Sylvain Meignier

Teva Merlin

LIUM SPKDIARIZATION: AN OPEN SOURCE TOOLKIT FOR DIARIZATION

Keywords: Speaker, Diarization, Toolkit

This paper presents an open-source diarization toolkit which is mostly dedicated to speaker and developed by the LIUM. This toolkit includes hierarchical agglomerative clustering methods using well-known measures such as BIC and CLR. Two applications for which the toolkit has been used are presented: one is for broadcast news using the ESTER 2 data and the other is for telephone conversations using the MEDIA corpus.

INTRODUCTION

In the NIST terminology, the process of diarization consists in annotating temporal regions of audio recordings with labels. The labels represent names of speakers, or their gender, the channel type (narrow bandwidth vs. wide bandwidth), the background environment (quite, noise, music...), or other characteristics present in the signal.

In the case of speaker diarization, the "who spoke when" annotation is performed without any prior information: neither the number of speakers, nor the identities of the speakers, nor samples of their voices are needed. The labels representing the speakers are automatically generated without matching the real identities of the speakers. A common approach for this task consists in detecting homogeneous audio segments, which each contain the voice of only one speaker. Then the generated segments are grouped into clusters, one speaker at a time.

The main recent methods are based on hierarchical clustering. The methods differ in choices of merging distance, of the stopping criterion and of the cluster model type (either mono-Gaussian models or Gaussian Mixture Models (GMMs)). The architecture of the system is partly guided by the nature of the documents it will be used on. According the results obtained in evaluation campaigns, systems can obtain very good results over broadcast news recordings by using BIC clustering followed by a CLR-like clustering [START_REF] Barras | Multi-stage speaker diarization of broadcast news[END_REF][START_REF] Deléglise | Improvements to the LIUM French ASR system based on CMU Sphinx: what helps to significantly reduce the word error rate?[END_REF]. Systems based on HMM-BIC [START_REF] Pardo | Speaker diarization for multiple-distant-microphone meetings using several sources of information[END_REF] or T-test distance [START_REF] Hieu Nguyen | T-test distance and clustering criterion for speaker diarization[END_REF] perform better than BIC clustering over meeting recordings. Whereas E-HMM shows better performance over telephone conversations [START_REF] Meignier | Step-by-step and integrated approaches in broadcast news speaker diarization[END_REF].

Several toolkits distributed under open-source licenses are available on the web. One of the oldest is the CMU Segmentation toolkit which was released in 1997 [START_REF] Siegler | Automatic segmentation, classification and clustering of broadcast news audio[END_REF] and was developed for the NIST broadcast news evaluation campaign. AudioSeg, under the GPL license, is a toolkit developed by IRISA during the ESTER 1 campaign in 2005. It includes an audio activity detector, BIC or KL2 segmenting and clustering tools and a Viterbi decoder. Mistral Seg, under the GPL license, is dedicated to speaker diarization and relies on the ALIZ É speaker recognition library. It was the starting point for the development of LIUM SpkDiarization.

The LIUM SpkDiarization toolkit can be used in various ways, to target diverse applications.

In its default configuration, it is oriented towards speaker diarization of broadcast news. The resulting diarization is well suited for speech recognition: each segment is from a single speaker over a single channel with a length shorter than 20 seconds. This system is described in section 2.1. The LIUM transcription system based on Sphinx, used during the ESTER 2 campaign, was described in [START_REF] Deléglise | Improvements to the LIUM French ASR system based on CMU Sphinx: what helps to significantly reduce the word error rate?[END_REF].

The toolkit provides elementary tools, such as segment and cluster generators, decoder and model trainers. Fitting those elementary tools together is an easy way of developing a specific diarization system. Section 2.2 shows how to build a diarization system for telephone conversations.

Technical information on how to use the toolkit is given in section 3. Moreover, it is easy to extend the toolkit by adding algorithms. Section 4 describes the main classes and algorithms available.

APPLICATIONS

Broadcast news diarization

The proposed diarization system was inspired by the system [START_REF] Barras | Multi-stage speaker diarization of broadcast news[END_REF] which won the RT'04 fall evaluation and the ESTER 1 evaluation. It was developed during the ESTER 2 evaluation campaign for the transcription and diarization tasks, with the goal of minimizing both word error rate and speaker error rate.

Automatic transcription requires accurate segment boundaries. Although non-speech segments must be rejected in order to minimize insertion of words and to save computation time, segment boundaries have to be set within non-informative zones such as filler words. Indeed, having a word cut by a boundary disturbs the language model and increases the word error rate.

Speaker diarization needs to produce homogeneous speech segments; however, purity and coverage of the speaker clusters are the main objectives here. Errors such as having two distinct clusters (i.e., detected speakers) corresponding to the same real speaker, or conversely, merging segments of two real speakers into only one cluster, get heavier penalty in the NIST time-based evaluation metric than misplaced boundaries [START_REF]Fall 2004 rich transcription (RT-04F) evaluation plan[END_REF].

The system is composed of acoustic BIC segmentation followed with BIC hierarchical clustering. Viterbi decoding is performed to adjust the segment boundaries. Music and jingle regions are removed using GMMs, and long segments are cut to be shorter than 20 seconds. A hierarchical clustering using GMMs for speaker models is computed over the clusters generated by the Viterbi decoding.

System description

The Sphinx 4 tools are used for the computation of features from the signal. For the first three steps described below, the features are composed of 13 MFCCs with coefficient C0 as energy, and are not normalized (no CMS or warping). Different sets of features are used for further steps, similarly computed using the Sphinx tools.

Before segmenting the signal into homogeneous regions, a safety check is performed over the features. They are checked to ensure that there is no sequence of several identical features (usually resulting from a problem during the recording of the sound), for such sequences would disturb the segmentation process.

Segmentation based on BIC

A pass of distance-based segmentation detects the instantaneous change points corresponding to segment boundaries. The proposed algorithm is based on the one described in [START_REF] Siegler | Automatic segmentation, classification and clustering of broadcast news audio[END_REF]. It detects the change points through a generalized likelihood ratio (GLR), computed using Gaussians with full covariance matrices. The Gaussians are estimated over a five-second window sliding along the whole signal. A change point, i.e. a segment boundary, is present in the middle of the window when the GLR reaches a local maximum.

A second pass over the signal fuses consecutive segments of the same speaker from the start to the end of the record. The measure employs ∆BIC, using full covariance Gaussians, as defined in equation 1 below.

The well known measures for segmentation task are the KL2 [START_REF] Siegler | Automatic segmentation, classification and clustering of broadcast news audio[END_REF], the Gaussian divergence [START_REF] Barras | Multi-stage speaker diarization of broadcast news[END_REF] and ∆BIC [START_REF] Chen | Speaker, environment and channel change detection and clustering via the bayesian information criterion[END_REF]. All of them are implemented in this toolkit.

BIC Clustering

The algorithm is based upon a hierarchical agglomerative clustering. The initial set of clusters is composed of one segment per cluster. Each cluster is modeled by a Gaussian with a full covariance matrix. ∆BIC measure is employed to select the candidate clusters to group as well as to stop the merging process. The two closest clusters i and j are merged at each iteration until ∆BICi,j > 0.

