Christine Michel

Élise Lavoué

KM AND WEB 2.0 METHODS FOR PROJECT-BASED LEARNING. MESHAT: A MONITORING AND EXPERIENCE SHARING TOOL

Keywords: Project-based learning, monitoring tools, metacognition, experience sharing, acquisition of expertise, Web 2.0. 1

Our work aims to study tools offered to students and tutors involved in face-to-face or blended project-based learning activities. To better understand the needs and expectations of each actor, we are especially interested in the specific case of project management training. The results of a course observation show that the lack of monitoring and expertise transfer tools involves important dysfunctions in the course organisation and therefore dissatisfaction for tutors and students (in particular about the acquisition of knowledge and expertise). To solve this problem, we propose a personalised platform (according to the actor: project group, student or tutor), which gives information to monitor activities and supports the acquisition and transfer of expertise. This platform is based on Knowledge Management (KM) and Web 2.0 concepts to support the dynamic building of knowledge. KM is used to define the learning process (based on the experiential learning theory) and the way the individual knowledge building is monitored (based on metacognitive concepts). Web 2.0 is used to define the way the experience is shared. We make the hypothesis that this approach improves the acquisition of complex skills (e.g. management, communication and collaboration), which requires a behavioural evolution. We aim to make the students become able 'to learn to learn' and evolve according to contexts. We facilitate their ability to have a critical analysis of their actions according to the situations they encounter.

INTRODUCTION

Project-based learning is often applied in the case of complex learning (i.e. which aims to make students acquire various linked skills or develop their behaviour). In comparison to traditional learning, this type of learning relies on co-development, collective responsibility and cooperation. Students are the principal actors of their learning. A significant enrichment arises from their activity, both for them and all the other students. A consequence of this approach is the segmentation of the class into sub-grouped projects, monitored by tutors. We generally observe that the coordination and harmonisation of tutors' activities are extremely difficult to operate when each group works autonomously, on different subjects and in real and varied environments (for example enterprises). It is even more difficult when the project is conducted over a long period (more than four weeks). In this context, the perception of individuals' and groups' activity is also very difficult, especially if no technical support for information and communication is used. Finally, the implementation of project-based learning in engineering schools, universities or professional training do not benefit from all its capacities [START_REF] Thomas | Preparing project managers to deal with complexity -Advanced project management education[END_REF]. Indeed, this learning should implement an educational model based on the Kolb's cycle [START_REF] Cortez | Learning to collaborate by collaborating: A face-to-face collaborative activity for measuring and learning basics about teamwork[END_REF], composed of four phases: concrete experience, reflective observation, abstract conceptualisation and active experimentation. However, it is often action (via the articulation conceptualisationexperimentation) which is favoured to the detriment of concrete experience and reflective observation [START_REF] Thomas | Preparing project managers to deal with complexity -Advanced project management education[END_REF].

To better understand the type of tool necessary to improve this training, we have studied a project management training course [START_REF] Michel | Knowledge Management Concepts for Training by Project: An Observation of the Case of Project Management Education[END_REF]. This course is supported by a rich and complex organisation, especially for tutors that we detail in Section 2. We have used KM methods to identify all the problems encountered by students and tutors and identify the following three main problems. 1. Difficulties in students acquiring some skills (e.g. project management organisation, use of monitoring tools and groupwork) and autonomy. 2. A lack of information so that tutors can monitor and evaluate students individually and by group. 3. A lack of tutors' communication and coordination so that they develop their expertise, knowledge and competences.

In Section 3, we study existing tools which can help to solve these problems, especially monitoring and experience sharing tools. We then observe that no existing tool could solve all these problems on its own. Therefore we propose a new tool named MEShaT (Monitoring and Experience Sharing Tool) before finally concluding with the future directions offered by this work.

CASE STUDY: A PROJECT MANAGEMENT TRAINING COURSE

The course organisation

The course is composed of a theoretical presentation of the principles and methods of project management and their practical application to a project (called 'PCo' for 'Collective Project') carried out by groups (12 groups of 8 students which answer to different industrial needs). Envisaged by Patrick Prévôt (Michel & Prévot,

#. MESHAT: A MONITORING AND EXPERIENCE SHARING TOOL

3 2009), the project management course lasts six months and corresponds to an investment of approximately 3000 students' working hours per project. The instructional objectives are to acquire hard competences (e.g. knowing how to plan the project (Gantt's chart), project management, managing resources, controlling quality) and soft competences (e.g. social competences of collaboration and communication, empathy, consideration of others, leadership). The pedagogical team (see Figure 1) is composed of 24 tutors (a technical and a management tutor per group), two managers (technical and management) in charge of the coordination of the technical and management tutors' activities, one teacher who presents the theoretical concepts and one director responsible for the organisation of the training of all groups.

The project is composed of four phases: 1. November: answer to the call for tender (formalisation of the client's requirements). 2. December: elaboration of a master plan (means, tools and organisation of the team project), definition of tools to drive the project (dashboard) and rules to test the deliverables quality (rules of receipt). 3. January to March: development of a product or a study. 4. Until mid-April: delivery of a technical report which describes the product and management report (a project closure report which is an analysis, from the student's point of view, of the flow and problems of the project). The project is closed by one dramatised presentation in front of all the actors of the project.

Figure 1 -Pedagogical team and course organisation

The course has been designed according to the experiential learning theory, well-known in KM, and is based on the expanded learning circle proposed by [START_REF] Berggren | Rethinking project management education: Social twists and knowledge co-production[END_REF]. This circle is based on the learning circle developed by [START_REF] Kolb | Learning styles and learning spaces: Enhancing experiential learning in higher education[END_REF], which consists of concrete experience, reflective observation, abstract conceptualisation and active experimentation, in combination with the different learning styles. [START_REF] Berggren | Rethinking project management education: Social twists and knowledge co-production[END_REF] expanded this model and propose a social twist of experiential learning (see Figure 2):

• The processes of articulation and reflection allow for the abstraction of knowledge.

• The processes of investigation and enaction contribute to the social character of knowledge and the diffusion of experience developed within the educational programmes. In the framework of the project, the personal experience of the student is a result of the education process constructed by following the right circle of the model (see Figure 2). The articulation phase corresponds to debriefing discussions and debate driven by the tutors (one face-to-face discussion per week). The teacher presents the 'soft' and 'hard' concepts to students during the course. During the realisation of the project, students discuss 'soft' concepts with their management tutor and 'hard' concepts with the technical tutor so as to analyse and understand them. Tutors therefore play the role of animators. This work is strongly linked with the reflection phase (especially reflective observations). Reflective observation can occur in a tacit way after these discussions with tutors or in a more formal way by realising the management report or other deliverables. Students choose, alone or according to tutors' instructions, the personal and social actions useful for the project or relevant according to the teaching objectives. It helps them build a unique experience, not well formalised by the teaching team. In this case, reflection is articulated with the personal and social actions and helps to apply 'hard' and 'soft' concepts and to build competences. It is also an occasion for each individual to express their personal experience.

Another characteristic of our project design is to promote, on the one hand, the processes of investigation and enaction, and, on the other hand, the process of diffusion. The courses in project management usually consist of realising a well-known project (a case study). In our case, the investigation process is emphasised by the fact that students have to solve an industrial problem without a predefined solution. It provides a real challenge that facilitates the construction of knowledge and improves enaction. The diffusion process is realised in the form of dramatised representations. Students present their good/bad practices and their feelings and judgments about the training and the tutors. These representations take part in a KM diffusion process, between the project team, the teaching team and the department. They also aim to support the reflection and conceptualisation processes necessary for students to realise the experience they gain by working in a group.

This combination of activities go with an evolution of behaviour in terms of skills (management, communication, collaboration and all 'soft' competences) and natural reactions (to be able to learn how to learn and to evolve in surprising or unknown situations) by supporting the students' capacity for self-critical analysis. This capacity mainly results from the training activities carried out with the tutors. Indeed the tutors play various roles which depend on the type of skills the students have to acquire. According to Garrot's taxonomy [START_REF] Garrot-Lavoué | Interconnection of Communities of Practice: A Web Platform for Knowledge Management[END_REF], for the acquisition of soft skills, tutors are social catalysts (by creating a friendly environment to incite students to participate), intellectual catalysts (by asking questions and inciting students to discuss and to criticise), 'individualisers' (by helping every student to overcome their difficulties, to estimate their needs, difficulties, preferences) and 'autonomisers' (by helping students to regulate their learning and to acquire autonomy). For the acquisition of hard skills, tutors are relational coaches (by helping students to learn how to work in a group and to become a leader), educationalists (by redirecting groups' activities in a productive way, clarifying points of methodology, supplying resources), content experts (by answering questions on the course contents), evaluators (by evaluating students and groups' productions and participation) and 'qualimetrors' (by measuring and giving feedback on the quality of the course).

