Sahar Ghannay

Antoine Caubrière

Yannick Estève

Nathalie Camelin

Edwin Simonnet

Antoine Laurent

Emmanuel Morin

End-to-end named entity and semantic concept extraction from speech

Keywords: End-to-end approach, Named entity recognition, Spoken language understanding, Automatic speech recognition, Deep learning

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Named entities are sequences of words that bring basic predefined semantic information that usually refers to locations, persons, organization. . . that can be denoted by proper nouns or that are unique in the real world, and they usually include numeric and temporal values. Named entities often constitute the first semantic bricks to extract in order to construct a structured semantic representation of a document content.

This work was supported by the French ANR Agency through the CHIST-ERA M2CR project, under the contract number ANR-15-CHR2-0006-01, and by the RFI Atlanstic2020 RAPACE project. In addition, authors would like to sincerely thank Sean Naren to make his implementation of Deep Speech 2 available, as well as the contributors to the NeuroNLP2 project.

Named entity recognition (NER) is among SLU tasks that usually extract semantic information from textual documents. Until now, NER from speech is made through a pipeline process that consists in processing first an automatic speech recognition (ASR) on the audio and then processing a NER on the ASR outputs. Such approach has some disadvantages.

For instance, ASR errors have a negative impact on the NER performances, introducing noise within the text to be processed [START_REF] Hatmi | Named entity recognition in speech transcripts following an extended taxonomy[END_REF]. Rule-based NER systems are usually built to process written language and are not robust to ASR errors. Machine learning based systems do not have good performance when they are trained on perfect transcriptions and deployed to process ASR ones, even if that can be partially compensated by simulating ASR errors in textual training data [START_REF] Simonnet | Simulating ASR errors for training SLU systems[END_REF]. Additionally, ASR systems are generally tuned in order to get the lowest word error rate on a validation corpus, but this metric is not optimal to the NER task. For instance, this metric does not distinguish between errors on verbs or proper nouns while such errors do not have the same impact for NER.

To compensate this problem, some dedicated metrics to tune ASR systems for better NER performances have been proposed, such as in [START_REF] Ameur | Investigating the effect of ASR tuning on named entity recognition[END_REF]. Another inconvenience is that usually no information about named entities are used in the ASR process, while such information could help to better choose the partial recognition hypotheses that are dropped away during the decoding process. As a consequence, even when confusion networks or word lattices are used to go beyond the 1best ASR hypothesis for a better robustness to ASR errors [START_REF] Hakkani-Tür | Beyond ASR 1-best: Using word confusion networks in spoken language understanding[END_REF], such search space have been pruned without taking into account knowledge on named entity.

In the past, an integrated approach built on a high coupling of ASR and NER modules has been proposed [START_REF] Servan | Conceptual decoding from word lattices: application to the spoken dialogue corpus media[END_REF], based on the finite-state machine (FSM) paradigm (i.e. transducer composition), showing that such integration can offer significant improvements in terms of NER quality. The main limit of this approach concerns the FSM paradigm itself, that is not able to natively model long distant constraint without combinatory explosion and that, by nature, can only express dependencies through a regular grammar. Another proposition to inject information about named entities in the ASR consists in directly adding some expressions of named entities into the ASR vocabulary [START_REF] Hatmi | Incorporating named entity recognition into the speech transcription process[END_REF], and to estimate a language model for speech recognition that take into account these named entity expressions. The main default of a such approach is that it cannot allow to detect named entity that were not injected in the ASR vocabulary.

All of these issues motivate our research work on neural end-to-end approach to extract named entities from speech. On a such way, a joint optimization is able for both ASR and NER in a NER task perspective, the architecture is more compact than the ones used in usual pipeline, and we expect to take benefit of the deep neural architecture capacities to capture long distant constraint at the sentence level. Very recently, a similar approach has been proposed by Facebook on a paper posted on the arXiv.org website [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF]. This end-toend approach is dedicated to domain and intent classification tasks, and experiments were carried on internal data close to the spirit of the ATIS corpus, as expressed by the authors. As an extension of our study on named entity recognition, we also applied the proposed approach to semantic concept extraction.

In this paper, we present a first study of an end-to-end approach to extract named entities. Our neural architecture is very similar to the Deep Speech 2 neural ASR system proposed by Baidu in [START_REF] Amodei | Deep speech 2: End-to-end speech recognition in English and Mandarin[END_REF]. To use it for named entity recognition, we apply a multi-task training and modify the sequence of characters to be recognized from speech. Experiments were carried on French data easily accessible, and so reproducible, that were distributed in the framework on evaluation campaigns and are still available. They constitute all the available data of speech with manual annotations on named entity for French.

In the last part of this paper, we explore the use of the proposed approach to process a slot filling task, that is very close to the named entity recognition task. This SLU task consists in detecting and extracting semantic concepts in speech, in the framework of a human/machine spoken dialog dedicated to hotel booking. This paper is structured as follows. Section 2 describes the neural ASR architecture we used. Section 3 explains how we propose to exploit a such neural architecture for named entity extraction from speech. Section 4 presents some propositions to optimize the system and also compensate the lack of manually annotated audio data. Section 5 presents our experimental results on NER, and last section 6 present some preliminary results on the slot filling task before the conclusion.

MODEL ARCHITECTURE

The RNN architecture used in this study is similar to the Deep Speech 2 neural ASR system proposed by Baidu in [START_REF] Amodei | Deep speech 2: End-to-end speech recognition in English and Mandarin[END_REF]. This architecture is composed of nc convolution layers (CNN), followed by nr uni or bidirectional recurrent layers, a lookahead convolution layer [START_REF] Wang | Lookahead convolution layer for unidirectional recurrent neural networks[END_REF], and one fully connected layer just before the softmax layer, as shown in Figure 1. The system is trained end-to-end using the CTC loss function [START_REF] Graves | Connectionist temporal classifi-cation: labelling unsegmented sequence data with recurrent neural networks[END_REF], in order to predict a sequence of characters from the input audio. In our experiments we used two CNN layers and six bidirectional recurrent layers with batch normalization as mentioned in [START_REF] Amodei | Deep speech 2: End-to-end speech recognition in English and Mandarin[END_REF].

Given an utterance x i and label y i sampled from a training set X = (x 1 , y 1 ), (x 2 , y 2 ), ..., the RNN architecture has to train to convert an input sequence x i into a final transcription y i s. For notational convenience, we drop the superscripts and use x to denote a chosen utterance and y the corresponding label. The RNN takes as input an utterance x represented by a sequence of log-spectrograms of power normalized audio clips, calculated on 20ms windows. As output, all the characters l of a language alphabet may be emitted, in addition to the space character used to segment character sequences into word sequences (space denotes word boundaries). The RNN makes a prediction p(l t |x) at each output time step t.

At test time, the CTC model is coupled with a language model trained on a big textual corpus. A specialized beam search CTC decoder [START_REF] Awni Y Hannun | First-pass large vocabulary continuous speech recognition using bi-directional recurrent DNNs[END_REF] is used to find the transcription y that maximizes:

Q(y) = log(p(l t |x)) + αlog(pLM (y)) + βwc(y) (1)
where wc(y) is the number of words in the transcription y.

The weight α controls the relative contributions of the language model and the CTC network. The weight β controls the number of words in the transcription.