∆BIC is defined in equation 1. Let |Σi|, |Σj| and |Σ| be the determinants of gaussians associated to the clusters i, j and i + j. λ is a parameter to set up. The penalty factor P (eq. 2) depends on d, the dimension of the features, as well as on ni and nj, refering to the total length of cluster i and cluster j respectively.

∆BICi,j = ni + nj 2 log |Σ|- ni 2 log |Σi|- nj 2 log |Σj|-λP (1)
P = 1 2 " d + d(d + 1) 2
« + log(ni + nj) (2)
This penalty factor only takes the length of the two candidate clusters into account whereas the standard factor uses the length of the whole data as defined in [START_REF] Chen | Speaker, environment and channel change detection and clustering via the bayesian information criterion[END_REF]. Experiments in [START_REF] Barras | Multi-stage speaker diarization of broadcast news[END_REF][START_REF] Tranter | Speaker diarisation for broadcast news[END_REF] show that better results are obtained by basing P on the length of the two candidate clusters only. However, both penalty factors are implemented in the toolkit.

Segmentation based on Viterbi decoding

A Viterbi decoding is performed to generate a new segmentation. A cluster is modeled by a HMM with only one state, represented by a GMM with 8 components (diagonal covariance). The GMM is learned by EM-ML over the segments of the cluster. The log-penalty between two HMMs is fixed experimentally.

The segment boundaries produced by the Viterbi decoding are not perfect: for example, some of them fall within words. In order to avoid this, the boundaries are adjusted by applying a set of rules defined experimentally. They are moved slightly in order to be located in low energy regions. Long segments are also cut recursively at their points of lowest energy in order to yield segments shorter than 20 seconds.

Speech detection

In order to remove music and jingle regions, a segmentation into speech / non-speech is obtained using a Viterbi decoding with 8 onestate HMMs. The eight models consist of 2 models of silence (wide and narrow band), 3 models of wide band speech (clean, over noise or over music), 1 model of narrow band speech, 1 model of jingles, and 1 model of music.

Each state is represented by a 64 diagonal GMM trained by EM-ML on ESTER 1 data. The features are 12 MFCCs completed by ∆ coefficients (coefficient C0 is removed).

Gender and bandwidth detection

Detection of gender and bandwidth is done using a GMM (with 128 diagonal components) for each of the 4 combinations of gender (male / female) and bandwidth (narrow / wide band). Each cluster is labeled according to the characteristics of the GMM which maximizes likelihood over the features of the cluster.

Each model is learned from about one hour of speech extracted from the ESTER training corpus. The features are composed of 12 MFCCs and ∆ coefficients (C0 is removed). The entire features of the recording are warped using a 3 second sliding window as proposed in [START_REF] Pelecanos | Feature Warping for robust speaker verification[END_REF], before the features of each cluster are normalized (centered and reduced).

The diarization resulting from this step fits the needs of automatic speech recognition: the segments are shorter than 20 seconds; they contain the voice of only one speaker; and bandwidth and gender are known for each segment.

The diarization system developed during the ESTER 2 evaluation campaign performs better than the one employed during the first edition of the ESTER campaign: it allowed a gain 0.8 point of word error rate when coupled with the same speech recognition system.

GMM-based speaker clustering

In the segmentation and clustering steps above, features were used unnormalized in order to preserve information on the background environment, which helps differentiating between speakers. At this point however, each cluster contains the voice of only one speaker, but several clusters can be related to the same speaker. The contribution of the background environment to the cluster models must be removed (through feature normalization), before a hierarchical agglomerative clustering is performed over the last diarization in order to obtain a one-to-one relationship between clusters and speakers.

Thanks to the greater length of the speaker clusters resulting from the BIC hierarchical clustering, more robust, complex speaker models can be used for this step. A Universal Background Model (UBM), resulting from the fusion of the four gender-and bandwidthdependent GMMs used earlier, serves as a base. The means of the UBM are adapted for each cluster to obtain the model for its speaker.

At each iteration, the two clusters that maximize a given measure are merged. The default measures are the Cross Likelihood ratio (CLR) [START_REF] Reynolds | Blind clustering of speech utterances based on speaker and language characteristics[END_REF] and the Cross Entropy (CE/NCLR) [START_REF] Solomonoff | Clustering speakers by their voices[END_REF][START_REF] Le | Speaker diarization using normalized cross-likelihood ratio[END_REF]. The GMM-KL2 measure described in [START_REF] Ben | Speaker diarization using bottom-up clustering based on a parameterderived distance between GMMs[END_REF], equivalent to the Gaussian divergence [START_REF] Barras | Multi-stage speaker diarization of broadcast news[END_REF] applied on GMMs, is also available.

The clustering stops when the measure gets higher than a threshold set a priori.

Evaluation

The methods were trained and developed according to data from the ESTER/, 1 (2003-2005) and ESTER 2 (2007-2008) evaluation campaigns. The results of the 2008 campaign are reported in [START_REF] Galliano | The ESTER 2 evaluation campaign for the rich transcription of French radio broadcasts[END_REF]. The data were recorded in French from 7 radio stations, and are divided into 3 corpora: the training corpus corresponding to more than 200 hours, the development corpus corresponding to 20 shows, and the evaluation corpus containing 26 shows.

During the evaluation, the LIUM obtained the best result: 10.80 % of Diarization Error Rate (DER) using the system described in section 2.1, completed by a post-filtering step. The post-filtering consists in removing segments longer than 4 seconds including silence, breath, and inspiration, as well as music fillers. Fillers are extracted from the first pass of the speech recognition process [START_REF] Deléglise | Improvements to the LIUM French ASR system based on CMU Sphinx: what helps to significantly reduce the word error rate?[END_REF].

The result was 11.03 % of DER without post-filtering. The default set of thresholds was determined using the ESTER 2 development corpus. Thresholds should be adapted for other corpus. Without skills in the field of speaker diarization, this task can be difficult. LIUM SpkDiarization includes an experimental tool that automatically performs the tuning by trying various sets of thresholds.

Table 2 shows the DERs obtained over the NIST RT'03 diarization corpus (3 shows of broadcast news in English) before and after tuning the thresholds. A gain of 1.3 point can be observed after tuning the thresholds.

Telephone

For the ANR project Port-Media, the LIUM needs to segment and transcribe telephonic conversations drawn from the French corpus MEDIA [START_REF] Devillers | The French ME-DIA/EVALDA project: the evaluation of the understanding capability of spoken language dialogue systems[END_REF]. This corpus contains telephonic dialogues which were recorded using a Wizard of Oz. Conversations focused on tourist information and hotel booking.

Reusing the toolkit developed for the broadcast news system allowed to quickly setup a telephonic diarization system.

System description

12 MFCCs are used, completed by the energy. The MFCCs are not normalized during the speech detection step whereas the cepstral mean is removed during the speaker detection step.

Speech detection

This detection relies on a Viterbi decoding using 3 GMMs corresponding to speech, silence, and dial tone. Each GMM is composed of 16 Gaussians with diagonal covariance, and trained via the EM-ML algorithm over 20 recordings (1 hour of data) which were segmented automatically and controlled by a human.