Tutors monitor a unique and non-reproducible project. They work with students most of the time face-to-face and no organisation, communication or capitalisation tool is proposed. For example, no specific tool is currently proposed to the tutors for the monitoring of students' activities or for their evaluation. The appreciation of students' activity is made in an implicit way, according to the number and the quality of face-to-face studenttutor interactions. In terms of communication and coordination, each tutor works individually with their group and does not communicate much with the other tutor of the same group (management or technical) in order to have a complete vision of the group's activity.

The observed problems

The observation methodology is adapted from the Method for Knowledge System Management (MASK) approach [START_REF] Benmahamed | From MASK Knowledge Management Methodology to Learning Activities Described with IMS -LD[END_REF]. This method, starting from documents produced by an organisation and talks with actors, allows the modelling of complex industrial systems by identifying and inter-relating various concepts: product, actor, activity, rules and constraint. Each concept is defined on a card; the Information, Constraint, Activity, Rule, Entity (ICARE) cards describe any object precisely intervening in the process. The Reuse, Improve and Share Experiment (RISE) cards describe any problem occurring during the process and specify the contexts, suggested solutions or recommendations. The elements described in the ICARE and RISE cards are organised overall in a chart, which shows their interrelationships (the method is completely described in [START_REF] Michel | Knowledge Management Concepts for Training by Project: An Observation of the Case of Project Management Education[END_REF].

For this research, we analyse results from RISE cards. The observation data are various experience feedbacks from students and tutors and were collected by 62 students in the fifth year of engineering school. The observed students are 23 males and 18 females who are between 22 to 25 years old. Thirty-eight of them have carried out the project management course the previous year, three of them are currently 'project leaders'. Observation consists of direct feedbacks made by interview of the course director, of six tutors and of three students currently 'project leaders' and by self-observation for the other 38 students. Indirect feedbacks are based on various groups' experience and analyses expressed in their 'management report', which is one of the projects deliverables. Twenty-four management reports have been considered (each one relating to the experience of a group). By this observation we have identified 36 different types of problems described in RISE cards. The type and frequency of the observed problems are presented in Figure 3. The majority of cards (57%) relate to a problem with the management of the teamwork by the team itself. More precisely, 29% relate to a lack of project management skills, 18% relate to difficulties working in group, 10% relate to problems with some students who think they are not responsible enough. Meanwhile, 31% of the problems concern tutors' activity and impact on the teaching organisation of the project. Indeed, 13% concern a lack of coherence, coordination and communication between tutors, which involves problems of information diffusion. For example, the instructions given to the project groups were described as ambiguous or contradictory. About 5% concern a lack of communication between tutors and students or a lack of presence of some tutors; 13% concern a lack of information for tutors on the teaching objectives or on the knowledge and skills they have to teach to students. Indeed, students feel alone when they have to learn using some tools or when they have to apply theoretical project management concepts. Students sometime do not understand the role tutors play and the help they can bring them. Moreover, 8% of the problems concern failure in the teaching design of the course (not enough time to work, a not adapted calendar and too short timing for the deliverables). Finally, many groups and tutors express the same problem concerning the monitoring of individuals' or groups' activity and students evaluation (4% of the problems). The students express a feeling of injustice concerning the individual evaluation because the notation is the same for all members of a project (with about + or -2 points according to their investment), even if the students are involved more or less than the others. All the tutors also express their difficulties in evaluating the students individually. These difficulties are explained by the intuitive and tacit character of the evaluations, by the lack of traceability of students' actions, and by the lack of discussion with their colleagues.

It is possible to partially solve problems concerning the course design and the course organisation by changing the timing and the teachers' and coordinators' responsibilities. Nevertheless many problems remain and most of them are directly or indirectly bound to tutors' activity. That is why we aim to help tutors, on the one hand, to monitor and to evaluate the students and the groups and, on the other hand, to exchange information, coordinate and develop their skills and expertise. Although the pedagogical context is not distance learning, we hope to benefit from using tools to support this activity. In the next part, we study knowledge management and Web 2.0 tools which are suitable for our case. We focus on monitoring tools and expertise sharing tools.

TOOLS TO SUPPORT LEARNING ACTIVITIES

In this part, we detail existing tools to help tutors to monitor students' activities and to communicate with the other tutors. We study how these tools can help tutors and solve the problems identified in the previous part. We finally show that none of them answer all the needs and therefore we develop our own tool.

Monitoring tools

Many tools have been developed to support tutors in the monitoring of distant and synchronous students' individual activities. ESSAIM [START_REF] Després | Synchronous Tutoring in Distance Learning[END_REF] gives a global view of a student's progress in the course and tutors have a perception of the activity with reference to the path, the actions and the productions of each student. FORMID [START_REF] Guéraud | Automatic Semantic Activity Monitoring of Distance Learners Guided by Pedagogical Scenarios[END_REF]) offers a tutor interface with a global view of a class during a session (e.g. students' login, their progress in the course) or a zoom-in on a precise course stage (successfully validated or not by the class, by a student or by a group of students so as to identify their difficulties). These tools work in a synchronous environment with automatically generated tracks. They are thus only meant for tutors and do not offer the possibility for students to regulate their learning for a long period. Furthermore, they are not meant for asynchronous learning situations for which tutors need information on students' activities over a long period.

Other tools are meant to help tutors to monitor asynchronous activities and entice students towards their autonomy or to regulate their learning by determining themselves the state of their progress in the course. Croisières [START_REF] Gueye | Instrumentation des activités du tuteur en ligne le cas de CROISIERES, dispositif de Formation Ouverte et à Distance en langues[END_REF] offers services which individually support students in their learning progress and assist them in autonomy situation. Students select their learning activities according to their objectives and learning strategies. Reflet [START_REF] Després | Reflet, un miroir sur la formation[END_REF]) is a tool meant for showing the state of progress of a student or a class. It supplies information to the tutors who monitor the students in distance training and to the students who have feedback on their progress with regard to the learning objectives and the other students. Students determine their state of progress in the course with regard to the tasks they have to carry out and tutors can deny students the validation of some of their tasks.

There are also tools to monitor the activities of groups, not simply individuals. SIGFAD [START_REF] Mbala | Supporting Distributed Collaborative Learning with Usage Analysis Based Systems[END_REF]) offers a support for actors' interactions in restricted groups (8-15 persons) in distance learning. It helps tutors to hold the groups, to boost them and indeed to conduct the course well. The interaction statistics allow one to model and to show the collaboration into groups, to estimate the group's life and evolution. SIGFAD supplies three main categories of estimations: at the level of the group (present, absent or still persons, the state of the group with regard to the realisation of the activities), at the level of individuals (their productivity in terms of the realisation of activities and their sociability which indicates their level of communication with the other members of the group) and at the level of the activity (level of realisation of an activity by all participants). TACSI [START_REF] Laperrousaz | Analyzing a collaborative writing activity in order to improve tutor's perception of individual contributions of learners[END_REF] offers more specifically a perception of the individual students' activity into the activity of their group. It distinguishes the perception of students' activity in an individual task (individual productions), the perception of students' activity in a collective task (their contributions in the collective activities and their contributions to the discussions) and the perception of students' situation in the group dynamics (social behaviour and sociometric status). The LCC (Learning to Collaborate by Collaborating) collaborative activity software [START_REF] Cortez | Learning to collaborate by collaborating: A face-to-face collaborative activity for measuring and learning basics about teamwork[END_REF] is used for teaching and measuring teamwork skills using technologically supported face-to-face collaborative activities. LCC allows seven variables to be measured: the first variables measure the activity score (i.e. the group's efficiency in performing the task assigned), while the last variables measure teamwork (corresponding to core components (skills) of teamwork like team orientation (TO), team leadership (TL), monitoring (MO), feedback (FE), back-up (BA) and coordination (CO)). Communication has not been included in the measurable variables.

The individual and collective indicators for the monitoring of students and project groups offered by these tools are relatively well adapted to our context. We especially adopt those proposed within the LCC framework [START_REF] Cortez | Learning to collaborate by collaborating: A face-to-face collaborative activity for measuring and learning basics about teamwork[END_REF] for the development of our own monitoring tool. However, the course which interests us does not use instrumented activity and thus does not allow using automatically collected tracks of students' activity which is why we have to think about other ways of collecting information on their activities.

