discussed in detail in the following subsections.

Texture Characteristics Map

A texture characteristics feature vector {v f } a,b has to be generated for each pixel within the original image, I, where f indicates the index of the vector element, while a and b indicate the spatial coordinates of a pixel. The GLCM is a matrix of frequency values that combinations of pixel intensities appear in some specific spatial arrangement within an image or sub-image. In this paper, the GLCM is generated for a sub-image that is attained through a sliding window, SW, of size N-pixel x N-pixel with centre positioned at (a,b) at any stage of the convolution throughout the overall image. There are four texture features calculated from the GLCM, namely: homogeneity, contrast, entropy and Angular Second Moment (ASM). Some of these features relate to certain texture characteristics in the image such as homogeneity or contrast. Other features describe aspects such as image complexity or the transition of pixel intensity values. However, in spite of each of the aforementioned features containing some degree of information about the texture characteristics of the image, it is difficult to establish which textural trait is represented by each feature.

Each entry in the GLCM corresponds to the number of occurrences of a pair of grey levels (i,j,d,θ) in the sliding window, where i denotes the grey level in the reference pixel, j denotes the grey level in the destination pixel, d is the interpixel distance and θ is the angle of offset between neighbouring pixels. Both i and j can take integer values between 1 and G, where G is the total number of grey levels. The grey levels are defined on a scale of 1 -12 instead of a typical scale of 1 -255. Quantisizing in this manner promotes computational parsimony and avoids sparse matrices. Pixel combinations that are close together tend to be more relevant than pixel combinations that are far away from each other in terms of interpixel distances. With this in mind, a value of 1 was chosen as the interpixel distance (i.e. only combinations of pixels which shared a corner or had a shared edge were counted). This allowed for an algorithm that considered a significant amount of useful information whilst minimising complexity and computing time. Four angles for the offset were chosen: θ = 0°, θ = 45°, θ = 90°, θ = 135°. The GLCM is calculated for each of the four offsets for each position of the sliding window. The GLCM is populated as per equation 1.

N N u v x y P i j d A N SW u v i SW u d v d j A θ = = = =   + + = =    ∑ ∑ (1) (2)
where d x and d y are the horizontal and vertical offsets between neighbouring pixels in the sliding window which are dependent on d and θ, and SW(u,v) gives the quantized pixel intensity value at the spatial coordinates u and v in the window.

An important prerequisite to the process of generating statistics from the GLCM is to normalise the matrix which is achieved through: ( ,,,) ( ,,, )

P i j d p i j d R θ θ = (3)
where R represents the total number of grey level pairs (i,j) for a given (d, θ) pair within the window. This normalised GLCM was used to calculate four values for each of the four texture measures corresponding to the four offset angles. As it is not known which angle of offset provides the most meaningful value for each texture measure, the average of the four texture measures was calculated and assigned to the texture measure in question, as per equation 4. (4)

The following features were determined from the GLCM:

1. Homogeneity gives a measure of the similarity in the image.

i-j n j i p n Hom

{ }

∑ ∑ = = = G i G j j i p ASM 1 1 2 ) , ( (8)
ASM ranges from 1/G 2 to 1. A value of 1 indicates a constant image.

k-means Clustering

The k-means clustering algorithm partitions N observations into k clusters in which each observation belongs to the cluster with the nearest cluster centre by iteratively minimizing the squared sum of a computed norm from each observation to its cluster centre, over all clusters. The result is a set of clusters that are as compact and well-separated as possible.

For a Euclidean norm, the overall objective function, J is minimized as

2 1 1 ∑ ∑ = = - = k j N l c l c A A J (9) where 2 ĉ l A A -
is the distance measure between a data point A l and the cluster centre A ĉ , is an indicator of the distance of the N ĉ data points from their respective cluster centres. An optimum value of k can generally be attained by considering the level of detail or precision required. For a higher k value, there will be a stronger correlation between pixels within each cluster. This is advantageous if one wishes to reduce the rate of misclassification. An ROC based optimization framework is explored in Section 3, where different k values are tested in an attempt to determine which produces the best outcome.

A schematic of the methodology is presented in Figure 1.

Figure 1. Flow chart of the proposed methodology.