NAMED ENTITY EXTRACTION PROCESS

In the literature, many studies focus on named entity recognition from text. State-of-the-art systems are based on neural networks architectures. Some of them rely heavily on handcrafted features and domain-specific knowledge [START_REF] Collobert | Natural language processing (almost) from scratch[END_REF][START_REF] Chiu | Named entity recognition with bidirectional LSTM-CNNs[END_REF].

Recent approaches [START_REF] Lample | Neural architectures for named entity recognition[END_REF][START_REF] Ma | End-to-end sequence labeling via bi-directional LSTM-CNNs-CRF[END_REF] takes benefits from both word and/or character-level embeddings learned automatically, by using combination of bidirectional LSTM, CNN and CRF. However, named entities recognition from automatic transcriptions is less studied. This task is made through a pipeline process that consists in processing first an automatic speech recognition (ASR) on the audio and then processing a NER on the ASR outputs [START_REF] Raymond | Robust tree-structured named entities recognition from speech[END_REF]. Usually, the named entity recognition task is to assign a named entity tag to every word in a sentence. A single named entity could concern several words within a sentence. For this reason, the word-level labels begin-inside-outside (BIO) encoding [START_REF] Ramshaw | Text chunking using transformation-based learning[END_REF] is very often adopted.

In this preliminary study, we focus on named entity extraction from speech using the network described above, without changing the neural architecture. We would like to evaluate if this neural architecture is able to capture high level semantic information that allow it to recognize named entities.

For that, we propose to modify the character sequence that the neural network has to produce: information about named entities are added in the initial character sequence. Instead of applying a BIO approach, we propose to add some tag characters in this sequence to delimit named entities boundaries, but also their category. We are interested to eight NE categories that are: person, function, organization, location, production, amount, time and event.

In our experiments, the system will attribute a starting tag or an ending one only before and after the named entities, the other words are not concerned. To distinguish the named entity category, we consider a starting tag for each NE category. Only one ending tag is used for all the NE categories, considering that since there is no overlap between named entities in a such representation, this information is sufficient to delimit the end of a named entity.

According to the eight named entity categories targeted by the task, nine NE tags has to be added to the character list emitted by the neural network: "< pers", "< f unc", "< org", "< loc", "< prod", "< amount", "< time", "< event", and " > . A such neural model predicts a character at each time step: in our experiments, each NE tag is considered as one single special character. With this way, the NE tags are included in the prediction process, and are taken into account by the CTC loss function during the training process.

MULTI-TASK TRAINING, DATA AUGMENTATION, AND STARRED MODE

Audio recordings with both manual transcriptions and manual annotations of named entities are relatively rare, while neural end-to-end approaches are known to need large amount of data to become competitive.

To compensate this lack of data, we first propose to apply a multi-task learning approach to train the neural network. This consists in starting to train it only for the ASR task, without emitting character used to represent named entities, on all the audio recordings available with their manual transcriptions. At the end, the softmax layer is reinitialized to take into consideration the named entity tag markers, and a new training process is realized, on the named entity recognition task, with only training data with manual annotations of named entities.

A second proposition consists in artificially increasing the training data for the named entity recognition task. For this purpose, we propose to apply a named entity recognition system dedicated to text data in order to tag the manual transcriptions used to train the ASR neural network. Then, these manual transcriptions automatically annotated with named entities can be injected in the training data used to train the neural network to extract named entities from speech.

In addition, since we want the system to focus on named entities, and since the CTC loss gives the same importance to each character, we propose to modify the character sequence that the neural network must emit to give more importance to named entities. This proposition is interesting to better understand how the CTC loss behaves on this case, and consists in replacing by a star "*" all character subsequences that do not contain a named entity. For instance, the character sequence presented in Figure 2 becomes: * < pers césar > * < time hier > * < loc paris > * < amount soixante dix sept ans >. We call this approach the starred mode, and we expect that it can make the neural model more sensitive to named entities.

EXPERIMENTS

Experimental setups

Experiments have been carried out on four different French corpora, including ESTER 1&2, ETAPE and Quaero. These corpora are composed of data recorded from francophone radio and TV stations, and are annotated with named entities. They are all the publicly available data of speech with manual annotations on named entities for French language. The ESTER corpora were divided into three parts: training, development and evaluation. ESTER 1 [START_REF] Galliano | The ESTER phase II evaluation campaign for the rich transcription of French broadcast news[END_REF] training (73 hours) and development (17 hours) corpora are composed of data recorded from four radio stations in French. ESTER 1 test corpus is composed of 10 hours coming from the same four radio stations plus two other stations, all of which recorded 15 month after the development data. ESTER 2 [START_REF] Galliano | The ESTER 2 evaluation campaign for the rich transcription of French radio broadcasts[END_REF] training corpus was not annotated with named entities and was not used in this study. The development (17 hours) and test set (10 hours) is composed of manual transcriptions of speech recorded from six radio stations (two of those radio stations were already used in ESTER 1). The ETAPE [START_REF] Gravier | The ETAPE corpus for the evaluation of speechbased TV content processing in the French language[END_REF] The performance of our approach is evaluated in terms of precision (P), recall(R) and F-measure for named entity detection, the named entity/value detection and the accuracy of the value detection when the named entities tags are correctly detected. These evaluations are made with the help of the sclite 1 tool.

Multi-task training

For multi-task training, we first train the E2E architecture only for ASR task, without emitting character used to represent named entities. The system is trained on all the audio recordings available with their manual transcriptions around 297.7 hours of training set, including the data described above. It composed of two convolution layers and six BLSTM layers with batch normalization, the number of epochs was set to 35. This system achieves 20.70% word error rate (WER) and 8.01% character error rate (CER) on the development corpus (30.2 hours) and 19.95% of WER and 7.68% of CER on the test set (40.8 hours). These results were obtained by applying a CTC beam search decoding coupled with a trigram language model. Once this system is trained, the softmax layer is reinitialized to take into consideration the named entity tag markers, and a new training process is realized, on the named entity recognition task, with only training data with manual annotations of named entities. In addition, for the training of both E2E and ASR systems, each training audio samples is randomly perturbed in gain and tempo for each iteration.

1 http://www.icsi.berkeley.edu/Speech/docs/sctk-1.2/sclite.htm

Experimental results

We present in this section some experimental results. Table 1 shows the performances of the end-to-end model (E2E) to detect EN categories (among the eight ones). That means that in this evaluation we do not take care of values associated to the detected EN. The starred mode is also experimented and is called (E2E*) in the table: this mode provides better results in this task than the normal mode. Last, we would like to compare these results to the ones obtained by a pipeline process, that consists in applying a text named entity recognition on the automatic transcripts produced by the end-to-end ASR system trained on the first step of the multi-task learning presented above.