The tools which help students to acquire autonomy incite them to evaluate their progress in the course, according to the tasks they have achieved and those they have to achieve. However, these tools are not adapted because they do not help students to build an individual reflection neither on the relevance of the knowledge they acquire and the modalities of this acquisition nor on their behavioural changes. These self-regulatory processes are individual and mainly result from the activities carried out with the tutors. We think it useful (Michel & Prévôt, 2009) to support these processes by using a metacognitive tool [START_REF] Azevedo | Understanding the complex nature of self-regulation in learning with computer-based learning, an introduction[END_REF] which takes into account students' point of view of cognition (e.g. activating prior knowledge, planning, creating sub-goals, learning strategies), metacognition (e.g. feeling of knowing, judgment of learning, content evaluation), motivation (e.g. self-efficacy, task value, interest, effort) and behaviour (e.g. engaging in help-seeking behaviour, modifying learning conditions, handling task difficulties and demands).

All the tools studied in this part are exclusively centred on students' activity and help neither students nor tutors to have reflections on their activity. In our context, in which the roles played by tutors are extremely varied, it is essential to have a base structuring this reflection. For example, [START_REF] Berggren | Rethinking project management education: Social twists and knowledge co-production[END_REF] propose to use a 'learning contract' defined as 'a number of fairly simple questions, such as: What do I want to learn? How will I learn this? Who can give support? When can I start? How will I know that I have learned? How will others realise that I have learned?' This contract could be useful not only for students but also for tutors.

Furthermore, all the tools do not help tutors to understand or interpret what they observe. They supply useful information for tutors but this information is rather quantitative than qualitative and thus does not allow the evaluation of the quality of the contributions or productions, or to explain students' behaviour neither individually nor inside the group. These tools can be useful for tutors only if they know how to use them, how to interpret the supplied information and how to react effectively and in an adapted way. Finally, these tools address every tutor individually and do not allow them to coordinate at the level of monitoring of the same project group and to exchange on their activity so as to acquire more expertise. All of which is why we go on to study in the next section the tools which support exchanges between tutors to allow them to help each other and to develop their skills.

Experience sharing tools

The results of a previous study [START_REF] Michel | Instrumented Collective Learning Situations (ICLS): The gap between theoretical research and observed practices[END_REF] about tools supplied to tutors shows that they do not have adapted tools to exchange or formalise their experience as allowed, for example, by Knowledge Based Systems (KBS) or experience booklets [START_REF] Kamsu Foguem | Knowledge formalization in experience feedback processes: An ontology-based approach[END_REF]. Furthermore, we observed that tutors are rather structured in a hierarchical way within the organisation and do not have coordination tools or dedicated spaces for meeting between peers.

To compensate for a lack of training and formal help, Communities of Practice (CoPs) of tutors emerge. Web technologies (e.g. forums, blogs, wikis) have allowed the emergence of online CoPs [START_REF] Cuthell | The role of a web-based community in teacher professional development[END_REF][START_REF] Pashnyak | What and Why do Classroom Teachers Blog[END_REF]. CoPs gather tutors together in an informal way because of the fact that they have common practices, interests and purposes (i.e. to share ideas and experiences, build common tools, and develop relations between peers). Members exchange information, help each other to develop their skills and expertise and solve problems in an innovative way. They develop a community identity around shared knowledge, common approaches and established practices and create a shared directory of common resources [START_REF] Wenger | Communities of practice: Learning, meaning, and identity[END_REF][START_REF] Garrot-Lavoué | Interconnection of Communities of Practice: A Web Platform for Knowledge Management[END_REF]. The use of technology does allow the accumulation of exchange, but these are relatively unstructured and not contextualised. Web tools such as blogs, mailing lists, chat and email, allow discussions without building concrete knowledge (only forums bring a slightly higher degree of explicit emergence, thanks to the spatial representation as discussion threads which highlights relations between messages).

Numerous works aim to answer the question by supplying tutors with tools to support specific activities. Some tools work through member participation and sociability, for example by offering a virtual 'home' like the Tapped In environment [START_REF] Schlager | Teacher professional development, technology, and communities of practice: Are we putting the cart before the horse? In: Designing for virtual communities in the service of learning[END_REF], others by supporting collaboration between members like CoPe_it! [START_REF] Karacapilidis | Web-based collaboration and decision making support: A multi-disciplinary approach[END_REF]. Other tools favour the creation of contextualised resources and contextual search facilities such as the learning environment doceNet [START_REF] Brito Mírian | Integrating Instructional Material and Teaching Experience into a Teacher's Collaborative Learning Environment[END_REF]. However, all these environments either favour sociability (engaging members to participate) to the detriment of the reification of the produced resources, or they favour the accumulation and indexation of contextualised resources, but to the detriment of sociability and member participation.

We have developed the TE-Cap platform [START_REF] Garrot-Lavoué | Interconnection of Communities of Practice: A Web Platform for Knowledge Management[END_REF]) so as to support a good structuralisation of the information without decreasing member participation (for example communication). Indeed, the tutors have discussions by way of contextualised forums: they associate tags with the discussions to describe the context. These tags are subjects of a tutoring taxonomy, shown in an interactive and evolutionary way (the tutors can propose new subjects for the taxonomy). This platform, associated with a monitoring tool, could answer our needs of knowledge and skills acquisition and capitalisation about the realisation of tutors' activity and about the use of the monitoring tools.

#. MESHAT: A MONITORING AND EXPERIENCE SHARING TOOL 10

A PLATFORM FOR TUTORS AND STUDENTS

We have designed a customised platform called MEShaT (see Figure 4). It proposes different interfaces according to the learning actor: a project group, a student or a tutor. Every interface consists of the following.

1. A monitoring tool (on the form of a dashboard) which helps the concerned actor to have a global view of their activity. 2. A publication tool which allows the spread of their experience. Three dashboards are offered; two for students (one to monitor the progress of their project and the other one to monitor their own learning process) and one for tutors (to monitor students' and groups' activities and students' learning).

• The project monitoring dashboard is a project management tool meant for the group and shows various indicators: the group's frame of mind (e.g. motivation, satisfaction, relationship with the client), the Gantt diagram, tasks to realise and the percentage of realisation, the working time of each member, the deliverables to produce and the delays. This tool is dedicated to the group leader for the project steering, to the members to situate themselves regarding the others and to express themselves. The indicators provide information to students for the metacognitive processes described below and to tutors for the monitoring of teamwork.

• The metacognitive tool takes into account students' individual point of view of their cognition, metacognition, motivation and behaviour so as to build reflexive indicators. Concerning cognition, students evaluate themselves in relation to the target competencies in project management (hard and soft) as well as to the ones necessary for the project realisation. They define the planning, the sub-goals and the learning strategies required to acquire these competencies. Regarding metacognition, students express their feeling about competencies and knowledge acquisition (level, form, context, judgment). Students more precisely

#. MESHAT: A MONITORING AND EXPERIENCE SHARING TOOL

11

describe their motivation about their self-efficacy, the value and the interest of the tasks and the required effort. They also formalise their behaviour by explaining how they engage in help-seeking strategy and the way they handle task difficulties and demands. We consider that it is important to reflect all these indicators to students so as to help them to build an individual reflection on the relevance of the knowledge they acquire, on the modalities of this acquisition and on their behavioural changes.

• The activities and learning monitoring tool is meant for tutors and shows information on the individual students' activity and the groups' activity thanks to indicators such as the group orientation, leadership, monitoring, feedback and coordination. These indicators are built thanks to the information given by students in the individual and group dashboards described above. Tutors therefore have access to all the information on student and group activities and can intervene when needed. The history helps them to understand the individual and group processes, to intervene with the students in an adapted way and to assess the students' work.

The publication tools are blogs and TE-Cap.

• Blogs (one per student and one per group) are spaces where students can freely describe, for example, the realisation contexts of their actions and their frame of mind. These blogs help the group members and the tutors to understand the project context, to explain the value of some indicators (as delays or the group's frame of mind) and so to anticipate or to solve problems more quickly.

• TE-Cap is offered to tutors to allow the emergence of a CoP composed of all the tutors who monitor a project. The indexation model is built on three main subjects, corresponding to the different types of expertise required for tutors: (1) their roles and tasks;

(2) the project calendar (so as to coordinate); and (3) the specific progress of every group. By exchanging, tutors will acquire expertise on their roles and knowledge on their application ground. TE-Cap can be considered as an expertise transfer tool.

A fixed section shows information accessible by all the actors: the schedule and the learning contract. The schedule helps students and tutors, of the same or different groups, to coordinate their activities. The learning contract defines simple questions for students such as: 'What do I want to learn? How will I learn this? Who can give support? When can I start? How will I know that I have learned? How will others realise that I have learned?' These questions are defined at the start of the project and are used to focus students' attention on the educational objectives throughout the project. This contract could be useful not only for students but also for tutors. Tutors can also refer to these kinds of questions to refocus on their roles. It is a means to coordinate tutors who have to implement the same educational means.