EVALUATION OF TECHNIQUE

The proposed technique was performed on an image of exposed reinforcement on an outer bridge beam (Figure 2). The DR and the MCR provide the coordinates for a point in the ROC space, which allows for a graphical illustration of the performance of the technique. A convenient way of ranking and analysing the performance of points in the ROC space is by means of the alpha-delta method [20,21]. Essentially, this method relies on calculating the angle, α, and the Euclidean distance, δ, between the best performance point (coordinates (0,100%)) and the considered point to give a measure of the performance of the considered point. For this situation only the delta, δ, parameter is required. A low value for δ is indicative of a strong performing technique. The detection and misclassification rates, along with the δ value, are summarized in Table 1 and the corresponding coordinate points are shown in the ROC space in Figure 5. A fitted curve is also shown for illustration purposes. The proposed technique performed well at defining the outer shape and size of the damaged region. However, as the value of k is increased, the detected regions become less homogenous with a greater prominence of undetected regions contained within the greater damaged area. It may be noted from the Figure 5 that when k is equal to either 3 or 4, a high performance level is achieved. The value of 3 for k is slightly better as evident from the lower value of δ. There is a relatively low detection rate in the case when k is equal to 5, while the converse is true for when k is equal to 2, i.e. there is a relatively high misclassification rate. As a result, relatively large values of δ accompany both of these cases.

A significant proportion of the misclassification rate may be attributed to the small spurious regions that are frequently included in the cluster corresponding to the damaged region. A simple way of reducing the misclassification rate without any significant reduction in the detection rate would be to apply an additional algorithm that removes these isolated regions that are below a certain area.

The result from performing k-means clustering directly on the colour image to group regions with similar pixel intensity values is graphically illustrated in Figure 6. It may be observed that this approach produced extremely poor results, so much so that it is not even apparent which cluster predominantly corresponds to the damaged region. This comparison highlights the usefulness of texture analysis on images featuring damaged regions that are more separable based on their textural characteristics rather than colour information. In this case the image was partitioned into 3 clusters; however other values of k performed to a similar level.

CONCLUSION

A texture based image processing technique to detect damage on the surface of bridge elements has been proposed. Although popular in other fields, image processing techniques have received little attention in the field of Structural Health Monitoring (SHM). Their potential as a tool that could be employed in a Building Management System (BMS) has been outlined. As a case study, the proposed technique was successfully applied to an image of a damaged concrete bridge beam. The statistics derived from the Grey Level Cooccurrence Matrix (GLCM) were found to be effective at describing the perceived texture in the image, while the kmeans clustering demonstrated a strong ability at grouping texture features corresponding to damaged regions for a range of k values. The ROC space was employed as a tool to evaluate the performance of the technique and as a means to obtain an optimum value of the k parameter to maximise the detection accuracy of the algorithm.

e

  Hom ranges from 0 to G-1. A value of 0 indicates a strong similarity in the image.2. Contrast is a measure of the local variations present in an image. If there is a high amount of variation the contrast will be high.Con ranges from 0 to (G-1) 2 . A value of 0 indicates a constant image.3. Entropy is a statistical measure of randomness. ranges from 0 to infinity.4. Angular Second Moment (ASM)represents the uniformity of distribution of grey level in the image.

Figure 2 .

 2 Figure 2. Sample Image of a Damaged Bridge Beam.

Figure 3 .

 3 Figure 3. Detected Regions for Various Values of k. The performance of the texture analysis based detection in conjunction with the k-means clustering for various values of k is evaluated by plotting performance points in the Receiver Operating Characteristic (ROC) space. The ROC space provides a common and convenient tool for graphically characterising the performance of NDT techniques and its usage has recently been extended to image detection [18]]. A box counting approach similar to the procedure described in [19] was employed to calculate the Detection Rate (DR) and Misclassification Rate (MCR) for each image. This involved visually segmenting the images and comparing them with the k-means clustered images.

Figure 4 .

 4 Figure 4. Visually Identified Damaged Region.

Figure 6 .

 6 Figure 6. Image Clustered Based on the Pixel Intensity Values

Texture Analysis based Detection and Classification of Surface Features on Ageing Infrastructure Elements

	Michael O'Byrne 1 , Bidisha Ghosh 2 , Vikram Pakrashi 3 , Franck Schoefs 4
	1,2 Trinity College Dublin, Department of Civil, Structural and Environmental Engineering, Dublin 1, Ireland
	3 University College Cork, Department of Civil and Environmental Engineering, College Road, Cork, Ireland
	4 LUNAM Université, Université de Nantes-Ecole Centrale de Nantes-CNRS, GeM, Institute for Research in Civil and
	Mechanical Engineering, UMR 6183& IXEAD/CAPACITES Scociety, University of Nantes 2, rue de la Houssinière BP

Table 1 -

 1 Performance of the Proposed Technique.

	k-clusters	DR	MCR	δ
	k = 2	96.55%	28.12%	0.283
	k = 3	88.61%	15.80%	0.195
	k = 4	85.43%	14.11%	0.203
	k = 5	72.00%	12.12%	0.305

Figure 5. Performance Points in the ROC Space for the Proposed Technique.

ACKNOWLEDGMENTS

The authors wish to thank the Irish Research Council for Science, Engineering and Technology (IRCSET) for providing a grant to support this research and CAPACITES/IXEAD society for the practical and financial assistance.