The text named entity recognition system used for this experiment is based on the combination of bi-directional LSTM (BLSTM), CNN and CRF modules [START_REF] Ma | End-to-end sequence labeling via bi-directional LSTM-CNNs-CRF[END_REF], and takes benefits from both word and character-level embeddings learned auto-matically during the training process. For this experiment, we used the NeuroNLP2 implementation 2 . Convolutional neural network encodes character-level information of a word into its character-level embedding. Then the character-and wordlevel embeddings are fed into the BLSTM to model context information of each word. On top of BLSTM, the sequential CRF is used to jointly decode labels for the whole sentence. In addition, this system can be enriched with syntactic information like part of speech tagging (POS). In our experiment, NeuroNLP2 is used as a NER system and Deep Speech 2 as the ASR system. Both are trained on the experimental corpus described in section 5.1. Automatic transcriptions of development and test data have been annotated with NER system. To measure the impact of POS, we used the MACAON system [START_REF] Nasr | Macaon: An NLP tool suite for processing word lattices[END_REF] to tag the experimental corpus on manual and automatic transcriptions. To feed NeuroNLP2, one-hot vectors represent POS information. Word embeddings, character representations and one-hot concatenations feed the BLSTM layer. As we can see in Tables 3, the pipeline process is a little bit less competitive than the end-to-end model to recognize EN category, while it is more efficient to extract EN values. Results also confirms that linguistic information like POS is really important for the NER task. Such observation will help for future work on the continuity of this study. As described in section 4, we applied NeuroNLP2 (the version using POS tagging) on the manual transcriptions of the ASR training data in order to augment the amount of "NER from speech" training data. In this experiment, the normal and starred modes were used. Table 4 shows the improvement got by the end-to-end system when training on these imperfect augmented data using the normal (E2E+) and the starred (E2E+*) modes. As we can see, the use of the augmented data was helpful for the starred mode.

EXTENSION TO SLOT FILLING TASKS

In order to deeper explore this end-to-end approach, we also carried on some experiments on a SLU task. In this context, semantic representation consists classically in the use of frames describing general concepts and their specific instances. A frame is composed by a data structure which represents a predefined concept by associating to the concept [START_REF] Hahn | Comparing stochastic approaches to spoken language understanding in multiple languages[END_REF]. We consider this task very close to the named entity recognition task explored above. By applying the same end-to-end approaches presented in the previous sections, we would like to check if the starred mode is still interesting, and also explore the impact of multitask learning in a scenario on which we own training data dedicated to two different applicative tasks.

Experimental corpora

For these experiments, we focus on two French corpora dedicated to semantic extraction from speech in a context of human/machine dialogues. The main target is the MEDIA corpus, that is dedicated to hotel booking [START_REF] Bonneau-Maynard | Semantic annotation of the French MEDIA dialog corpus[END_REF]. The other one is the PORT-MEDIA corpus, dedicated to reservation of theater tickets [START_REF] Lefevre | Leveraging study of robustness and portability of spoken language understanding systems across languages and domains: the PORTMEDIA corpora[END_REF]. Both are composed of telephone conversations, and where collected through a wizard of Oz approach, in which a human plays the role of the machine.

The MEDIA corpus is composed of 1257 dialogues. It is split into three subparts: a training corpus containing 17.7k sentences, a development corpus containing 1.3k sentences, and a test corpus of 3,5k sentences. 76 semantic tags have to be recognized (e.g. "number of room", "hotel name", "localization", "month (date)", "room equipment",.... The PORT-MEDIA corpus contains 10.4k sentences, and uses 35 semantic tags, very close to tags existing in MEDIA. For both MEDIA and PORTMEDIA corpora we removed short speech segments inferior to 1 second, excluding short answers like 'yes' or 'no' usually easy to detect.

Since training data for speech recognition on telephone conditions are more rare than for broadcast news, all the data used to pre-training an end-to-end ASR system were converted into telephone format. We also used the MEDIA training data and the PORT-MEDIA training data for the ASR pre-training. Last, we injected data from the DECODA corpus [START_REF] Bechet | DECODA: a call-centre human-human spoken conversation corpus[END_REF], a corpus of human/human conversations from the Parisian public transportation call-center: this corresponds to around 74h of audio signal with manual transcriptions.

In order to try to take benefits from the PORTMEDIA data, we used them in a SLU pre-training step, that uses words and semantic tags as outputs, just after the ASR pre-training that uses only words as outputs. Figure 3 illustrates this training process. In a contrastive experiment, we also skipped the SLU pre-training step (dashed line). All the results given in the next section were reached without beam search applied on the neural outputs: only the greedy mode was used. 3. Training steps to build an end-to-end SLU system dedicated to the MEDIA data.

Results

Concept error rate is a metric very commonly used in previous paper on SLU, especially when using the MEDIA corpus [START_REF] Servan | Conceptual decoding from word lattices: application to the spoken dialogue corpus media[END_REF][START_REF] Hahn | Comparing stochastic approaches to spoken language understanding in multiple languages[END_REF][START_REF] Vukotic | Is it time to switch to word embedding and recurrent neural networks for spoken language understanding?[END_REF]: for this reason, we used this metric in our experiments.

Table 5 shows that the use of data from a different applicative domain (buying theater tickets instead of booking hotel rooms) seems really useful: on the test MEDIA corpus, the CER decreases of 4% (29.3 to 28.1) when the PORTMEDIA data are used in a SLU pre-training step. Table 6 shows the impact of the starred mode that is again more efficient than the normal mode, since the CER continues to decrease from 28.1% to 27.0% on the MEDIA test set.

Last, table 7 allows us to compare the end-to-end approach to a pipeline approach, as we did for named entity recognition. The end-to-end ASR system made during the first step described in figure 3 reaches a word error rate of 20.4% on the MEDIA test data. The Pip-SLU system consists in applying on these automatic transcriptions a neural encoder-decoder architecture with attention mechanism (NEDAM) trained to recognize semantic concepts. This SLU architecture has been presented in [START_REF] Simonnet | Exploring the use of attention-based recurrent neural networks for spoken language understanding[END_REF] and more details are given in [START_REF] Simonnet | ASR error management for improving spoken language understanding[END_REF]. We observe that the end-to-end SLU approach, in normal mode and trained without using additional semantic training data from PORTMEDIA, reached better results than the Pip-SLU system. And, as seen before, using both SLU pre-training with additional data and starred mode still decreases the CER, for a global reduction of 15% (32.0 to 27.0). This paper presents a first study about end-to-end named entity and semantic concept extraction from speech. By integrating in the character sequence emitted by a CTC end-toend speech recognition system some special characters to delimit and categorize named entities or semantic concepts, we showed that such extraction is feasible. To compensate the lack of training data, we propose a multi-task learning approach (ASR + NER or ASR + SLU), in addition to an artificial data augmentation of the training corpus with automatic annotation for named entities, or to a transfer learning applied on semantic data coming from another domain for semantic concept extraction. A starred mode is also proposed to make the neural network more focused on named entities or semantic concepts. Experimental results show that this end-toend approach in starred mode with training augmentation provides better results than a pipeline approach for both named entity and semantic concept extractions. On the other side, we observed that performances of this end-to-end approach to extract named entity values are worse than the ones got by the pipeline process. As a conclusion, this study presents promising results in a first attempt to experiment an end-toend approach to extract named entities and semantic concepts.

It constitutes an interesting start point for future work that could help to improve its performances, or that could study intermediate representations within the neural architecture in order to better understand how the neural network handles the semantic level of speech.

Fig. 1 .

 1 Fig. 1. Deep RNN architecture used to extract named entities from French speech.

Fig. 2 .