The information on the dashboards can be modified by their owner(s) and are not visible for everybody. Students can modify their blog and their individual dashboard by means of a data entry interface. The groups' dashboard is updated by the project leader, using individual information. Leaders confirm the data and decide what is published on the blog. The tutors' dashboard is directly updated by them and automatically updated according to the information entry on the groups' and students' interfaces. Tutors also contribute directly to the CoP. Tutors have access to the groups' and students' interfaces. The project leaders have no access to the individual dashboards of their group members. The learning contract cannot be modified during the course progress. It is updated at the end of the project, according to the events which were related on blogs and on TE-Cap.

MEShaT is meant for the complex educational context of project-based learning, using the Kolb's learning process. The metacognitive tool, the blogs, TE-Cap and the learning contract, favour the reflexive observation and concrete experience phases of the Kolb's cycle, the monitoring tools help action phases (conceptualisation and experimentation). Moreover, MEShaT solves some of the problems identified in Section 2.2. Monitoring tools and blogs facilitate groupwork, group cohesion and the professionalism of students by making the consequences of their acts more tangible and by informing them. Metacognitive tools and blogs help students to acquire knowledge and reinforce their motivation (by a better understanding of what they have to do and why they do it). If these phenomena do not naturally appear, tools will help the tutors to make them emerge. Indeed, MEShaT reinforces the tutor-student link by allowing the continuous monitoring of the knowledge acquisition process. It also helps tutors to assume some of their roles, like their roles of relational coach and social catalyst (concerning groupwork or leadership), their role of intellectual catalyst (by asking precise and conceptualised questions to incite students to discuss or ask critical questions) and their roles of expert and pedagogue. Moreover, the association of Te-Cap with the learning contract offers tutors a space for refining or developing their expertise.

CONCLUSION AND FUTURE DIRECTIONS

Our work aims to study how KM methods and Web 2.0 tools can be useful in face-to-face or blended project-based learning activities. We propose to make use of them to design a monitoring and expertise transfer tool proposed to tutors and students. To understand better the needs and expectations of each actor, we are especially interested in the case of project management training. Indeed, this type of learning is complex since it has for an objective the acquisitions of soft and hard knowledge and relies on rich and varied social organisations. In the first part of this article we described a course that has been designed according to the experiential learning theory and based on an expanded learning circle. We then expose the observed problems, like the lack of monitoring and expertise transfer tools, which involve important dysfunctions in the course organisation and therefore dissatisfaction for tutors and students (in particular about the acquisition of knowledge and expertise). The study of existing tools highlights two points:

1. There is no tool which helps both tutors and students.

2. There are no clear strategies proposed to acquire, transfer and capitalise on the actors' experience. Indeed, studied tools do not offer metacognitive functions, formal or informal publication tools (such as knowledge books or blogs) or tools to support CoP.

Therefore, to solve this problem, we propose to associate personalised monitoring tools (one for the project group, one for the student and one for the tutor) with tools for the transfer of experience and the acquisition of knowledge. Regarding the monitoring: the 'team feedback' is a dashboard for the project management, the 'student feedback' is a metacognitive tool and the 'tutor feedback' is a monitoring tool for individuals' and groups' activity. The tool for the acquisition of knowledge considers two types of knowledge: the acquired experience is formalised in a kind of knowledge book called a 'learning contract', the experience being acquired is revealed and capitalised in blogs (for students and project groups) and within a CoP supported by TE-Cap (for tutors). We describe their articulation in a platform: MEShaT. This platform is dedicated to project management education but can also be used to support different types of face-to-face project-based learning activities. Indeed, all the phases of the Kolb's cycle are taken into account. Furthermore, it supports the acquisition of various experiences: those of the individuals (students and tutors) and those of the social organisations (project group, CoP of tutors). Our future work will consist of testing this platform over a long time so as to experimentally validate our hypotheses. We will also observe how the actors (students, tutors and course designer) appropriate this type of technology and how they participate in the redefinition of their roles.

ACKNOWLEDGEMENT

The author would like to thank René Peltier, director of Airbus KM service (Toulouse) until 2007, for his help in the adaptation of KM methods for our context.

7.

Figure 2 -

 2 Figure2-The expanded learning circle[START_REF] Berggren | Rethinking project management education: Social twists and knowledge co-production[END_REF]

Failure

  Figure 3 -Observed problems

Figure 4 -

 4 Figure 4 -MEShaT: Monitoring and experience sharing tool for project-based learning


Francesco Dell' Isola A N D Kolumban

A qualitative analysis of the dynamics of a sheared and pressurized layer of saturated soil

Keywords: saturated binary mixture, soil-water interaction, sheared saturated soil, soft basal sliding, thermodynamic stability, singular perturbations

A layer of a saturated binary mixture of soil and water, both of which are true density preserving, is considered. This layer is subjected from above to normal and shear tractions and an inflow of water, and from below to drainage of water and abrasion of till from the rock bed. Sliding processes along the top and bottom interfaces, as well as deformational creep of the sediment and water constituents within the layer generate heat, but here the purely mechanical problem is analysed. We study the steady-state plane flow with vanishing abrasion and balanced inflow and drainage of water. The differential equations governing the horizontal creep flows of the sediment and water decouple from the equations describing the vertical profiles of the vertical water velocity and the solid volume fraction. A stiff second-order ordinary differential equation is shown to describe the distribution of the latter; it genuinely depends on the inflow of water, the fluid viscosity and the thermodynamic pressure, a variable not present in classical formulations and introduced by Svendsen and Hutter in 1995. The singular nature of this equation is resolved by methods of matched asymptotic expansions.

It is shown that in conformity with thermodynamics in the sediment layer, two regions of more dense and less dense solid fraction arise, one of which is a boundary layer. This boundary layer is formed where the fluid enters the sediment layer. Moreover, by using the thickness of this boundary layer as the internal length parameter, we find several constitutive equations for the thermodynamic pressure which adequately describe this creeping flow problem. Viewed as a model for the saturated till layer below ice sheets, the analysis shows that the question of whether soft basal sliding may develop catastrophically is a question of thermodynamics rather than dynamics.

Introduction

In dell [START_REF] Dell' Isola | What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets?[END_REF], referred to henceforth as I, we presented a saturated binary mixture model of a granular solid and fluid both of which are true density preserving. This model may serve for the description of the dynamics of the thin sediment-water layer below temperate glaciers or ice sheets (see figure 1). In particular, it was shown that the water and till flow within this layer was governed by the [START_REF] Dell' Isola | Continuum mechanical modelling of the dissipative processes in the sediment-water layer below glaciers[END_REF][START_REF] Dell' Isola | What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets?[END_REF].

water inflow from the ice sheet above it, the drainage of water into the rock bed, and the amount of till abraded at the rock-bed interface. The redistribution of mass by the flows of water and sediment within the layer is governed by the force balances of these two constituents; in these balances internal friction and interface friction at the ice-sediment-layer interface and the rock-bed interface are essentially balanced by the pressure and driving shear stresses exerted by the ice sheet from above. The latter are so dominant that gravity forces within the layer can be ignored. The lubrication is provided to the system primarily by the melting processes due to the geothermal heat, the heat generated by viscous dissipation and the work done by the Darcy forces within the layer, and the heat generated by the viscous sliding of the ice over the ice-sediment interface. It was further made clear in I that a binary mixture model of viscous constituents was needed for properly describing the thermodynamically coupled processes, and that the earlier models by [START_REF] Macayeal | Irregular oscillations of the West Antartic Ice Sheet[END_REF], [START_REF] Kamb | Rheological nonlinearity and flow instability in the deforming bed mechanism of the ice stream motion[END_REF] and Alley et al . (1987a, b) were likely to be too simple to properly describe the difficult thermomechanical problem.

In § 5 of I, it was made plausible that steady plane shear flow of water and sediment in a layer of constant depth in which the horizontal and vertical velocity components are assumed to be functions only of the vertical coordinate, is likely to form a wellposed boundary-value problem; however, no explicit solution was constructed. In this paper we focus our attention on a very similar problem; our emphasis will now be to construct explicit solutions to a certain boundary-value problem that still contains the essential ingredients of the shear flow that prevails in the till layer below ice sheets. However, we focus attention on the across-layer solid volume fraction profiles, how they form as a result of the across layer water flow, which is an essential ingredient of the subglacial till mechanism. We shall demonstrate that the ther-modynamic stability condition and the dynamic equations of balance of mass and momentum constrain the functional behaviour of the thermodynamic pressure of the solid constituent.