Only the speech segments are kept for the next step.

Speaker detection

The speaker detection method is based on the E-HMM approach described in [START_REF] Meignier | Step-by-step and integrated approaches in broadcast news speaker diarization[END_REF].

The conversation model is based on an HMM with 2 states. Each state characterizes a cluster, i.e. speaker, and the transitions model the changes between speakers.

A UBM with 16 diagonal components is trained over 4 hours of speech automatically extracted by the speech detector.

A first speaker model is trained on all the speech data. The diarization is modeled by a one-state HMM and the speech segments are labeled as speaker S0. A second speaker model is then trained using the three seconds of speech that maximize the likelihood ratio between model S0 and the UBM. A corresponding state, labeled as S1, is added to the previous HMM.

The two speaker models are adapted according to the current diarization. Then, Viterbi decoding produces a new diarization. The adaptation and decoding steps are performed while the diarization differs between two successive runs.

Evaluation

The development corpus is composed of 9 dialogues (33 minutes) whereas the test corpus is composed of 8 dialogues (23 minutes). In the MEDIA corpus, each part of the conversation was recorded separately. In the evaluated corpus, both parts of the conversation were mixed, and provided as a single channel, 8 kHz signal.

The manual transcriptions of the dialogue are available. The boundaries of the segments were manually checked and corrected to be accurate enough for diarization evaluation.

Table 3 shows the DER obtained through development and evaluation. The system obtains 2.47 % of DER over the test corpus. This error rate is very low but the task is quite easy: there is a lot of silence among speaker utterances and there is very little speech overlap.

USING THE LIUM SPKDIARIZATION TOOLKIT

LIUM SpkDiarization is written in Java, targeting version 1.6 of the language. It requires a Sun JRE. In order to compile or execute the toolkit, the following 3rd party packages are needed:

• gnu-getopt package to manage command lines with long options. • lapack package to manage matrices (blas, f2util and lapack).

Only the inversion method based on Cholesky decomposition is used, for inversion of full covariance matrices of Gaussians. • Sphinx4 and jsapi packages to compute MFCCs.

Quick Start

For convenience, those 3rd party packages are included in the precompiled version. This version also includes a UBM, gender models, speech/non-speech models, and MFCC configuration files. The execution of the jar file directly invokes the speaker diarization method dedicated to broadcast news recordings (as described in section 2.1).

Advanced Use

Most of the tools in the package take a diarization as input and generate another diarization as output. The exceptions are model trainers, which generate a model instead of a diarization.

The main tools allow performing segmentation, silence detection, hierarchical clustering, and Viterbi decoding using GMM models trained with EM or MAP. Another set of tools helps to handle the diarization, models or features files. The typical actions applied to diarizations are: filtering, merging, splitting, printing, or extracting.

Figure 1 shows a sample script for training a UBM. The first call of the java virtual machine initializes the model. The initial model contains one gaussian learned over the training data. Iteratively, the gaussians are split and trained (up to 5 iterations of EM algorithm) until the number of components is reached. The second call trains the GMM using the EM algorithm. After 1 to 20 iterations, the algorithm stops if the gain of likelihood between 2 iterations is less than a given threshold.

#!/bin/bash show="ubm" # Input segmentation file, %s will be substituted with $show seg="./%s.seg" # Where is the mfcc, %s will be substituted with the name of the segment show fMask="./mfcc/%s.mfcc" # The MFCC vector description, here it corresponds to 12 MFCC + Energy # spro4=the mfcc was computed by SPro4 tools # 1:1:0:0:0:0: 1 = present, 0 not present. # order : static, E, delta, delta E, delta delta delta delta E # 13: total size of a feature vector in the mfcc file # 1:0:0:1 CMS by cluster fDesc="spro4,1:1:0:0:0:0,13,1:0:0:1" # The GMM used to initialize EM, %s will be substituted with $show gmmInit="./%s.init.gmms" # The output GMM, %s will be substituted with $show gmm="./%s.gmms" # Initialize the UBM, ie a GMM with 8 diagonal Gaussian components java -Xmx1024m -cp ./LIUM_SpkDiarization.jar fr.lium.spkDiarization.programs.MTrainInit --sInputMask=$seg --fInputMask=$fMask --fInputDesc=$fDesc --kind=DIAG --nbComp=8 --emInitMethod=split_all --emCtrl=1,5,0.05 --tOutputMask=$gmmInit $show # Train the UBM via EM java -Xmx1024m -cp ./LIUM_SpkDiarization.jar fr.lium.spkDiarization.programs.MTrainEM --sInputMask=$seg --fInputMask= $fMask --emCtrl=1,20,0.01 --fInputDesc=$fDesc --tInputMask=$gmmInit --tOutputMask=$gmm $show

Experimental Use

Methods currently under development are stored in a Java package named "experimental". Classes of this package may be greatly modified or removed at any time.

In version 3.5 of LIUM SpkDiarization, classes for named identification of speakers are being developed [START_REF] Jousse | Automatic named identification of speakers using diarization and ASR systems[END_REF]. Classes provide new word transcription containers including named entity annotations, Semantic Classification Tree and methods for named identification of speakers. However, this development affects other classes, so developers are incited to minimize the connections between experimental packages and stable packages.

PROGRAMMING WITH THE TOOLKIT

Containers

There are three main containers: one for show annotation, one for acoustic vectors, and one for models.

Cluster and segment containers

Segment and Cluster objects allow managing a diarization. A segment is an object defined by the name of the recording, the start time in the recording, and the duration. These three values identify a unique region of signal in a set of audio recordings.

A cluster is a container of segments, where segments are sorted first by name of recording, then by start time. A cluster should contain segments of the same nature: speakers, genders, background environments, etc.

Clusters are stored in an associative container, named Clus-terSet, where the key, corresponding to the name of the cluster, is mapped to the cluster. Therefore, each cluster name should be unique in a ClusterSet. Figure 3 shows the standard way of iterating over clusters and segments. This class design helps data processing when the methods iterate on each segment of each cluster. This access fulfills the majority of the algorithms of hierarchical classification.

No constraint exists for the relationship of a given acoustic feature to a segment. An acoustic feature can belong to any one segment or several segments. No mechanism of checking is provided, and such checking remains the responsibility of the programmer. Some situations require a temporal sequential access to the acoustic features, while for others random access is preferred, with possible access to cluster membership. Methods are provided to convert a ClusterSet into another container: a ClusterSet can be changed into a set of segments sorted first by record name, then by starting index; or into an array of segments where the index in the array corresponds to the index of an acoustic feature. This last container is available only if the ClusterSet refers to only one recording.

The toolkit uses its own diarization file format. However, diarizations can be saved to or loaded from files at the Sphinx CTL format that contains the list of utterances to decode.

Acoustic feature container

A FeatureSet stores the acoustic features, which are computed on the fly from the audio recording using Sphinx 4 classes or read from a file containing vectors of parameters. The supported file formats are Sphinx format, SPro4 format, and gzipped-text in which each line corresponds to a vector. The access to acoustic features of a Fea-tureSet is driven by the start index and end index stored in segments.