 2 Fig. 2. Example of mapping the real NE tags to character sequence. This sentence means, in English and case sensitive: "the sculptor Caesar died yesterday in Paris at the age of seventy-seven years"

  2 https://github.com/XuezheMax/NeuroNLP2

  Fig.3. Training steps to build an end-to-end SLU system dedicated to the MEDIA data.

Table 1 .

 1 Named entity category detection results for E2E and E2E* (starred mode) systems Table2evaluates the quality of the category/value pairs that have been recognized. While precision and recall do not have the same behavior between normal and starred mode, both modes gets the same F-measure value.

	System Corpus Precision Recall F-measure
	E2E	dev	0.85	0.57	0.68
	E2E	test	0.83	0.52	0.64
	E2E*	dev	0.75	0.65	0.71
	E2E*	test	0.82	0.57	0.67

Table 2 .

 2 Named

		entity category+value pair detection results
	for E2E and E2E* systems
	System Corpus Precision Recall F-measure
	E2E	dev	0.64	0.45	0.53
	E2E	test	0.55	0.36	0.44
	E2E*	dev	0.57	0.47	0.52
	E2E*	test	0.47	0.38	0.42

Table 3 .

 3 NER results for the pipeline approach (Pip) on the test data. When POS are used to tag ASR outputs before NER processing, the system is called Pip+POS

	System	Detection Precision Recall F-measure
	Pip	category	0.75	0.56	0.64
	Pip+POS category	0.74	0.58	0.65
	Pip	cat+value	0.58	0.43	0.49
	Pip+POS cat+value	0.57	0.45	0.50

Table 4 .

 4 NER results on the test data for the E2E system trained with imperfect augmented data (E2E+) in comparison to the E2E system trained with imperfect augmented data and the starred mode (E2E+*)

	System Detection Precision Recall F-measure
	E2E+	category	0.82	0.57	0.67
	E2E+* category	0.76	0.63	0.69
	E2E+	cat+value	0.55	0.40	0.46
	E2E+* cat+value	0.49	0.41	0.47
	name a set of roles: these roles are represented by slots. In
	this framework, SLU corresponds to a slot filling task and,
	classically, this task can be defined as a concept tagging pro-
	cess, which is the extraction of a sequence of concepts out of
	a given word sequence

Table 5 .

 5 Comparison of semantic concept detection results for E2E systems on the test MEDIA corpus according to the use of not of the PORT-MEDIA corpus before fine-tuning on the MEDIA training data. Results are evaluated with the concept error rate (CER) metric.

	System	CER (%)
	E2E without PORTMEDIA	29.3
	E2E pretrained (SLU) with PORTMEDIA	28.1

Table 6 .

 6 Semantic concept detection results for E2E and E2E* systems on the test MEDIA corpus. In both condition, the PORT-MEDIA corpus was used during the SLU pretraining

	System CER (%)
	E2E	28.1
	E2E*	27.0

Table 7 .

 7 Comparison of semantic concept detection results for E2E systems and a pipeline of neural system (ASR + SLU) on the test MEDIA corpus

	System	CER (%)
	Pip-SLU	32.0
	E2E without PORTMEDIA	29.3
	E2E* pretrained (SLU) with PORTMEDIA	27.0
	7. CONCLUSION


A Maurel-Pantel

M Lamberti

M L Raffa

C Suarez

F Ascione

F Lebon

Modelling of a GFRP adhesive connection by an imperfect soft interface model with initial damage

Keywords: Adhesive bonding, Imperfect interface model, GFRP connection, CT-scan, Damage, Porosity 2019 MSC: 00-01, 74S05, 74k30, 74R10

In this paper a methodology to model a GFRP adhesive connections by using an imperfect soft interface model is presented. The model based on Kachanov's theory considered a cracked thin adhesive. Within this framework, the mechanical properties and the initial damage (diffuse initial cracks) of the adhesive layer has been experimentally evaluated. With a modified Arcan system, static tests were performed on adhesively bonded assemblies in tensile and shear solicitation mode considering three different adhesive thicknesses. The experimental results highlighted how the thickness of adhesive influences the mechanical strength and stiffness of the bonded connection. CT-scans were performed to measure the porosity rate in the adhesive layer. Furthermore, the excellent comparison of numerical and experimental data of an adhesive GFRP bonded connections allow us to consider the imperfect soft interface model proposed as highly competitive to evaluate complex structure performance in civil engineering context.

A parametric analysis has been proposed to provide a formula able to describe the full response of the structure at varying adhesive property.

Introduction

During the last decade, the applications in the field of civil engineering of composite structures made of FRP (Fibre Reinforced Polymers) involving adhesives are grew exponentially due to the ability to tailor its structural performance, high axial resistance, high resistance to aggressive environment [START_REF] Correia | GFRP pultruded profiles in civil engineering: hybrid solutions, bonded connections and fire behaviour[END_REF][START_REF] Liao | Effects of environmental aging on the properties of pultruded GFRP[END_REF][START_REF] Cabral-Fonseca | Artificial accelerated ageing of GFRP pultruded profiles made of polyester and vinylester resins: characterisation of physical-chemical and mechanical damage[END_REF], considerably lightweight when compared to conventional materials, and quick installation time.

One of the most promising application is the realization of a beam-to-column connection by using structural adhesives that is becoming a valid alternative to the classical bolted connection. From nineties [START_REF] Mosallam | Performance of pultruded FRP connections under static and dynamic loads[END_REF] [START_REF] Bank | Design and performance of connections for pultruded frame structures[END_REF][6] [START_REF] Smith | An experimental study of the behavior of connections for pultruded GFRP I-beams and rectangular tubes[END_REF][8] [START_REF] Mottram | Further tests on beam-to-column connections for pultruded frames: Web-cleated[END_REF][10] to nowadays [START_REF] Qureshi | Behaviour of pultruded beam-to-column joints using steel web cleats[END_REF] [START_REF] Qureshi | Response of beam-to-column web cleated joints for FRP pultruded members[END_REF][13] [START_REF] Lamberti | Influence of web/flange reinforcement on the GFRP bonded beams mechanical response: A comparison with experimental results and a numerical prediction[END_REF] beam-to-column connections were bolted and composed of I profiles based on the experience from steel applications. One of the principal drawback of these kind of connections is the bearing failure that limits the strength and stiffness.

On the contrary, in bonded connections due to the absence of holes, stresses are more uniformly distributed over the bonded surfaces. Indeed, the lack of holes avoid the presence of stress concentration, damage to the fibers and reduce the risk of moisture penetration in members. Moreover, adhesively bonded joints offer many advantages for the design of structures. But to improve the confidence that currently limits the use of this technology, several authors try to develop experimental [START_REF] Chataigner | Use of a single lap shear test to characterize composite-to-concrete or compositeto-steel bonded interfaces[END_REF][16] [START_REF] Jumel | Measurement of interface cohesive stresses and strains evolutions with combined mixed mode crack propagation test and backface strain monitoring measurements[END_REF] or numerical [START_REF] Freddi | An interphase model for the analysis of the masonry-FRP bond[END_REF][19] [START_REF] Maurel-Pantel | A cohesive zone model for fracture initiation and propagation of fused silica direct bonding interface[END_REF] approaches.