The equation from which this result is derived is an ordinary differential equation for the distribution of the solid volume fraction across the layer. Genuine quantities describing this equation are the across-layer fluid-flow rate, the fluid viscosity and the thermodynamic pressure of the solid constituent. In classical theories of saturated soils, the latter two are both ignored (see, for example, [START_REF] Vulliet | Set of constitutive models for soils under slow movement[END_REF][START_REF] Drew | Averaged equations for two-phase flows[END_REF][START_REF] Drew | Application of general constitutive principles to the derivation of multidimensional two-phase flow equations[END_REF][START_REF] Mackenzie | The generation and compaction of partially molten rock[END_REF]. This equation is second order in the spatial derivative, and the term with the highest derivative is small, giving reason for the use of matched asymptotic expansions. We demonstrate that for Stokes flow, thermodynamic restrictions place this boundary layer at the top of the layer. The solid volume fraction is highest at the rock-bed interface; it is practically constant throughout the layer but quickly decreases as the upper boundary is approached. This demonstrates that the boundary layer develops where the water enters the layer.

Beyond this result, this application of the model also offers guidelines as to the estimation of explicit expressions for the thermodynamic pressure as a function of the solid volume fraction. These functional relations are obtained from requirements of the thickness of the boundary layer. The problem as such does not introduce an internal length scale; the boundary-layer thickness which we choose to be 10 -3 -10 -2 m (i.e. of the order of several particle diameters) serves as this length scale. In fact, its thickness is related to the exact value of the flow rate from above, and the above figures correspond to 10 -3 -10 0 m a -1 as incoming velocity. Together with the thermodynamic stability requirement that the Helmholtz free energy be a convex function of the solid volume fraction, its choice determines the qualitative behaviour of the thermodynamic pressure as a function of the solid volume fraction; it must possess a strong (exponential-like) singularity at a finite value of the solid volume fraction in order that the internal length scale assumes physically meaningful values. We offer explicit proposals for this dependency. Experiments ought to isolate the correct choice.

In § 2 we present the governing equations specialized for the problem at hand. To fully understand equations (2.1), (2.9) and (2.12) the reader may have to consult I; however the remaining text is disjoint from I and self-consistent. Section 3 presents the asymptotic analysis for steady-state conditions and shows that the two-point boundary problem for the solid volume fraction profile is singular; techniques of matched asymptotic expansions are used to solve it. These methods are then also used in the specification of the constitutive relation for the thermodynamic pressure in § 4. In § 5 we summarize our findings and draw inferences.

Governing equations

To list the governing equations that form the basis of this study, let Oxyz be a Cartesian coordinate system with origin O, horizontal axes (x, y) and vertical axis z pointing upwards opposite to the direction of gravity. Consider a layer bounded by z = f b (x, y, t) (bottom surface) and z = h(x, y, t) (top surface) and of infinite horizontal extent. Let this layer be filled by a saturated mixture of sediment and water. The solid volume fraction, the velocity fields of the fluid and solid and the temperature field within this layer are driven by the mass, momentum and energy conservation conditions at the bounding surfaces; they are derived in I and are linked to processes of ice-sheet flow for z > h(x, y, t) and bedrock deformation for z < f b (x, y, t). Here we treat the input quantities at z = h(x, y, t) and at z = f b (x, y, t) as prescribed, and we ignore temperature variations, i.e. consider isothermal conditions, since our focus is a qualitative analysis of the till-layer behaviour.

We restrict considerations to plane flow and thus ignore the third, y-coordinate. Moreover, we suppose all process quantities except the saturation pressure to be independent of the horizontal x-coordinate, so that the z-coordinate and the time t will remain as the only surviving independent variables. The analysis will show that with these prerequisites the solid volume fraction profile as well as the horizontal velocity profiles of the till and the fluid within the layer can be determined analytically and/or numerically as functionals of the input quantities.

Time-independent steady conditions prevail, if abrasion of till from the bedrock is ignored, the incumbent pressure is time independent and the drainage of water equals the constant inflow of melt water from above. This steady problem, special as it is, will allow in-depth analysis of the processes and thus provides hints as to the proper parametrization of some of the constitutive equations arising in the model.

From § 2, formula (20), of I, we deduce the following reduced forms of the balances of mass and momentum for the solid and the fluid:

∂ν ∂t + (νw s ) = 0, - ∂ν ∂t + ((1 -ν)w f ) = 0, (-νβ s -νp + µ s w s ) + (p + (1 -ξ s )β s )ν -ν(1 -ν)α(w s -w f ) = 0, (-(1 -ν)p + 4 3 µ f w f ) -(p + (1 -ξ s )β s )ν + ν(1 -ν)α(w s -w f ) = 0, -ν ∂p ∂x + (µ s u s ) -ν(1 -ν)α(u s -u f ) = 0, -(1 -ν) ∂p ∂x + (µ f u f ) + ν(1 -ν)α(u s -u f ) = 0, in z ∈ (f b , h), t > 0,                                      (2.1)
in which the prime denotes differentiation with respect to z, and the various symbols have the following meaning: ν is the solid volume fraction; u s , u f are the horizontal velocity components of the solid and fluid, respectively; w s , w f are the vertical velocity components of the solid and fluid, respectively; p is the saturation pressure; β s (ν) is the thermodynamic pressure; ρf , ρs are the true fluid and sediment mass densities; µ f , µ s are the (apparent) fluid and solid viscosities; α =: ρf g/K; a := ρf /ρ s ;

ξ s := ρ s ρ = ν ρs ν ρs + (1 -ν)ρ f = ν ν + (1 -ν)a ;
g is the gravity constant; and K is the soil permeability. The thermodynamic pressure β s (ν) is related to the inner free energy ψ I (ν, ϑ = const.) via

β s (ν) = (ν ρs + (1 -ν)ρ f ) ∂ψ I ∂ν (ν, ϑ = const.) (2.2)
and will henceforth be written as

β s = β 0 + βs (ν), βs (0) = 0. (2.3)
In the ensuing analysis we shall propose explicit expressions for the function β s (ν); this must be done in conformity with the thermodynamic stability requirement that ψ I is a convex function of ν. Thus ∂ 2 ψ I /∂ν 2 must always be positive semi-definite; this implies

dβ s dν -β s 1 ν + b 0, b = a 1 -a , (2.4)
a condition which must be satisfied by every constitutive relation for β s . Equations (2.1) are six partial differential equations for ν, p, w s , w f , u s , u f , of which the first four are decoupled from the remaining two. Moreover, it follows from (2.1) 5,6 that ∂p/∂x does not depend on x, so that p is linear as a function of x.

Equations (2.1) must be complemented by boundary and initial conditions. Before we turn to these, let us transform (2.1) to an analytically more convenient form. Adding (2.1) 1,2 and integrating the resultant equation over z yields

νw s + (1 -ν)w f = W 0 C (t), (2.5)
where W 0 C (t) is an integration constant, a function of t, called the vertical component of the composite velocity.

Next, by summing (2.1) 3,4 and integrating the resulting equation over z one obtains the saturation pressure in the form

p = -νβ s + µ s w s + 4 3 µ f w f + p 0 (t).
(2.6)

Evaluating p and substituting the resulting expression into (2.1) 3 or (2.1) 4 leads to the following equation:

ν F (ν) -ν( 4 3 µ f w f ) + (1 -ν)(µ s w s ) -ν(1 -ν)α(w s -w f ) = 0, (2.7)
where

F (ν) := (ν -ξ s )β s -ν(1 -ν) dβ s dν .
(2.8) Equations (2.1) 1 , (2.5) and (2.7) form a well-posed initial boundary-value problem (IBVP) for ν, w s and w f , provided the inflow of the fluid (melting rate) at the top boundary, (1-ν(h, t))w f (h, t), and abrasion rate at the bottom boundary, νw s (f b , t), are a priori known, the incumbent pressure, p i (t), at the top surface is given and the drainage function at the bottom interface, (1 -ν(f b , t))w f (f b , t), is prescribed. In addition, an initial distribution for the volume fraction, ν(z, 0), must be prescribed, and the kinematic conditions be obeyed that (i) the top boundary moves with the solid particles, whereas (ii) the bottom interface velocity coincides with the bottom abrasion rate. These requirements can be expressed by the following statements.