Common access to the acoustic features is illustrated in figure 3. There are two ways to access to a feature at a given index. The safe method takes two parameters: the name of the recording and the index of the acoustic feature to return. The second way activates the current recording in the FeatureSet before getting the acoustic features. The second way avoids testing for each feature access whether the current recording is the active one in the FeatureSet. Transformations can be applied before using the acoustic features. The first and second order derivatives as well as energy and its derivatives can be computed or deleted after reading the raw features. Feature distribution can be centered and/or reduced, given mean and variance vectors computed over a segment, over a cluster, over all the features of the recording, or over a sliding window. Indeed, a FeatureSet gets segments or clusters information from the ClusterSet given as a parameter when the FeatureSet instance is created. Feature warping is only suitable for sliding windows and can be combined with the previous normalization, before or after.

Section 2.1 shows that systems depend on various acoustic features. Segmentation and BIC clustering use only static and energy coefficients, speech / non-speech detection needs static and delta, and CLR clustering needed normalized static and delta, etc. Transformations reduce the number of feature sets stored on disk.

Models

Algorithms need to manage mono-Gaussian models with full or diagonal covariance or Gaussian Mixture Models (GMMs). Model classes follow the heritage graph shown in figure 4. The root class "Model" stores scores: the likelihood of the current feature, the sum and the mean of likelihoods accumulated by several invocations of the likelihood computation method. Accumulators should be initialized before use and reset by setting the accumulator to zero. In conjunction with the reset method, those storages permit to easily compute likelihood of a feature, n features, or segments.

Full and diagonal Gaussians implement an inner class to accumulate the statistics needed during an EM or MAP training. Those accumulators allow adding or removing weighted acoustic features to/from the accumulator before generating a new model. An illustration can be found in section 4.2.

Clustering

All clustering algorithms follow a bottom-up hierarchical approach (see figure 6). At initialization, the process trains the initial model of each cluster and computes the similarity measures between pairs of clusters. The process continues until the measure gets above a given threshold. According to the measures, at each iteration, the two most similar clusters are merged into a new cluster. During the merging, the model of the new cluster is trained and the similarities between this cluster and others are computed.

Decoding

A basic Viterbi decoder is available and the HMM models are based on the transformation of a set of GMMs. Each GMM is associated with an HMM. By default an HMM contains only one state but the minimum duration can be controlled by duplicating the state to form a string. HMM transition is fixed internally to 0, but the log penalties to switch between two HMMs needs to be set.

Decoding, as presented in figure 7, performs the forward pass in which statistics are accumulated. The best path across the states is defined by a diarization using the GMM name as cluster name. Aligned states are pushed as segments in the corresponding clusters. An interesting way to improve the toolkit will be implementing some missing methods. For example, methods such as [START_REF] Pardo | Speaker diarization for multiple-distant-microphone meetings using several sources of information[END_REF][START_REF] Hieu Nguyen | T-test distance and clustering criterion for speaker diarization[END_REF] are very useful to develop a system dedicated to meeting diarization.

Efforts should be done to bring the diarization toolkit closer to Sphinx 4. In particular, Sphinx 4 configuration management tools are very flexible and could be an efficient replacement for a number of scripts used with this toolkit. Moreover, the Viterbi decoder and access to acoustic features could adopt the Sphinx interface, thus helping developers to use both toolkits together.

Fig. 1 .

 1 Fig. 1. Example of script for LIUM SpkDiarization

Fig. 2 .

 2 Fig. 2. Incomplete class diagram of ClusterSet, Cluster and Segment

/Fig. 3 .

 3 Fig. 3. FeatureSet, ClusterSet, Cluster and Segment usage

Fig. 4 .

 4 Fig. 4. Incomplete class diagram of models

4. 2 .

 2 Algorithms Training During the training of a model, the features indexed in the cluster are scanned and EM statistics are stored in the accumulators of the model. After the accumulation, we estimate the model by EM or MAP using the accumulators. The same algorithm is employed for training a mono-Gaussian model and for a GMM.

  Figure 5 illustrates an iteration of the EM algorithm. // Initialize the statistic and score accumulators gmm.initStatisticAccumulator(); gmm.initScoreAccumulator(); for(Segment segment: cluster) { featureSet.setCurrentShow(segment.getShowName()); // Iterate over features of the segment for(int i = 0; i < segment.getLength(); i++) { float[] feature = featureSet.getFeature(segment.getStart()+i); // Get the likelihood of the feature (1) double lhGMM = gmm.getAndAccumulateLikelihood(feature); for (int j = 0; j < gmm.getNbOfComponents(); j++) { // Read the likelihood of component j computed in (1) double lhGaussian = gmm.getComponent(j).getLikelihood(); // Add weighted feature in the accumulator of the GMM gmm.getComponent(j).addFeature(feature, lhGaussian / lhGMM); } } } // Compute the model according to the statistics gmm.setModelFromAccululator(); // Reset the statistic and score accumulators gmm.resetStatisticAccumulator(); gmm.resetScoreAccumulator();

Fig. 5 .

 5 Fig. 5. Training a GMM from a cluster

/

  / Get an instance of the BIC clustering class BICHClustering clustering = new BICHClustering(clusterSet, featureSet, parameters); // Set the threshold double threshold = 0.0; // Initialize the clustering: train models, compute measures between clusters clustering.init(); // Get the highest measure of the two candidates for merging double measure = clustering.getScoreOfCandidatesForMerging(); while (measure > threshold) { // Merge the two candidates, \ie // clustering.getFirstCandidate() and clustering.getSecondCandidate() clustering.mergeCandidates(); // Get the highest measure of the two candidates for merging measure = clustering.getScoreOfCandidatesForMerging(); } // Get the resulting diarization return clustering.getClusterSet();

Fig. 6 .

 6 Fig. 6. Using a clustering algorithm

Fig. 7 .

 7 Fig. 7. Viterbi decoding5. CONCLUSIONThis paper presents a diarization toolkit mostly dedicated to speaker. Developed by the LIUM, this toolkit is published under the GPL license. When used for broadcast news diarization, it represents the state of the art in terms of performance. But its components can also be employed for other tasks with only minor work.An interesting way to improve the toolkit will be implementing some missing methods. For example, methods such as[START_REF] Pardo | Speaker diarization for multiple-distant-microphone meetings using several sources of information[END_REF][START_REF] Hieu Nguyen | T-test distance and clustering criterion for speaker diarization[END_REF] are very useful to develop a system dedicated to meeting diarization.Efforts should be done to bring the diarization toolkit closer to Sphinx 4. In particular, Sphinx 4 configuration management tools are very flexible and could be an efficient replacement for a number of scripts used with this toolkit. Moreover, the Viterbi decoder and access to acoustic features could adopt the Sphinx interface, thus helping developers to use both toolkits together.

Table 1 .