Recently, several experimental and numerical investigations were performed by some authors [START_REF] Ascione | Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections[END_REF] [START_REF] Ascione | Pseudoductile failure of adhesively joined GFRP beam-column connections: An experimental and numerical investigation[END_REF] [START_REF] Razaqpur | GFRP hollow column to built-up beam adhesive connection: Mechanical behaviour under quasi-static, cyclic and fatigue loading[END_REF] to assess strength and stiffness of GFRP adhesive connection showing that their overall performance can match or overcome the performance of similar bolted connections in FRP structures. In the above mentioned papers the role of GFRP geometry was investigated varying the profiles adopted. In details, in [START_REF] Ascione | Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections[END_REF][22] I-profiles (Fig. 1(a)) were used for the beam and the column while in [START_REF] Razaqpur | GFRP hollow column to built-up beam adhesive connection: Mechanical behaviour under quasi-static, cyclic and fatigue loading[END_REF], a square tube was used for the column and U-profiles for the beam (built-up) as depicted in Fig. 1(b). The first type of connection (I-profiles) presented similar strength respect to the analogous bolted connections while the last one showed an increase in terms of strength and stiffness equal to 45%. If the overall mechanical response was deeply investigated, the role of adhesive layer was not sufficiently studied. In particular, its thickness and its mechanical properties have to be deeply investigated in view of a further improvement of the mechanical response of such a bonded connection as well as for proposing design formulas.

The present paper proposes a methodology to model a GFRP adhesive connection in a complex structure by using an imperfect soft interface model (in the sense of [START_REF] Benveniste | Imperfect soft and stiff interfaces in twodimensional elasticity[END_REF] [START_REF] Hashin | Thermoelastic properties of fiber composites with imperfect interface[END_REF]) previously presented in [START_REF] Bonetti | A model of imperfect interface with damage[END_REF]. In a first section a summary of previous experimental results obtained on a GFRP beam to column connection is proposed. Then in a second section the imperfect interface model is described. This model is derived by an asymptotic analysis [START_REF] Lebon | Asymptotic behavior of a hard thin linear elastic interphase: an energy approach[END_REF] on a micro cracked adhesive based on Kachanov assumptions [START_REF] Tsukrov | Effective moduli of an anisotropic material with elliptical holes of arbitrary orientational distribution[END_REF][29] successfully applied to composites materials [START_REF] Raffa | Derivation of a model of imperfect interface with finite strains and damage by asymptotic techniques: an application to masonry structures[END_REF][START_REF] Rekik | Homogenization methods for interface modeling in damaged masonry[END_REF][START_REF] Orefice | Experimental/numerical study on the interfacial damage of bonded joints for fibre-reinforced polymer profiles at service conditions[END_REF]. The Kachanov theory consists to consider in a micro cracked adhesive the following main assumptions: a non interaction between the crack, a constant stress vector along the crack, and to ignore the effect of the crack edge in the stress field. The choice of this model was done thanks to the possibility to take into account some bonding variabilities such as thickness variation, porosity, and initial damage. In a third section, experimental investigations are proposed in terms of adhesive stiffness and initial damage evaluation. Based on aforementioned experimental results, the interface model is enhanced. Finally the model is implemented in a finite element software and its validation is proposed comparing numerical results with those obtained experimentally [START_REF] Ascione | Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections[END_REF].

GFRP Beam-to-column adhesive connection: experimental tests on complex structure

Some of the authors have experimentally investigated in a previous research program [START_REF] Ascione | Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections[END_REF] the behavior of full-scale bolt-free GFRP beam-to-column connection under static load. Both the beam and the column had I-profile with dimensions of 200x100x10 mm. Four beam-to-column connection prototypes were tested varying the position of the connection respect to the column height and the strengthening system adopted. In all cases, the beam flanges and web were bonded to the column compression flange by 50x50x6 mm seat angles. The connections which mechanical behavior is here numerically investigated are depicted in Fig. 2. They have been originally designated as BTCJ fc and BTCJ fcr where BTCJ stands for Beam-to-Column Junction, fc for flange connection, the letter r for reinforced, respectively. More in detail, as shown in Fig. 2(b), the strengthening system (to avoid premature failure of the column) consisted of pultruded GFRP strips (170x45x10 mm) and an angle at the column web/flange connection. The column can be considered fixed at the bottom with its unsup- ported length being 650 mm. To support the column at its bottom, it has been inserted inside a 350 mm high stiff steel jacket welded to a thick steel plate that was bolted to the testing machine platen (Fig. 2). The beam was loaded monotonically in displacement control at a rate of 1 mm.min -1 by a servo-controlled universal testing machine. The beam and column assembly was load by a point load applied near the free end of the beam at 450 mm from the beam-column flange connected to the beam (Fig. 2). The experimental results are reported in Fig. 3 in terms of Load-beam vertical deflection. The latter is relative to the same cross-section where the load is applied. The connection exhibited basically a linear response up to failure. The un-strengthened connection reached a maximum applied load of 15.4 kN, while the strengthened one failed at about 23 kN. It must be pointed out that the deflection values in Fig. 3 represent the deflection of the beam as a cantilever plus the deflection caused by the column end rotation, the local deformation of the column web and the joint rotation.

All the graphs exhibit nonlinearity at low load levels, followed by a linear part and again ending with a nonlinear segment. The initial nonlinearity is the result of the specimen initial seating and not a characteristic of the connection.

Imperfect interface model

The proposed imperfect interface model coupling unilateral contact and damage is obtained via homogenization techniques and by an asymptotic approach within the small perturbations framework [START_REF] Lebon | Asymptotic behavior of a hard thin linear elastic interphase: an energy approach[END_REF][START_REF] Rekik | Homogenization methods for interface modeling in damaged masonry[END_REF]. The damaging behavior is modeled using the approach introduced in [START_REF] Bonetti | A model of imperfect interface with damage[END_REF][START_REF] Raffa | Derivation of a model of imperfect interface with finite strains and damage by asymptotic techniques: an application to masonry structures[END_REF][START_REF] Orefice | Experimental/numerical study on the interfacial damage of bonded joints for fibre-reinforced polymer profiles at service conditions[END_REF]: the thin glue interphase sandwiched between the two GFRP structures is assumed to be a microcracked material undergoing a degradation process. Each step of the proposed modeling strategy, sketched in Fig. 5, is described below.

Step 1: The real microstructure of the glue comprises various microcracks families with randomly distributed lengths and orientations. Within the non-interacting approximation [START_REF] Sevostianov | On some controversial issues in effective field approaches to the problem of the overall elastic properties[END_REF] framework only one family of parallel microcracks which is representative of the macroscale behavior of the glue has been chosen denoting the equivalent length of microcracks family as l. Furthermore, the cracks orientation has been assumed parallel to the bonding plate.