(1) At the top interface z = h(t):

w f (1 -ν) = V f0 , ∂h ∂t = w s , -αν l p i = -ν(β s + p) + µ s w s , -(1 -αν l )p i = -(1 -ν)p + 4 3 µ f w f ,              (2.9)
in which V f0 is the volume flow per unit area of water from the top into the layer (see I, formula (61)). The first of (2.9) is a mass balance, the second a kinematic statement, and the third and forth combine the continuity of the traction condition across the top surface with the postulate of how this traction is divided amongst the constituents (see I, formulae (32), ( 33), in which l = 2 3 ). Adding (2.9) 3,4 and using (2.6) implies that p i (t) = p 0 (t).

(2.10)

With this result and (2.6), relations (2.9) may be rewritten as follows:

w f (1 -ν) = V f0 , ∂h ∂t = w s , C 1 := (ν -αν l )p i + ν(1 -ν)β s -(1 -ν)µ s w s + 4 3 νµ f w f = 0.        (2.11) (2) At the bottom interface z = f b (t): ∂f b ∂t = -w b = - M b s ρ r , (1 -ν) sgn(w f -w b )(w f -w b ) = M b f ρf = m b f ρf σ 4 f , ν(w s -w b ) = - M b s ρs                  (2.12)
and

σ f := (1 -ν)p -4 3 µ f w f . (2.13)
Here ρ r is the rock density and M b s /ρ r the abrasion rate, while M b f /ρ f is the drainage rate of water into the rock bed. (2.12) 1 is the kinematic equation and (2.12) 2,3 are jump conditions of mass, and a constitutive relation for the drainage function proposed in I, formula (52), has been used. Note, that requesting vanishing abrasion rate makes the bottom-interface location steady, so that z = 0 may be identified with it. In this case (2.12) reduce to

w b = w s = 0, (1 -ν)w f = m b f ρf σ 4 f , at z = 0. (2.14)
If at the same time ν, V f0 and p i are also time independent then (2.1) 1 and (2.11) 1 imply

(1 -ν)w f = V f0 ∀z ∈ [0, h],
(2.15) and thus M b f /ρ f = V f0 , which in our application is negative. (3) Initial conditions t = 0. As ∂ν/∂t, ∂f b /∂t and ∂h/∂t are the only field variables of which the time derivatives appear in the field equations, initial conditions must be imposed for these. We shall denote them by ν 0 (z), h 0 and f b0 .

We conclude this formulation of the problem by making plausible that the above IBVP is well posed. To this end let ν(z, t 0 ) be known and evaluate (2.5) at the bottom and top interfaces at t = t 0 ; this yields

ν(f b )w s (f b ) + (1 -ν(f b ))w f (f b ) = W 0 C (t 0 ), ν(h)w s (h) + (1 -ν(h))w f (h) = W 0 C (t 0 ).
(2.16)

Note that from (2.9) and (2.12), w s (f b ) and w f (h) are known because the water inflow at the top and the abrasion rate at the bottom are prescribed. Thus, (2.16) constitutes two equations for w f (f b ) and w s (h) as functions of W 0 C (t 0 ). Next, from (2.11) 3 we see that C 1 depends on w s (h) and w f (h):

C 1 = Ĉ1 (w s (h), w f (h)) = 0.
(2.17) However, recalling from (2.5) that

w s = ν ν 2 (w f -W 0 C ) + w f 1 - 1 ν , ∀z ∈ [f b , h],
(2.18)

we alternatively write

C 1 = C1 (w f (h), w f (h), W 0 C (t 0 )) = 0 and as w f (h) is known, C 1 = Č1 (W 0 C (t 0 ), w f (h)) = 0. (2.19)
Moreover, from (2.12) 2 we may derive

C 2 := (1 -ν(f b ))(w f (f b ) -w b ) - m b f ρf σ 4 f = 0, (2.20) in which σ f is defined in (2.13). This shows that C 2 is a function of w f (f b ), w f (f b ) and w s (f b ), namely C 2 = Ĉ2 (w f (f b ), w f (f b ), w s (f b )) = 0. (2.21)
Using (2.18) at z = f b and (2.16) 1 , we may write instead of (2.21)

C 2 = Č2 (w f (f b ), W 0 C (t 0 )) = 0. (2.22)
Next, consider the equation (2.7) in which w s is replaced by use of (2.5). What emerges is a second-order ODE for w f (z). Two initial conditions for this ODE are obtained from (2.22) and (2.16) 1 . Via integration we obtain

w f = wf (z; W 0 C (t 0 )).
(2.23)

Evaluating the function ∂ wf (•)/∂z for z = h we obtain

w f | z=h = ∂ ∂z wf (h; W 0 C (t 0 )) =: w f (h; W 0 C (t 0 )). ( 2
[µ f ] 2×10 -3 kg m -1 s -1 [|V f0 |] 10 -3 -10 0 ma -1 [H] 1-10 m [β1]
1 0 5 -10 7 Pa α 10 9 -10 11 kg m -3 s -1 m b f 10 -28 -10 -31 kg -3 m 2 s 7

Asymptotic analysis for steady-state drainage and vanishing abrasion rate

Consider equation (2.7) with the specializations (2.14) and (2.15):

ν F (ν) -ν( 4 3 µ f w f ) + ν(1 -ν)αw f = 0, (1 -ν)w f = V f0 , (3.1)
in which α may, but need not, be treated as constant. Introducing the scalings

z = [H]z, w f = [V f0 ] wf , µ f = [µ f ]μ f , F(ν) = [β 1 ] F (ν), (3.2)
in which the bracketed terms have fixed values of a typical order of magnitude for the variable which they are scaling, and the variables (•) are dimensionless, equations (3.1) can be transformed to the following dimensionless second-order ODE:

ν F (ν) ν + δ f μf 1 1 -ν -η f = 0, (3.3)
in which primes are redefined as (•) = d/dz and

δ f : = 4 3 [µ f ][|V f0 |] [H][β 1 ] = O(10 -20 -10 -17 ), η f : = α[|V f0 |][H] [β 1 ] = O(10 -7 -10 -4 ).        (3.4)
The coefficients δ f and η f are dimensionless quantities determined exclusively by the scales and by α of which the above estimates were obtained using the values in table 1 as suggested in I. Both coefficients are small and the differential equation (3.3) defines a singular perturbation problem. A more convenient form of (3.3) is obtained by the transformation

y = 1 1 -ν , h(y) := - F ((y -1)/y) (1 -y)y , y ∈ [1, ∞); (3.5) then (3.3) becomes (μ f δ f )y + (h(y) + μ f δ f )y -η f = 0. (3.6) It follows also from (2.8) that h(y(ν)) = -(1 -ν) 3 βs 1 ν + b + d dν βs , (3.7)
which is an explicit dependence on ν. The differential equation (3.6), even though it is determining the solid mass distribution in the layer, is governed by the viscosity of the fluid. If the latter is constant, μ f = 0, and μf = 1, so that

δ f y + h(y)y = η f (3.8)
describes the constant fluid-viscosity case. Imposing inviscidity of the fluid implies δ f = 0 and reduces (3.8) to first order. Likewise, assuming no inflow (and no outflow) through the layer, V f0 = 0, implies δ f = 0 and η f = 0, whence y = 0 or ν(z) = const. Apart from this the equation is chiefly governed by thermodynamics of the solid, as h is given by (3.7) in terms of βs and d βs /dν. In the geophysical geotechnical literature (see, for instance, [START_REF] Drew | Averaged equations for two-phase flows[END_REF][START_REF] Ehlers | Constitutive equations for granular materials in geomechanical context[END_REF], βs is not even introduced and the fluid is in most cases assumed to be inviscid, so that η f would have to vanish. This then would mean that V f0 had to vanish in this case: no water flow across the layer would be permissible.

Returning to the full equation (3.6) or (3.8), we now impose the boundary conditions. At the top interface (2.11) 3 must hold; eliminating w f and w s in the third of these equations and non-dimensionalizing the resulting equation yields

(ν -αν l ) p i [β 1 ] + βs ν(1 -ν) + δ f μf νν (1 -ν) 2 = 0, at z = 1.
(3.9)

At the bottom boundary (2.12) must hold, of which the steady state reduction takes the form

(1 -ν)w f = V f0 = - m b f ρf σ 4 f , at z = 0. (3.10)
Substituting in turn relation (2.13) for σ f and equation (2.6) for p, and non-dimensionalizing the resulting expression as before, yields

(1 -ν) p i [β 1 ] -βs ν(1 -ν) + δ f μf νν (1 -ν) 2 -F = 0, at z = 0, (3.11)
where

F := V f0 ρf m b f 1/4 1 [β 1 ]
O(10 -1 -10 0 ), (3.12)

and an estimate for F has been determined with the aid of table 1. Introducing the transformation (3.5), (3.9) and (3.12) take the forms

-δ f μf y + 1 y βs - 1 y -1 p i [β 1 ] + y y -1 F = 0, at z = 0, -δ f μf y + 1 y βs + 1 -α y -1 y l-1 p i [β 1 ] = 0, at z = 1,          (3.13)
in which βs is now regarded as a function of y, and p i and F are prescribed. The differential equation (3.6) and the boundary conditions together define a nonlinear two-point boundary-value problem (TPBVP) which we will solve as δ f → 0, in which case it is prone to develop boundary layers either at the top or at the bottom interfaces, and in principle such layers are possible at the interior of the interval z ∈ [0, 1]. The question of where the boundary layer forms is one of thermodynamics, as it will depend on the sign and form of the function h(y) in y ∈ [1, ∞) and, consequently, can be traced back to the functional form of the Helmholtz free energy. The question is non-trivial because h(y) is a first-order (linear) differential operator in βs through (2.8). In the linear case, when µ f = 0 and the coefficient h = h(z) of the first-order derivative in the considered ODE is a function of z only, then h > 0 (h < 0) locates the boundary layer at z = 0 (z = 1), and when h changes sign at z = zT ∈ [0, 1] such that h(z T ) = 0, there is a transition layer near zT (see Bush 1992, p. 155), where this computation is done explicitly.