 1 Table 1 shows the current result on the test corpus of ESTER 2: a DER of 10.01 % with no post-filtering. The gain of one point of DER results from improvements in the management of consecutive identical features and of aberrant likelihoods in the Viterbi decoder after the campaign. DER over the ESTER 2 test corpus

	Corpus	%Miss. %F.A. %Sub.	DER
	africa 1	0.5 %	1.2 %	8.2 %	9.85 %
	inter	1.7 %	1.8 %	7.9 % 11.42 %
	rfi	0.0 %	0.7 %	2.9 %	3.72 %
	tvme	0.5 %	2.7 %	9.7 % 12.89 %
	ESTER 2 Total	1.0 %	1.6 %	7.4 % 10.01 %

Table 2 .

 2 DER over the RT'03 test corpus

	Thresholds %Miss. %F.A. %Sub.	DER
	default	0.2 %	2.5 %	5.0 % 7.65 %
	tuned	0.2 %	2.5 %	3.7%	6.36 %

Table 3 .

 3 DER over the MEDIA development and evaluation corpus

	Corpus %Miss. %F.A. %Sub.	DER
	Dev	2.0 %	1.3 %	1.2 % 4.51 %
	Test	1.6 %	0.6 %	0.3 % 2.47 %

ACKNOWLEDGEMENTS

We are grateful to Vincent Jousse and Gael Salaun for their helpful contributions during the development of this toolkit.

This research was supported by the ANR (French National Research Agency) under contract numbers ANR-06-MDCA-006 and ANR-08-CORD-026-01.


Mohammad Sharifipour

Christophe Dano
email: christophe.dano@ec-nantes.fr

Pierre-Yves Hicher

WAVE VELOCITIES IN ASSEMBLIES OF GLASS BEADS USING BENDER-EXTENDER ELEMENTS

Keywords: elastic properties, glass beads, bender-extender elements, wave propagation, Hertz's theory

Experiments of wave propagation through assemblies of glass beads, using bender-extender elements, are presented in this paper. Wave velocities are determined using many procedures of interpretation to be meticulously accurate about the results. The experimental results are then compared to theoretical predictions and experimental results in granular materials found in the literature. The effect of the beads diameter on the shear wave velocity is also investigated.

BENDER-EXTENDER ELEMENTS

Bender elements were developed at the end of the 70's by [START_REF] Shirley | Shear-wave measurements in laboratory sediments[END_REF]. The technology has been gradually improved since that date. Bender elements were for instance implemented in different geotechnical devices -triaxial cells to study both clays and sands, both reconstituted or natural soils, oedometer cells -and even put into centrifuges [START_REF] Ismail | An innovative facility to measure shear-wave velocity in centrifuge and 1-g models[END_REF]. Bender elements, whose working principle was previously described in [START_REF] Dyvik | Lab measurements of Gmax using bender elements[END_REF] and [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF], are piezoelectric transducers from which a shear wave can be transmitted and received. From the induced electric signals, the elastic properties of a soil in the small strain domain can be identified.

More recently, [START_REF] Lings | A novel bender/extender element for soil testing[END_REF] developed a new type of piezoceramics transducers called bender-extender elements from which both shear waves (S-waves) and compression waves (P-waves) can be transmitted and received. Therefore, from the velocities of the S-waves and of the P-waves, it is possible to calculate the Young's modulus Emax, the shear modulus Gmax and the Poisson's ratio  in the small strain domain. [START_REF] Dano | Characterization of Loire River sand in the small-strain domain using new bender-extender elements[END_REF] showed an application of such bender-extender elements on a Loire River sand.

However, the bender elements technique and its most recent improvements suffer from a lack of standardization. Indeed, although the bender elements technique has proved its efficiency, in spite of many experimental as well as numerical research works, there is no harmonization in the interpretation of the bender elements test results probably due to the fact that the method requires an educated judgment and that the wave propagation happens in a discontinuous and heterogeneous medium containing different phases (solids, water, air).

The authors have chosen to carry out experiments in reference materials, namely spherical glass beads. The results of a first series of tests are presented in this paper.

EXPERIMENTAL PROCEDURE

The tested material is composed of solid, spherical and smooth -visually -soda lime glass beads (PGC Scientifics, Ref. 41-5500-01 for the beads of 1mm in diameter, Ref. 41-5500-02 for the beads of 2mm in diameter). Glass beads of unknown origin and 3 mm in diameter were also used. Their grading curves are represented in Figure 1 where m and v represent respectively the mean value and the variance of the diameter of the glass beads. The chemical composition is mainly silica, calcium oxide and sodium oxide. The specific gravity of the PGC glass beads is 2,54 g/cm 3 (ASTM D854). The elastic modulus and the Poisson's ratio of the material are respectively close to 60 GPa and 0.3 as indicated in information brochures by the manufacturers of soda lime glass beads.

The previously dried beads were placed manually, without well-ordered structure, and compacted by shocks on the mould used for the preparation of the samples. Preparation by raining was not possible here because beads bounce outside the mould. However, this procedure was repeatable enough. It induced density between 1.61 g/cm 3 and 1.64 g/cm 3 , except for the first test for which the density was 1.54 g/cm 3 . Samples were 100 mm in diameter and the height to diameter ratio was close to 2. No saturation was applied. The tests were conducted in drained conditions with confining pressures between 100 and 500 kN/m 2 .

Bender-extender elements were carefully aligned because of polarization and possible subsequent boundary effects. Bender-extender elements were 10 mm large, 2.5 mm high and about 0.5 mm wide.

THEORETICAL PREDICTIONS [START_REF] Hertz | Über die Berührung fester elastischer Körper[END_REF] theoretically predicted that in a 1D chain of elastic spherical beads, the velocity Vw of an acoustic wave depends on the normal load F applied to the chain following a power law:

6 / 1 3 / 1 3 / 1 w F R E V   (1)
where E,  and R are respectively the elastic modulus, the density and the radius of the beads. Many experiments were performed to confirm or invalidate the predictions by Hertz [START_REF] Duffy | Stress-strain relation and vibrations of a granular medium[END_REF][START_REF] Warren | Elastic properties of granular materials under uniaxial compaction cycles[END_REF][START_REF] Pilbeam | Acoustic velocities and energy losses in granular aggregates[END_REF][START_REF] Goddard | Nonlinear elasticity and pressure-dependent wavespeed in granular media[END_REF][START_REF] Jia | Ultrasound propagation in externally stressed granular media[END_REF][START_REF] Coste | Propagation d'ondes dans un milieu granulaire modèle[END_REF]. An obvious conclusion is that the velocities scale up with the pressure following a power law. However, in disordered assemblies of spheres, the power law exponent is experimentally between 1/4 and 1/3, rather than the theoretical value 1/6. [START_REF] Coste | Propagation d'ondes dans un milieu granulaire modèle[END_REF] reviewed the sources of discrepancy between theoretical and experimental data. On the one hand, the sources of discrepancy are "local" and related to the assumptions of the Hertz's contact law : the beads are not perfectly spherical and smooth, they can be covered with a thin layer of degraded material, sliding can occur in the contact area … On the other hand, the waves propagate through a mass of beads in which the contacts between grains and therefore the force chains that support and transmit the loads are more or less randomly distributed (effect of packing).