Step 2: The effective mechanical properties of the idealized microcracked material of Step 1 are obtained through a Kachanov-type homogenization technique [START_REF] Tsukrov | Effective moduli of an anisotropic material with elliptical holes of arbitrary orientational distribution[END_REF][START_REF] Sevostianov | On some controversial issues in effective field approaches to the problem of the overall elastic properties[END_REF] properties depend on the microcracks density ρ, which 3D form is ρ = l 3 V ,

V being the volume of the representative elementary domain. In section 4, it will be shown that l can be experimentally characterized. As an example, the Young's modulus in the normal-to-bonding plane direction

E N is equal to E 0 1 + Cρ
where E 0 is the Young's modulus of the undamaged material and C is given by 16

(1 -ν 2 0 ) 3
, where ν 0 is the Poisson ratio of the undamaged material. Note that the cracks density ρ can evolve thus it is representative of a damage parameter. An evolution law is introduced on l (or equivalently on ρ). To this purpose, the variation in time of l can be associated to a pseudo-potential of dissipation φ that is given by the sum of a quadratic term (rate-dependent) and a positively 1-homogeneous functional (rate-independent) [START_REF] Bonetti | A model of imperfect interface with damage[END_REF]. The pseudo-potential of dissipation reads as:

φ( l) = 1 2 η l2 + I ]0,∞[ ( l)
where η is a positive viscosity parameter (which depends on the thickness of the glue) and I B denotes the indicator function of a set B, i.e. I B = 0 if x ∈ B and I B = ∞ otherwise. The term I ]0,∞[ forces the crack length to assume non-negative values (i.e. the crack length can only increases) and renders the irreversible character of the degradation process of the glue. In addition, the damage begins only if the elastic work is greater that a given value ω (which depends on the thickness of the glue) [START_REF] Bonetti | A model of imperfect interface with damage[END_REF]. It is established that a Kachanov-type material is a soft material, i.e. the stiffness of the glue is of the same order as its thickness [START_REF] Raffa | Normal and tangential stiffnesses of rough surfaces in contact via an imperfect interface model[END_REF]. However, to impose unilateral contact (non-penetration condition) in the asymptotic expansions (Step 4), the glue is considered as a soft material only in traction (see first line of Equation ( 1)).

Step 3: The homogenized material defined in step 2 is used to model a thin glue interphase of thickness ε. This interphase is sandwiched between two GFRP layers (denoted also adherents). We make the assumption that the bonding between the interphase and the adherents is perfect (i.e. continuity in interface separation and stress vector).

Step 4: Using matching asymptotic expansions [START_REF] Lebon | Asymptotic behavior of a hard thin linear elastic interphase: an energy approach[END_REF], the small parameter being the thickness of the glue, it is obtained at the limit that the interphase volume of the glue is replaced by an interface S of normal unit n (see fig. 5). More precisely, it is obtained a relationship across the surface S between the two adherents linking the stress vector σn and the interface separation [u]:

         σn = K(l) [u] + + τ n on S τ [u] .n = 0, τ ≤ 0, [u] .n ≥ 0 on S η l = ω -1 2 K ,l (l) [u] + . [u] + + on S (1)
where (), l denotes the partial derivative in l, ()

+ is the positive part of a function, [u] + = [u] if [u] .n ≥ 0, [u] + = [u] -[u] .n if [u]
.n ≤ 0. The parameter η (resp. ω) is the limit of η ε (resp. ω ε). Finally, as classically, K is the stiffness of the interface (the ratio between the stiffness of the glue and its thickness). Further details on asymptotic expansions, can be found in [START_REF] Lebon | Asymptotic behavior of a hard thin linear elastic interphase: an energy approach[END_REF].

The interface constitutive law obtained in Equation ( 1) is a spring-like nonlinear interface model with a nonlinear evolution (i.e. damage) as related in Fig. 5.

Note that the stiffness K keeps in memory the mechanical features of the original interphase (geometry, mechanical properties and damage). The adhesive used in experimental investigation [START_REF] Ascione | Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections[END_REF] was the Sikadur-30 produced by Sika [START_REF]SikaDur30[END_REF]. Such an adhesive is a 2-components thixotropic structural adhesive, a mixture of epoxy resin and special fillers, designed to bond at temperatures between 8 manufacturers. [START_REF]SikaDur30[END_REF] in Fig. 6. It is composed of Aluminum 2017 whose mechanical properties are summarized in the table 2. The aluminium samples are manufactured in such a way as to maintain a constant total height of the glued specimen equal to 64 mm. The total height includes the height of two half aluminum samples and the thickness of the adhesive joint as depicted in Fig. 6. The samples are designed with a straight edge in order to have a homogeneous stress field at the interface in considering absence of defects.

Adhesive experimental characterization

Static tests based on Arcan device

Static tests are performed using the modified Arcan device [START_REF] Cognard | Development of an improved adhesive test method for composite assembly design[END_REF]. This device permits to apply to adhesively bonded assembly different types of load. It is composed of two half discs with several attachment points along the perimeter.

These attachment points allow setting up the device on a standard tensile testing machine. For the present investigation, the Arcan system was adapted to use cylindrical specimens. The positioning and the holding of the test sample are carried out using flanges. These flanges fix the sample with screws uniformly distributed on its periphery, which prevents the adhesive from being preloaded (Fig. 7). To keep a good stiffness gap, the half-discs are made of 40CMD8S Steel and the flanges of 7075 Aluminium. The static tests were carried out on a tensile test machine, an electromechanical Instron testing system (Fig. 8). The Arcan device is connected to the machine with a ball joint that guarantees isostatism and alignment of the applied force. The tests were performed at a quasi-static speed of 0.5 mm.min -1 . The load is measured with a sensor with a capacity of 50 kN .

Bonding protocol

Three different adhesive joint thicknesses, noted t a , have been tested: 1, 5, and 10 mm. For each test configuration, a minimum of five samples are tested to obtain an admissible statistic. In order to ensure the effectiveness of the bonding and to decrease dispersion, the aluminium surfaces was cleaned with acetone. To position the aluminium half samples and the adhesive, a mounting was designed as depicted in Fig. 9. It allows to respect the coaxiality between the two aluminium half samples and has the advantage of being able to bond five samples at the same time. The half samples are placed on a lower base.

The adhesive is applied to the bonding surfaces. The other half samples are placed on the upper base. The half samples are flanged in order to be attached to the base to facilitate positioning on other half samples. A guidance system allows the upper base to be positioned on the lower base and the half samples to Then, it is necessary to wait for the polymerization of the adhesive which lasts 7 days at room temperature.

Tensile tests

In Fig. 11, three of the total four graphs depict the stress-displacement curves 195 obtained for a tensile loading for the three different adhesive thicknesses. In details, on the vertical axis the tensile stress and on the horizontal axis the normal displacement of the test machine are reported. For each test, the fracture was cohesive (i.e it means that the fracture occurred exclusively in the adhesive and not at the interface). The mechanical behaviour of the adhesive was linear with a brittle behaviour. In the test presented here, the contribution of the aluminum substrate to the measured stiffness is neglected, because the Young's modulus of the adhesive is 8 times lower than the modulus of the aluminum substrate. Results reported in Table 3 show that there is no dispersion on normal stiffness K exp N and normal critical stress at rupture σ c N over our five tests (the maximal coefficient of variation is less than 8.5%). It should be noted that the normal stiffness K exp N and the normal critical stress at fracture σ c N decrease as a function of adhesive thickness. In the forth graph of Fig. 11, the stiffness of the interface has been plotted as a function of the thickness of the adhesive, and it can be seen that the stiffness decreases quasi-linearly as a function of the thickness. The critical stress values are higher than those provided by the manufacturer, probably because we bond at an intermediate temperature (24 • C) with extreme thickness values. Indeed, the manufacturer advises to use 3 mm and not to exceed 5 mm in thickness on vertical surfaces in order to avoid the collapse of the adhesive during the gluing process. In civil engineering context, one of the main difficulties is to control adhesive thickness (low thickness and low variability) for very large bonded surfaces.