To corroborate this qualitative behaviour of the above nonlinear singular perturbation problem we solve (3.8) subject to the boundary conditions: y(0) = y 0 , y(1) = y h , with y 0 > y h .

(3.14)

These boundary conditions imply ν(0) > ν(1) which is the physically expected behaviour. The inequality can be qualitatively inferred from (3.13) (see Appendix A).

The outer solution of (3.8) takes the form

H(y, y * ) + C 0 = η f (z -z * ), with H(y, y * ) := y y * h(ȳ) dȳ, (3.15)
where C 0 is a constant of integration. Suppose now that h(y) > 0 ∀y ∈ [1, ∞) and assume that the boundary layer is at z = 0. Then writing z = δ p f ζ, accordingly transforming the differential equation (3.8), balancing the terms on the left-hand side and applying the principle of least degeneracy (see Bush 1992, p. 159) yields p = 1 and

d 2 y dζ 2 + h(y) dy dζ = δ f η f (3.16)
as the transformed ODE in the stretched coordinates. Its lowest-order solution in the limit η f δ f → 0 can be obtained by dropping its right-hand side, implying the first integral dy dζ + H(y, y * ) = C 1 , (3.17) and the second

ζ = y 1 dȳ C 1 -H(ȳ, y * ) + C 2 . (3.18) At z = 0, i.e. ζ = 0, y = y 0 , which fixes C 2 so that ζ = y y 0 dȳ C 1 -H(ȳ, y * ) . (3.19)
Matching this solution with the outer solution requires that, as

ζ → ∞, y → y h . Thus +∞ = y h y 0 dȳ C 1 -H(ȳ, y * ) . (3.20)
The integrand must therefore be non-integrable at the upper limit ȳ = y h ; the necessary condition for this to hold is

C 1 = H(y h , y * ), (3.21) so that -∞ = y 0 y h dȳ H(y h , y * ) -H(ȳ, y * ) . (3.22)
Moreover, to have this equal to -∞, H(y h , y * ) < H(y + h , y * ). So, as y h is the smallest value which y can attain, H(y, y * ) is monotonically increasing in y, and thus h(y) is indeed positive. Repeating this analysis for h ≶ 0 and y h ≶ y 0 we find that, irrespective of whether y h > y 0 or y h < y 0 : (1) the boundary layer is at z = 0, if h > 0; (2) the boundary layer is at z = 1, if h < 0.

This demonstration is not a rigorous proof that the same properties also apply when (3.8) is being solved subject to the two boundary conditions (3.13), but we take the position that alternatives are unlikely; indeed in Appendix A we parametrize the solution of the ODE (3.8) in terms of the variables y 0 and y h and prove that no further singularity arises when mixed boundary conditions like (3.13) are considered.

Here it suffices to state that with (3.17) and (3.21) we have

dy dz (y) = - 1 δ f y y h h(ȳ) dȳ < 0. (3.23)
In absolute value, the largest derivative arises at y = y 0 , the edge of the boundary layer. Since h is monotonically increasing with y, (3.23) implies the bounds

- 1 δ f max y∈[y h ,y 0 ] h(y) (y 0 -y h ) dy dz (y) - 1 δ f min y∈[y h ,y 0 ] h(y) (y 0 -y h ). (3.24)
This allows us to find estimates for y in (3.13) that support the computation in Appendix A.

It is now necessary to use the thermodynamic inequality (2.4) together with (3.7) to see whether h obeys one or both of the above inequalities. It is easy to see that (2.4) and the thermodynamic pressure βs > 0 imply h < 0, thus excluding any boundary layer at the bottom interface.

The specification of βs

The inner solution of (3.8) has the form

ζ = z -1 δ f = y 0 y dȳ H(y 0 , y * 0 ) -H(ȳ, y * ) . ( 4.1)
Assume now that h(y) is bounded ∀y ∈ [y h , y 0 ]; then according to the mean value theorem of integral calculus

H(y 0 , y * ) -H(y, y * ) = -h(y 0 )(y -y 0 ) + o(|y -y 0 |), (4.2)
which upon substitution in (4.1) implies

(z -1) h(y h ) δ f = ln y h /y 0 -1 y/y 0 -1 + O(|y -y 0 |). (4.3)
This equation allows us to estimate h(y 0 ). To this end we note that the right-hand side is negative for y ∈ [y h , y 0 ] for y h < y 0 , and varies from -∞ to 0 with a logarithmic singularity at y h . The thickness of the boundary layer is obviously δ f /|h(y 0 )| and not δ f . To have it of reasonable thickness, i.e. to have it of the dimension of several particle diameters we choose ε = 10 -p , p ∈ [2, 4], where

ε := δ f |h(y 0 )| ⇒ |h(y 0 )| = δ f ε , (4.4)
implying h(y 0 ) 10 -18 -10 -13 with a mean of, perhaps, 10 -15 .

To model this boundary layer we pick two trial functions as examples

(1) h(y) = -exp(-k 1 /ν(y)),

(2) h(y) = -1 + tanh 2 (k 2 /ν(y)).

(4.5)

These trial functions exhibit the fortunate behaviour that explicit analytical expressions for βs can be found (e.g. by maple) which satisfy the thermodynamic stability inequality. These choices are very delicate as the trial functions for βs ,

ν 2m , m > 0; ln(ν * -ν); ν ν -ν * 2n , n > 0; tanh -1 (ν/ν * ), (4.6)
where ν * ∈ [0, 1], lead to values of ε = 10 -p with p > 10. This is physically meaningless, because in physical units the boundary layer would turn out to be of the order of magnitude of 10 -8 m! In other words logarithmic and algebraic singularities of βs at ν * are not sufficiently strong to generate a boundary layer of the order of 10 -3 to 10 -2 m (which would physically be expected). Exponential singularities are needed for βs at the point ν = ν * , and such singularities are exactly obtained with the choices (4.5). We cannot give a systematic rule of how these functions were determined. It was essentially trial and error by selecting either h(y) or βs (y) and determining the other function by using (3.7). The choices needed to be such that the thermodynamic stability requirement was satisfied and ε in (4.4) assumed reasonable values. Using (4.5) in (4.4) yields

(1) h(y 0 ) = exp -

k 1 ν(y 0 ) = 10 -15 ⇒ k 1 13.6, (2) h(y 0 ) = 1 -tanh 2 k 2 ν(y 0 ) = 10 -15 ⇒ k 2 7.2,        (4.7)
with the functions (4.5) being given and definition (3.7) of h(y) in terms of βs and its derivative integration determining βs . The constant of integration β 0 must then be chosen such that the resulting βs function is in conformity with the thermodynamic stability condition. β 0 = 0 in both cases is sufficient for this. We refrain from presenting these results explicitly, because they can easily be obtained by using e.g. maple.