EXPERIMENTAL SIGNALS

The experimental work presented in this paper aims at proving the efficiency of the bender-extender elements for the identification of the elastic properties of soils. The subject is not to discuss about the Hertz's theory but to find consistent pressure-dependent power laws for the wave velocities, and therefore for the elastic properties (Emax, Gmax, ). In Figure 2, typical input and output signals for S-wave and P-wave propagating through 1 mm glass beads under a pressure of 300 kN/m 2 are shown. For comparison, amplitudes were normalized by the absolute maximum amplitude. No differences between sinusoidal or square signals were notable, whereas the frequency of the input signal has a notable effect on the quality of the output signal.

INTERPRETATION OF PULSE TESTS

As previously mentioned, the interpretation of bender-extender elements tests is not an easy task since the physical phenomena induced by the propagation of a wave into a soil are complex. In the literature, three kinds of interpretation method can be found.

The most often used method consists in identifying the deflection of the output signal that corresponds to the arrival of the wave on the receiver [START_REF] Jovicic | Objective criteria for determining Gmax from bender element tests[END_REF][START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF]. However, near-field effects and wave reflections on the sample boundaries usually inflect the signal and make the determination of the travel time difficult [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF].

The second method consists in comparing the input and the output signals by cross-correlation [START_REF] Viggiani | Interpretation of bender element tests[END_REF][START_REF] Mohsin | Automating Gmax measurement in triaxial tests[END_REF]. The travel time corresponds then to the time that fits at best the two signals. The third kind of interpretation methods based on Fourier transformation [START_REF] Mancuso | Numerical analysis of in situ S-wave measurements[END_REF][START_REF] Theron | Interpretation of side-mounted bender elements using phase shift and group velocity[END_REF] were not considered here.

All the indicators [START_REF] Jovicic | Objective criteria for determining Gmax from bender element tests[END_REF][START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF][START_REF] Arroyo | Source near-field effects and pulse tests in soil samples[END_REF] show that near-field effects, though not quantitatively important here, have to be nevertheless considered for the precise determination of the travel time of the shear waves.

TRAVEL TIME OF THE WAVES

In this section, the travel time of the waves determined by two methods is compared. The peak-to-peak time (denoted PP in Figure 2) has to be considered as a reliable estimate of the travel time Tp for the P-wave or Ts for the S-wave. However, the correct travel time has to be determined from the delay time denoted AA' in Figure 2. AA' is the period between the beginning of the input pulse and the arrival of the wave on the receiver. For the P-wave, the determination of AA' is relatively easy since the first deflection of the output signal corresponds to the arrival of the P-wave (Fig. 2a). As previously indicated, for the S-wave, near-field effects induce the propagation of a parasite wave that causes the receiver to bend before the arrival of the shear wave. In Fig. 2b, PW corresponds to the arrival of the P-wave identified in Fig. 2a. The point A' that marks the arrival of the shear wave, is located using recommendations by [START_REF] Jovicic | Objective criteria for determining Gmax from bender element tests[END_REF] and [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF]. The delay times AA' and PP are usually close, indeed equal.

Cross-correlation is also calculated in order to identify the time Tcc that fits at best the input and the output signals. Examples are shown in Figure 3 for a sample of 1 mm glass beads under a pressure of 400 kN/m 2 . Assuming that the sample behaves as a linear system, [START_REF] Mohsin | Automating Gmax measurement in triaxial tests[END_REF] indicated that one of the peaks of the cross-correlation should correspond to the correct delay time. The authors added that the cross-correlation method provides a reliable indication of the travel time for frequencies greater than a critical frequency which increases with the effective confining stress. Finally, [START_REF] Mohsin | Automating Gmax measurement in triaxial tests[END_REF] presented experimental results on sands from which they conclude that the third peak of the cross-correlation corresponds to the correct arrival of a shear wave.

Values of AA', PP and Tcc for four tests on 1mm glass beads with confining pressures equal to 300 kN/m 2 and 400 kN/m 2 are reported in Table 1. In Table 1, P and S respectively stands for a P-wave and a S-wave, Tp and Ts are the values of the travel time considered for the calculation of the wave velocities Vp for the P-wave and Vs for the S-wave respectively. A slight uncertainty of about 0.02 ms can be observed depending on the interpretation method. That uncertainty induces a relative uncertainty on the shear modulus Gmax/Gmax close to 10 %.

PRESSURE -DEPENDENT WAVE VELOCITY

It is well-known that the velocities Vp and Vs can be calculated following :

P P T L V  (2) S S T L V  (3)
where L is the distance covered by the wave. The distance is the length between the tips of the bender-extender elements [START_REF] Jovicic | Objective criteria for determining Gmax from bender element tests[END_REF][START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF]. The length is corrected from the volumetric variation of the sample during isotropic loading or unloading.

Figure 4 represents the velocities Vp and Vs (in m/s) as a function of the mean effective pressure p' (in kN/m 2 ). As expected, the velocities increase with the effective pressure following power laws such as : (5)

Exponents in equations ( 4) and ( 5) are almost similar. Therefore, it induces an almost constant value for the Poisson's ratio  since :

2 S 2 P 2 S 2 P V V V 2 V 2 1      (6)
as previously observed in a Loire River sand [START_REF] Dano | Characterization of Loire River sand in the small-strain domain using new bender-extender elements[END_REF]. Here, the value of the Poisson's ratio is between 0.13 and 0.17. Such a value is typical of many soils.

EFFECT OF BEADS SIZE

After being validated, the procedure is used to compare the velocity of shear waves propagating through assemblies of glass beads of different size. Two tests on samples of 1 mm beads with initial void ratios e0 respectively equal to 0.56 and 0.58 (independent from the previous test), two tests on samples of 2 mm beads (e0 equal to 0.58) and two tests on samples of 3 mm beads (e0 respectively equal to 0.57 and 0.55) were carried out along isotropic stress paths. Calculated velocities are reported in Figure 5.

The main observation is that the value of the exponent decreases whereas the diameter of the beads increases. However, curve fits slightly depend on the experimental scattering. Even if this do not change the previous observation, the results has to be taken with care. Indeed, previous papers [START_REF] Chang | Effects of gradation on shear modulus of Denver sands at small strains[END_REF][START_REF] Hicher | Microstructure influence on soil behaviour at small strains[END_REF] indicated that the shear modulus is not affected by the mean diameter of the soil particles. Nevertheless, this observation leads to examine even more the validity of the method for the measurement of wave velocities in the small strain domain.

COMMENTS

Experimental results presented in this paper are consistent with previous published results synthesized above. The exponents characterizing the pressure-dependent relations for the velocities are between 0.22 and 0.29, depending on the size of the particles. These relatively high values for the exponents compared to the theoretical predictions by Hertz can be attributed to the disordered structure of the sample and the preparation method that probably induced an anisotropic fabric.

CONCLUSIONS

Experiments of wave propagation through samples of glass beads are carried out in order to validate the bender-extender elements technique. Indeed, the method has already shown its effectiveness in the determination of elastic properties of sands. However, it suffers from a lack of validation in standard materials such as glass beads. The velocities of both compression waves and shear waves are experimentally determined. These velocities evolve as a power law of the effective pressure. The exponents of these power laws and the values of the Poisson's ratio calculated from the S-wave and P-wave velocities are consistent with current results found in the literature. However, further work has to be carried out in order to explain the dependence of the power law exponent on the beads size.