Thickness K exp N K exp N σ c N σ c

Shear tests

Similary to the case of tension test, in Fig. 12 three of the total four graphs depict the stress-displacement curves obtained for a shear loading for the three different adhesive thicknesses. In details, on the vertical axis the shear stress and on the horizontal axis the displacement of the test machine are reported.

For each test, the fracture was both cohesive and adhesive, these particular fracture surfaces observed are due to two successive shear phases: a pure shear phase followed by a mixed mode phase after the initiation of local fracture.

As in tensile, the shear mechanical behaviour of the adhesive is linear with a brittle behaviour. Results reported in Table 4 show that tangential stiffness K exp T and tangential critical stresses at fracture σ c T over our five tests (the maximal coefficient of variation is less than 5%). As previously, the critical stress values are globally higher than those provided by the manufacturer. For 10 mm thickness, a smaller value is observed probably due to the limitation Globally, the same trends in tensile and in shear has been obtained.

CT-scan of the joint

The imperfect interface model assumes the description of initial damage by Kachanov's theory. For which the effect of a given number of diffuse cracks can be considered as the effect of a single large crack to describe the loss of bonding stiffness as a function of the initial cracking rate. In this section, the decrease of bonding stiffness is expressed as a function of thickness based on Thickness called Imorph [36][37]. This software allows to perform segmentation between pores and adhesive, in order to construct the boundary surfaces of the two phases and calculate a porosity rate ρ in the volume of the joint V . In Fig. 14 the 3D reconstruction of pores obtained with the software is presented for the 1 mm adhesive joint. The number of pores seems very diffuse and quite important visually, the software is then able to quantify the volume of each phase. The values of the porosity rates calculated for the three thicknesses are reported in Table 5. The analogy with the Kachanov model allows us to correlate an initial damage length l 0 characteristic of the overall porosity volume l 3 0 (i.e. the sum of each porosity is equivalent to a single porosity of length l 0 ).

K exp T K exp T σ c T σ c

Thickness

Volume Porosity Volume Initial t a of the joint rate of porosity Damage Length (mm)

V (mm 3 ) ρ = l 3 0 V (%) l 3 0 (mm 3 ) l 0 (

Discussion on the model assumptions

Results of the experimental investigations allowed us to give an insight on the imperfect interface model proposed in section 3. Indeed, static tensile and shear tests showed that the normal and tangential stiffnesses of the interface decrease with the increase of the adhesive thickness as in Eq.1. 3D CT-scans demonstrates the possibility to correlate the decrease in stiffness with a porosity rate which can be considered as an initial damage. This parameter can be correlated to an initial damage length l 0 by analogy with Kachanov's theory. Table 5 describes a quasi-linear relation between the thickness and the initial damage length l 0 and Fig. 15 describes a quasi-linear relation between the stiffness and l 0 . The following expression can be proposed:

   K N = f (thickness) = f (l 0 ) K T = f (thickness) = f (l 0 ) (2)
In the imperfect interface model, the adhesive is characterized by an initial damage l(t = 0) = l 0 . The value l 0 depends on the adhesive thickness used and the quality of bonding of the beam-to-column connection. On experimental results obtained with monotonic mechanical tests carried out on the beam-tocolumn connections described in Fig. 3 and in static tests related in Fig. 11 and in Fig. 4, a brittle mechanical behavior of bonded connections is observed. It means that no significant damage evolution is observed in Sikadur30 adhesive. Thus, the connections is modeled with l = 0 in Eq.1. This initial value is identified experimentally for the elementary samples and identified by inverse method for the GFRP adhesive connection.

Finite element simulations

The imperfect model presented in section 3, is implemented in the commercial finite element software COMSOL Multiphysics. In particular, both experimental tests on specimens for evaluating adhesive properties and on beamto-column full scale specimens are simulated. Finally, comparisons between numerical and experimental investigation are performed. 2. The interface model which mechanical properties are collected in Table 2 provides the connection between the two substrates and describes the behaviour of the adhesive by integrating the effect of the adhesive thickness. The mesh of the specimen is described in Fig. 16.

After a mesh sensitivity study lead on the elastic response of the interface, the model includes 10,000 3D tetraedric elements, a finer mesh size (minimal 0.1 mm) is used at the interface. Boundary conditions correspond to experimental tests: the specimen is embedded on the plane surface noted A in Fig. 16 anda displacement along the vertical axis is imposed on the plane surface noted B.

The numerical normal and tangential stiffnesses have been identified by comparison with experimental global response (see Fig. 11 and Fig. 4). The numerical stiffnesses identified are reported in Table 6. The maximal relative standard deviation on the normal stiffness is 1.24% and on the tangential stiffness is 6.21%.

It is important to note that the differences between the experimental values and those identified numerically are very small confirming the assessment of the previous section.

Thickness K num N K exp N K num T K exp T (mm) (N.mm -3 ) RSD (%) (N.mm -3 ) RSD (%) 1

Application of the model to GFRP beam-to-column connections

In order to validate the imperfect interface model and its efficiency to model a GFRP adhesive connection. Both complex structures of GFRP beam-to-column connection, depicted in Fig. 2, are simulated using finite elements method. The GFRP panels are considered transversally isotropic which material parameters are reported in Table 7. The behaviour of the adhesive is described with the imperfect interface model where the adhesive stiffness depends of the damage variable l 0 as checked with the experimental analyses. The imperfect interface model framework presented in section 3, is applied at our parallelepipedic rectangular bonding thin interphase where L 1 is its large side, L 2 is its small side, and ε is its thickness. The homogenization of the adhesive and the asymptotic approach (from step 2 to step 4) lead to the following expression for the tangential and normal stiffness for a rectangular bonding interface [START_REF] Raffa | Derivation of a model of imperfect interface with finite strains and damage by asymptotic techniques: an application to masonry structures[END_REF][38]:

   K N = f (l 0 ) = 3E T L1L2 16l 3 0 (1-ν 2 ) K T = f (l 0 ) = 3E T L1L2(2-ν) 32l 3 0 (1-ν 2 ) (3)
where E T is the tensile Young modulus of the adhesive as related in Table 305 1 and ν is the Poisson ratio. The adhesive thickness is constant and equal to 1 mm, thus, the value of l 3 0 is constant for all interface zones considered. This parameter has to be identified by inverse method for these specific GFRP adhesive connections. The mesh of the GFRP structure is described in Fig. 17 The model includes 126,000 3D tetraedric elements, the mesh is refined at the 310 bonding interface. The boundary conditions correspond to the test conditions: the column is fixed at bottom and a displacement is imposed in the same cross section where the load was applied during experiments. In Fig. 18 the deformed structure and the von Mises stress field from the simulation results are reported for the reinforced BTCJ fcr. It should be noted that numerical simulation gives a good prediction of the GFRP beam-to-column connections (see Fig. 19). The l 3 0 value identified by inverse method is equal to 0.028 mm 3 . The good agreement underline the capacity of the imperfect interface model to model this complex structures. Using this model, we are able to propose formulas to design and verify bonded connections. For instance, the results summarized in Fig. 20

Conclusions

The mechanical properties of a structural adhesive available on the market has been experimentally evaluated by means of modified Arcan device. A monotonic load was applied on the adhesive bonded assembly. The results obtained by experimental tests have permitted to model a GFRP adhesive connection of a complex structures by using an imperfect soft interface model previously presented by some of the authors. The results of the study support the following conclusions:

1) The thickness of adhesive layers influences significantly interface mechanical properties. In particular in reducing the thickness from 10 to 1 mm, it is possible to obtain an increase of 25% and 8% in terms of normal strength and stiffness, and an increment of 57% and 19% in terms of tangential strength and stiffness. Furthermore, the adhesive presents a brittle mechanical behavior and an initial damage (i.e an initial porosity rate in Kachanov's theory) depending of the geometry, the thickness of the joint and the bonded GFRP structure considered.