The formulae for βs that are obtained by using (4.5) are very lengthy and inconvenient expressions. Thus it may be advantageous to try to select βs in simple form such that the thermodynamic stability condition (2.4) is satisfied and to determine the function h(y) by differentiation. This we have done in several cases and table 2 gives the selection of five different choices of which one does not conform with the stability condition. For the first choice (a), βs is exponentially decaying as ν → 0 for all k > 0 and assumes a finite value at ν = 1. The corresponding function -h(y(ν)) is zero at ν = 0, very small in its neighbourhood, forms a hump with a maximum at

(a) βs(ν) = exp - k ν OK (b) βs(ν) = (ν + b) 2 exp - k ν OK (c) βs(ν) = 1 (1 -ν) 3 exp - k ν OK (d) βs(ν) = exp 1 1 -ν exp - k ν NO (e) βs(ν) = 1 (νL -ν) γ exp - k ν , γ 3 O K ( a ) h ( y ( ν )) = -(1 -ν) 3 e -k/ν 1 ν + b + k ν 2 OK (b) h(y(ν)) = -(1 -ν) 3 (ν + b)e -k/ν 3 + k b ν 2 + k ν OK (c) h(y(ν)) = -e -k/ν k ν 2 + 1 ν + b + 3 1 -ν OK (d) h(y(ν)) = -(1 -ν) 3 e 1/(1-ν) e -k/ν 1 ν + b + 1 (1 -ν) 2 + k ν 2 NO (e) h(y(ν)) = - (1 -ν) 3 (νL -ν) γ e -k/ν 1 ν + b + γ νL -ν + k ν 2 OK
about ν 0 and finally reaches zero at ν = 1. This qualitative behaviour also persists for the choice (b) of table 2; in fact it can be shown that βs

(ν) = (1 -ν) γ exp(-k/ν), -3 < γ < ∞
generates such a hump for -h(y(ν)), whereas the choice (c) (γ -3) makes -h(y(ν)) monotonically increasing with increasing ν with an algebraic singularity at ν = 1. If βs (ν) is not finite at ν = 1 but has an exponential singularity, the thermodynamic stability condition can no longer be satisfied (case (d) of table 2). Now it can be shown (see Appendix A) that with the hump-like h(y(ν)) the original boundary condition (3.13) at z = 0 cannot be satisfied (as can be easily inferred with the aid of (3.24)); by contrast, however, this is possible for a function h(y(ν)), which becomes singular as ν → ν L , where ν L = 1 in case (d) of table 2. As physically ν = 1 can never be achieved, functions βs (v), and consequently h(y(ν)), must be modified as shown in item (e) of table 2, in which ν L is a constitutive quantity (a constant) with a value of approximately 0.8-0.85.

Concluding remarks

In this paper a layer of saturated binary-mixture of soil and water, of which both are true density preserving, is considered. This layer is subjected from above to the overburden pressure of the overlying ice and the shear traction exerted by its horizontal movement. Melt water from the ice above is pressed into the layer. At the lower boundary, the rock bed, abrasion of till may add sediment mass to the layer and drainage of water contributes to a true filtering process from above through the layer, thereby affecting the sediment concentration profile and influencing the effective resistance of the layer to horizontal shearing. It turned out that the determination of the vertical flow plus the vertical profile of the solid volume fraction uncouple from those of the horizontal flow (except for the abrasion rate), and ignoring the abrasion rate led to a steady problem if also the bordering tractions were assumed to be time independent.

The analysis of this steady problem is interesting because it shows that the distribution of the solid volume fraction across the layer is determined by the vertical water transport through the layer, the viscosity of the water and the constitutive equation for the thermodynamic pressure of the solid. All three are lumped together in one differential equation for the solid volume fraction profile (see (3.6) or (3.8)). In a theory ignoring the thermodynamic pressure, i.e. assuming the Helmholtz free energy to be independent of the solid volume fraction-this is so for most von Terzaghi type theories (see [START_REF] De Boer | Highlights in the historical development of the porous media theory[END_REF][START_REF] Mackenzie | The generation and compaction of partially molten rock[END_REF][START_REF] Ehlers | Constitutive equations for granular materials in geomechanical context[END_REF] and others)-this equation collapses to a physically non-acceptable statement, implying that the effect of the filter flow on the distribution of the solid volume fraction cannot be studied †.

The problem is also interesting because the differential equation exhibits boundarylayer structure; the boundary layer grows linearly both with the fluid viscosity and the water transport across the layer. However, it is also influenced by the behaviour of the thermodynamic pressure as a function of the solid volume fraction. This function must satisfy the thermodynamic stability criterion that the Helmholtz free energy is a convex function of the solid volume fraction, and this condition constrains the boundary layer to be at the top rather than at the bottom surface (when the granules are rock material and the fluid is water). This property has important glaciological implications, because high solid volume fraction concentrations are to be expected at the (abrading) bed. This high value is reduced through the boundary layer, so that under Stokes flow conditions the larger part of the layer has relatively large values of the solid volume fraction, conditions which favour low shear velocities within the layer. Conversely, if the boundary layer were at the bottom surface, where the solid volume fraction is minimal, the larger part of the layer would have low solid volume fraction, making the layer weak to shear deformations.

This physical mechanism has never been envisaged by geologists and glaciologists who deal with the destabilization of an ice sheet such as West Antarctica (see, for example, Alley et al . 1987a, b;[START_REF] Macayeal | Irregular oscillations of the West Antartic Ice Sheet[END_REF][START_REF] Kamb | Rheological nonlinearity and flow instability in the deforming bed mechanism of the ice stream motion[END_REF]and others). In I, the previous formulations might have been too simple and might have missed some destabilizing mechanisms that enhance the potential for the disintegration of the West Antarctic Ice Sheet. We proved in I by applying a systematic mixture model [START_REF] Svendsen | On the thermodynamics of a mixture of isotropic materials with constraints[END_REF] that additional processes contribute to this destabilization, but did not give a direct demonstration. However, we proved in the present paper that a classical mixture theory which ignores the dependence of the Helmholtz free energy on the solid volume fraction is too simple to discover the behaviour, and † Indeed, (3.10) reduces in this case to y = αH 2 /µ f = 1/ε ( 10 15 ), of which the solution subject to y(0) = y 0 , y(1) = y h produces a solid volume fraction profile which at z = 1 2 is larger than unity, ν( 12 ) 1 + 8ε, which is physically meaningless.

Proc. R. Soc. Lond. A (1998)

Figure 1 .

 1 Figure 1. A sketch of the thermodynamic processes affecting the saturated till layer below ice sheets. The arrows on the right indicate the mass flow of water and sediments into and out of the layer, those on the left indicate the flow of heat. The various boxes describe the physical processes that are specified by the mathematical model of dell' Isola[START_REF] Dell' Isola | Continuum mechanical modelling of the dissipative processes in the sediment-water layer below glaciers[END_REF][START_REF] Dell' Isola | What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets?[END_REF].

Table 1 .

 1 ), and so w s (h) is now known from (2.16) 2 . Since the vertical velocity profiles of the solid and fluid are thus fully determined we may evaluate at time t = t 0 . A forward step in time now determines v, h, f b at time t = t 0 + ∆t. Thus the problem is well posed.From this point onwards we now suppose steady conditions with vanishing abrasion rate and time-independent incumbent pressure. Characteristic values of physical quantities

	.24)

Table 2 .

 2 Properties of functions βs and corresponding functions h which do (OK) or do not (NO) satisfy the thermodynamic stability criterion

Proc. R. Soc. Lond. A (1998) 454, 3105-3120 Printed in Great Britain

Proc. R. Soc. Lond. A (1998)

we show how thermodynamic completion of such a model does allow this expected behaviour.

Future analyses will have to include acceleration terms and the abrasion process and thus focus on time-dependent behaviour.

K.H. acknowledges financial support by the Alexander von Humboldt Foundation and the Max Planck Society through the Max Planck Prize. We thank Professor L. W. Morland for his thorough review.

Appendix A.

In this appendix we demonstrate that the boundary conditions (3.14) are in conformity with the boundary conditions (3.13), provided βs is chosen accordingly. The required properties βs must fulfil are (1) βs (ν) → 0, exponentially as ν → 0,

(2) βs (ν) → ∞, algebraically, with a power γ 3 for ν → ν L , where ν L ∈ (α -1/(l-1) , 1).

To see this, consider the boundary condition (3.13):

The boundary layer is located at z = 1, and |y | is very large and needs to be estimated. Such an estimate follows from (3.23) and takes the form

At z = 0, i.e. y = y 0 , the term y in (A 1) 1 is given by (3.8) with δ f = 0, while at z = 1 (A 2) must be substituted in (A 1) 2 , implying

or, after some trivial manipulations, βs

However, in the case of constant viscosity, μf = 1, and as in the physically admissible range for y we have

F. dell' Isola and K. Hutter (see (3.12)), these relations become (approximately)

) which imply (under the above-stated general properties for βs , which are, for instance verified by the example given in case (e) of table 2) that

Indeed, the factor of p i /[β 1 ] on the right-hand side of (A 5) 2 must be non-positive, implying (A 6) 2 . Moreover,

appearing in (A 5) 2 , must be sufficiently negative to counterbalance the last addend on the right-hand side. Because of the second itemized property of βs , this is possible for all y ≈ y L (ν ≈ ν L ).