FIG. 1 .

 1 FIG. 1. Grain size distribution of glass beads.

  FIG. 2. Examples of input and output experimental signals.

  FIG. 3. Cross-correlation of both P-wave and S-wave.

  FIG. 4. Pressure-dependent velocity of waves.

  FIG. 5. Size effect of the beads on the velocity of S-waves.

TABLE 1 . Comparison of travel time.

 1

	p'	Wave	PP	AA'	Tcc	Tp	Ts	Figure
	kN/m 2	S or P	ms	ms	ms	ms	ms
	300	P	0.38	0.36	0.35	0.36	-	2a
	300	S	0.61	0.61	0.61	-	0.61	2b
	400	P	0.36	0.35	0.36	0.36	-	3a
	400	S	0.56	0.56	0.56	-	0.56	3b


Christophe Dano

Hocine Hareb

Pierre-Yves Hicher

Characterization of Loire river sand in the small strain domain using new bender-extender elements

Keywords: Young's modulus, shear modulus, Loire River sand BENDER-EXTENDER ELEMENTS

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

Since their appearance at the end of the 70's [START_REF] Shirley | Shear-wave measurements in laboratory sediments[END_REF], bender elements have become an usual geotechnical testing device. Bender elements are piezo-ceramics transducers which could be embedded into different laboratory apparatus such as triaxial cells (see for instance [START_REF] Dyvik | Lab measurements of G max using bender elements[END_REF][START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF][START_REF] Kuwano | Shear stiffness anisotropy measured by multi-directional bender element transducers[END_REF][START_REF] Lo Presti | Anisotropy of small strain stiffness of undisturbed and reconstituted clays[END_REF][START_REF] Dano | Evolution of elastic shear moduli in granular materials along isotropic and deviatoric stress paths[END_REF], oedometer cells [START_REF] Dyvik | G max measured in oedometer and DSS tests using bender elements[END_REF]…These transducers transmit and receive shear waves (also noted S-waves). The wave propagation causes very small strains (ε ≤ 0.001 %) and enables the determination of the shear modulus G max in the small strain domain [START_REF] Viggiani | Interpretation of bender element tests[END_REF][START_REF] Dano | Evolution of elastic shear moduli in granular materials along isotropic and deviatoric stress paths[END_REF]. A review of the bender elements technique can be found in the paper by [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF].

Independent compression waves transducers (P-waves) were sometimes associated with bender elements in order to identify another parameter of the Hooke's law, either the Young's modulus E max or the Poisson's ratio ν [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF].

However, the simultaneous use of compression wave transducers and shear wave transducers has not been extensively developed until now. In order to remedy this inconvenience, [START_REF] Lings | A novel bender/extender element for soil testing[END_REF] described a new transducer called bender-extender element. An unique couple of such bender-extender elements can transmit and receive both P-waves and S-waves : this property results from a slight modification of bender elements.. Therefore, these elements can be 1 Civil Engineering Laboratory of Nantes Saint-Nazaire, Member of the Research Institute in Civil and Mechanical Engineering, Ecole Centrale Nantes, BP 92101, 44321 NANTES (France). E-mail: Christophe.Dano@ec-nantes.fr 2 Formerly Master of Science at the Civil Engineering Laboratory of Nantes Saint-Nazaire 2 used to easily identify the Young's modulus E max and the shear modulus G max in the small strain domain simultaneously : in this paper, they are tested on a Loire River sand as presented later on.

This simplicity also holds true in respect of the acquisition data system. The device requires a personal computer and a control box as shown in Fig. 1. Likewise, the sample preparation is hardly changed by the introduction of the bender-extender elements embedded into the lower and upper pedestals of a conventional triaxial cell.

The principle of bender-extender elements is straightforward. The transmitter is excited by an electric signal : the new user-friendly system allows the experimenter to choose between a square signal, a sinusoidal signal or an user-defined signal. The input signal induces longitudinal (for Pwaves) or tangential vibrations (for S-waves) which are propagated through the sample. The receiver is then submitted to longitudinal or tangential displacements which are inversely converted into an output electric signal. The input and output electric signals are recorded on the PC for a subsequent analysis. It has to be noted that the displacement amplitude in extension is about one order of magnitude smaller than the bending displacement [START_REF] Lings | A novel bender/extender element for soil testing[END_REF]. This can explain the fact that the P-waves output signals are sometimes more difficult to interpret than the S-waves output signals.

FIG. 1. Bender-Extender elements into the triaxial cell. PHYSICAL PROPERTIES OF LOIRE RIVER SAND

The Loire River sand consists of recent alluvial deposits of the Loire River, close to its mouth in the west part of France. It is composed of sub-rounded particles and elongated shell fragments. The grading curves obtained on two samples are represented in Fig. 2. The mean grain size D 50 is 520 µm. The coefficient of uniformity C u is equal to 3.5. The coefficient of curvature C c is equal to 0.8. Therefore, the Loire River sand is a poorly graded sand (ASTM D2487-93).

The specific weight γ s of the Loire River sand grains is 26.2 kN/m 3 (ASTM D854-92). The minimum unit weight γ min (ASTM D4254-91) and the maximum unit weight γ max (ASTM D4253-93) are respectively equal to 15.1 kN/m 3 (e max = 0.738) and 18.5 kN/m 3 (e min = 0.415).

LARGE STRAIN BEHAVIOR OF LOIRE RIVER SAND

A first series of drained triaxial tests on saturated samples of Loire River sand (100 mm in diameter, 200 mm in height) was carried out, following the French Standard P 94-074. The sand 3 was deposited by five successive layers. Each of them was compacted by tamping. The dry unit weight was then close to 17.5 kN/m 3 . The saturation phase led to B-values greater than 0.95. Samples were consolidated under an effective mean stress between 100 and 400 kN/m 2 . They were finally sheared at a constant shear rate equal to 1.67 x 10 -5 s -1 .

The shortening of the sample was measured on an external gauge whereas the axial load was determined by an internal load cell. Volume changes were measured in a burette. Experimental results are presented in Fig. 3. Each test is doubled. The behavior of the Loire River sand is typical of a dense sand. The values of the parameters of the linear elastic perfectly plastic model assuming a Mohr-Coulomb yield criterion, namely :

• the tangent modulus E at the origin of the deviator stress q -axial strain ε 1 curve, measured for an axial strain equal to 0.1 % ;

• the Poisson's ratio ν at the origin of the volumetric strain ε v -axial strain ε 1 curve ;

• the angle of dilation ψ determined at the maximum volumetric strain rate in the dilating stage ;

• the angle of friction ϕ' p at the peak stress and the angle of friction ϕ' res in the residual state determined in the Mohr-Coulomb diagram;

• the cohesion c' determined in the Mohr-Coulomb diagram are reported in Table 1 where e 0 is the initial void ratio.