2) Results of the experimental investigations on elementary samples allowed us to give an insight on the imperfect interface model. The CT-scan demonstrated that is possible to correlate the decrease in stiffness with a porosity rate or initial damage. This parameter being correlated to an initial damage length l 0 by analogy with Kachanov theory. Numerical results of elementary tests are in very good agreement with experimental ones.

3) The results of imperfect interface model are in very good agreement with the experimental results of a bonded GFRP connection previously tested by the authors. The imperfect interface model is considered as an useful instrument to study the performance of GFRP adhesive connection in civil engineering context.

4) A parametric analysis have been undertaken in order to define a new formula able to describe the nonlinear response of the bonded connection in terms of vertical deflection at varying of adhesive property.

After the first encouraging results, the next goal for the authors will be the investigation of the influence of adhesive mechanical properties on cyclic behaviour with particular attention on damage evolution. It will be possible in the future to reactivate the l parameter in order to describe the mechanical response of these connections to cyclic solicitations (loads/unloads) or connections with different geometries. [START_REF] Razaqpur | GFRP hollow column to built-up beam adhesive connection: Mechanical behaviour under quasi-static, cyclic and fatigue loading[END_REF]

Figure 1 :

 1 Figure 1: Homogeneous clamping device for the test samples

Figure 2 :

 2 Figure 2: Details of the beam-to-column connections tested: (a) BTCj fc, (b) BTCj fcr.

Figure 3 :

 3 Figure 3: GFRP beam column experimental tests: Load-beam tip deflection.

Figure 4 :

 4 Figure 4: Imperfect interface modeling methodology

Figure 5 :

 5 Figure 5: Interface constitutive law of the imperfect interface model proposed in Equation (1) for different values of η. (a) normal stress component and (b) two tangential stress components.

145 4 . 1 .

 41 Adhesive and Substrate

Figure 6 :

 6 Figure 6: Cylindrical samples used for the mechanical tests.

Figure 7 :

 7 Figure 7: Homogeneous clamping device for the test samples.

Figure 8 :

 8 Figure 8: Arcan fixture is mounted in the Instron tensile machine.

Figure 9 :

 9 Figure 9: Mounting of samples to check the coaxiality and thickness of the adhesive joint.

Figure 10 :

 10 Figure 10: Two examples of bonded specimens.

Figure 11 :

 11 Figure 11: Experimental tensile tests results: Stress-displacement curves obtained for each thickness considered and Evolution of normal stiffness in function of the adhesive thickness. Numerical results of simulation of tensile tests with our imperfect interface model implemented in a finite element software.

Figure 12 :

 12 Figure 12: Experimental shear tests results: Stress-displacement curves obtained for each thickness considered and Evolution of tangential stiffness in function of the adhesive thickness. Numerical results of simulation of shear tests with our imperfect interface model implemented in a finite element software.

Figure 13 :

 13 Figure 13: In situ 3D measurements: CT-scan Slices of adhesive joints.

Figure 14 :

 14 Figure 14: 3D reconstruction of pores obtained with Imorph software [36][37].

Figure 15 :

 15 Figure 15: Stiffness of the adhesive joint in function of the initial damage l 0 measured with analysis of CT-scan measurements.

Figure 16 :

 16 Figure 16: Mesh of the specimen tested in shear and tensile loadings.

5. 1 .

 1 Validation of the model on adhesive tests Both the tensile and shear tests on the adhesive are simulated. Aluminum substrates are modelled by an isotropic linear elastic behaviour. The material parameters are reported in Table

Figure 17 :

 17 Figure 17: Mesh of the GFRP structure : beam to column connection reinforced (BTCJ fcr).

  .

Figure 18 :

 18 Figure 18: Numerical simulation results: deformed structure and von Mises stress field.

Figure 19 :

 19 Figure 19: Comparison between numerical prediction and experimental results for both beam to column adhesive connection structures.

  allows to model the effect of the adhesive Young modulus on the vertical deflection of the GFRP beam-to-column adhesive connection BTCJ fcr under a load applied equal to 15kN. On the basis of numerical results the following formula has been proposed in order to propose a first design rule of BTCJ fcr structure: v = aE -b (4) with a = 95.68 and b = -0.64 identified on 8 different calculations with a excellent coefficient of correlation (R 2 = 0.9948). The parametric analysis is 315 able to predict the nonlinear answer of the structure in taking into account the adhesive behavior included in the imperfect interface model.

Figure 20 :

 20 Figure 20: Variation of the vertical deflection of GFRP beam to column adhesive connection BTCJ fcr in function of the Young modulus of the adhesive.

Table 1 :

 1 Properties of the epoxy adhesive (SikaDur-30) after 7 days of curing provided by

	SikaDur30		Values (MPa)	Test standards
	Young Modulus	E C	9, 600	ASTM D695
		E T	11, 200	ISO 527
	Compressive Strength σ C 70 -80 (at 15 • C) et 85 -95 (at 35 • C)	EN 196
	Tensile Strength	σ N	24 -27 (at 15 • C) et 26-31 (at 35 • C)	NF EN ISO 527-3
	Shear Strength	σ T	14 -17 (at 15 • C) et 16-19 (at 35 • C)	FIP 5.15

• and 35

•

. The curing takes place in 7 days at room temperature. The properties of the glue given by the manufacturers are collected in Table

1

. The substrates take the form of cylindrical specimens as depicted

Table 2 :

 2 Material properties of the Aluminum 2017 provided by manufacturers.

Table 3 :

 3

	N

Tensile tests results: average values and relative standard deviation (RSD) of normal stiffness and normal stress for different thickness of the adhesive.

Table 4 :

 4 Shear tests results: average values and relative standard deviation (RSD) of tangential stiffness and tangential stress for different thickness of the adhesive.

Table 5 :

 5 Analysis of CT-scan measurements on initial samples bonded: Volume of porosity in function of the thickness of the adhesive.

	mm)

Table 6 :

 6 Values and deviations from experimental values of tangential and normal stiffness for different thickness of the adhesive obtained by inverse identification based on finite element simulation of tensile and shear tests.

Table 7 :

 7 Mechanical properties of GFRP pultruded laminates provided by the manufacturer.

Acknowledgement

This project has received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 843218-ASSO (Adhesive connection for Secondary Structures in Offshore wind installations).