SMALL STRAIN BEHAVIOR OF LOIRE RIVER SAND

As previously stated by many authors [START_REF] Iwasaki | Effects of grain size and grading on dynamic shear moduli of sands[END_REF][START_REF] Hicher | Elastic properties of soils[END_REF], the tangent modulus E greatly underestimates the value of the Young's modulus because of the inaccuracy of conventional triaxial tests [START_REF] Scholey | A review of instrumentation for measuring small strains during triaxial testing of soil specimens[END_REF]. In the small strain domain (ε ≤ 0.001 %), it is well-known that the Young's modulus E max and the shear modulus G max follow power laws such as [START_REF] Hardin | Elastic wave velocities in granular soils[END_REF][START_REF] Iwasaki | Effects of grain size and grading on dynamic shear moduli of sands[END_REF][START_REF] Hicher | Elastic properties of soils[END_REF]

E × = (1) G n G max ' p e k G × = (2)
where e is the void ratio ; p' is the mean effective stress (in kN/m²) ; k E , k G , n E and n G are constant values experimentally determined. If E max and G max are expressed in MN/m², then k E is between 10 and 25 and k G is usually between 4 and 10 [START_REF] Hardin | Elastic wave velocities in granular soils[END_REF][START_REF] Iwasaki | Effects of grain size and grading on dynamic shear moduli of sands[END_REF][START_REF] Hicher | Elastic properties of soils[END_REF][START_REF] Dano | Evolution of elastic shear moduli in granular materials along isotropic and deviatoric stress paths[END_REF]. The coefficients n E and n G are close to 0.5. Wave propagation tests on the Loire River sand were performed in order to establish similar equations for the Young's modulus E v,max and the shear modulus G vh,max where the subscript "v" means that the wave are vertically propagated and the subscript "h" means that the shear wave is horizontally polarized [START_REF] Kuwano | Shear stiffness anisotropy measured by multi-directional bender element transducers[END_REF].

Small strain experiments were carried out on a dry Loire River Sand in order to obtain a clear output signal for the P-waves (greatly affected by the aqueous phase). The sand was deposited by five successive layers. Each of them was compacted by tamping. The dry unit weight was then close to 17.5 kN/m 3 . A vacuum of 30 kN/m² was applied to the specimen during set-up within the cell. The vacuum was released and the specimen opened to the atmosphere during the application of a cell pressure σ' c of 50 kN/m². Volume changes are determined by means of the external displacement gauge and the pressure-volume controller used to apply the cell pressure in return for some corrections due to the load cell movement.

The sample was subjected to the following loading program :

• an isotropic compression stress path from 50 kN/m² to 400 kN/m² ;

• an isotropic unloading from 400 kN/m² to 100 kN/m² ;

• an isotropic compression stress path from 100 kN/m² to 500 kN/m² ;

• an isotropic unloading from 500 kN/m² to 200 kN/m² ;

• a shearing stress path at a constant cell pressure σ' c = 200 kN/m² with a shear rate of 1.67

x 10 -5 s -1 until ε 1 = 3.8 % ; • a discharge to an isotropic stress state with a mean effective stress p' = 200 kN/m² ; • an isotropic compression stress path from 200 kN/m² to 500 kN/m². Bender-extender elements were excited by sinusoidal input signals with a frequency of 5 kHz and an amplitude of 10 V. Typical signals obtained on the Loire River sand are shown in Fig. 4. [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF] and [START_REF] Jovicic | Objective criteria for determining G max from bender element tests[END_REF] have put forward that the ratio R d = L / λ w (where L is the distance of propagation of the wave and λ w the wave length) controls the shape of the Swave output signal. Here the ratio R d is close to 3. This implies that near-field effects have to be taken into account for the determination of the propagation time T s of the shear wave [START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF][START_REF] Jovicic | Objective criteria for determining G max from bender element tests[END_REF] : the arrival of the shear wave on the receiver corresponds to the first sign change of the signal derivative, as indicated in Fig. 4. As for the P-wave, the determination of the propagation time T P is straightforward : the first deviation of the output signal coincides with its arrival on the receiver (Fig. 4). The respective velocities V P and V S of the P-wave and the S-wave are therefore calculated [START_REF] Viggiani | Interpretation of bender element tests[END_REF][START_REF] Brignoli | Measurement of shear waves in laboratory specimens by means of piezoelectric transducers[END_REF][START_REF] Jovicic | Objective criteria for determining G max from bender element tests[END_REF]:

6 P P T L V = (3) S S T L V = (4)
where L is the distance of propagation between the tips of the transducers.

Finally, the following equations are used to calculate the parameters of the Hooke's law :

2 S 2 P 2 S 2 P 2 S max , v V V V 4 V 3 V E - - × ρ = (5) 2 S max , vh V G ρ = (6) 2 S 2 P 2 S 2 P V V V 2 V 2 1 - - × = ν (7)
where ρ is the density of the Loire River sand.

Along isotropic loading or unloading stress paths, the Young's modulus E v,max and the shear modulus G vh,max evolves as indicated in Fig. 5. The following equations are deduced from the experimental results :

• before shearing These equations prove the fabric change caused by the shearing phase. However, what is notable is the common value of the powers n E and n G in the equations ( 8) and ( 9) and in the equations ( 10) and (11). It means that the Poisson's ratio does not change along isotropic stress paths. If n E = n G , then :

1 k 2 k 1 G 2 E G E - = - = ν (12) 7
Equation ( 12) applied to the tests on the Loire River sand leads to a value of the Poisson's ratio ν equal to 0.26 before shearing and equal to 0.32 after shearing. This result is in accordance with the numerical results obtained by [START_REF] Aubry | Identification of elastic coefficients through resonant tests of soils samples[END_REF] who consider that the value of the Poisson's ratio ν does not depend on the mean effective stress p' if p' is greater than 150 kN/m².

CONCLUSIONS

Improved piezo-ceramics transducers have been set up within a conventional triaxial cell in order to study the mechanical behavior of the Loire River sand in the small strain domain (ε ≤ 0.001 %). An unique couple of bender-extender elements enables to transmit and receive both shear waves and compression waves. Therefore, the Young's modulus E max and the shear modulus G max can be simultaneously determined along isotropic and / or deviatoric stress paths.

8

This new device was tested on the Loire River sand. Typical laws for the Young's modulus and the shear modulus were found.

  FIG. 2. Grading curves of the Loire sand.

  FIG. 3. Large strain triaxial tests results.

  FIG. 4. Electric signals obtained by use of bender-extender elements.

TABLE 1 . Parameters of the elastic perfectly plastic model.

 1

	Test	σ' c	e 0	E	ν	ψ	c'	ϕ' p	ϕ' res
	reference
		kN/m 2		MN/m 2		degrees	kN/m 2	degrees	degrees
	100a	100	0.51	93	0.22	10.7
	100b	100	0.48	97	0.27	12.4
	200a	200	0.52	126	0.25	9.3	0	39.2	33.9
	200b	200	0.48	118	0.23	8.9
	400a	400	0.49	140	0.24	7.2
	400b	400	0.50	146	0.21	6.9

ACKNOWLEDGMENTS

The authors would like to acknowledge the companies RATP, INTRAFOR (France) for their financial support and the company GDS Instruments for their efforts in the development of the bender-extender elements.