Introduction

Section C (the present document) is about science, more precisely the basics of research through explanatory definitions and three research approaches (quantitative approach, qualitative approach, and mixed methods approach). Indeed, the students who are interested in the humancentred design have to know the scientific methods used along the design process. Section D will deal with ethical considerations in research and Section E with article writing.

Human-Centred Research & Design for Inclusive Mobility. Section C-Doing Science

Section C deals with the aspects of research which can be useful to the students and future research candidates interested in the design of human-centred technologies and services, humanmachine systems, and socio-cyber-physical systems. Some general concepts related to science and research are defined in the first chapter ( § C.1). Next, three kinds of research approaches of human and social sciences are described, namely, the quantitative, qualitative and mixed methods research approaches ( § C.2); indeed, these approaches are widely used along the design process of human-centred technologies, particularly in the phases of needs analysis, specifications, tests and evaluations (Figure 2). The conclusion is about the concept of validity.

C.1 The Scientific Démarche

We sometimes hear in conversation "We, in science, we…", where "we" is a student, a teacher or a researcher in mathematics, engineering & technology, physics or computer science and the audience someone who comes from human and social sciences. And yet, history, literature and psychology (for example) are also sciences taught at university. Therefore, it may be that, even among researchers, there is a misconception concerning what science is.

The two first divisions ( § C.1.1 and § C.1.2) deal with science-related definitions in order to get things straight and establish a frame of reference for the present work.

C.1.1 General Definitions

C.1.1.a Science, Scientific

From a dictionary viewpoint, for example, Merriam-Webster 4 or Collins 5 , science is defined as knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method or, merely, a body of facts learned by study or experience, whereas knowledge refers to understanding, comprehension. But regarding the value of truth, there are other viewpoints, more circumspect, for instance that science is "imperfect and fallible" and can "tolerate lack of truth," it can be seen as "a practical way to increase our ability to predict and control the natural world, and does not carry the ambition of finding underlying 'truths' of nature" (Zimring,p. 59).

In a general way, it is admitted that science refers to bodies of knowledge and research to the practice aiming at increasing knowledge; it is also admitted that all academic areas have their bodies of knowledge.

Science as practice can also be connected to characterizations of conduct, for example, rigorous 4 Merriam-Webster.com Dictionary: https://www.merriam-webster.com/ 5 Collins Online Dictionary: https://www.collinsdictionary.com/ science (Casedevall & Fang, 2016), cultural practice [START_REF] Višňovský | Science as cultural practice[END_REF], or ethical conduct [START_REF] Niemi | Six challenges for ethical conduct in science[END_REF].

Scientific can be seen as a "label" that qualifies concepts that are inherent in science, for example, "to apply a scientific method to test ideas about canoe history" [START_REF] Luukkanen | The bark canoes and skin boats of Northern Eurasia[END_REF] or "all scientific explanations are tentative" [START_REF] Clark | What is a science[END_REF]; the word 'scientific' also applies to multitude of other concepts such as attitude, thinking and reasoning, or proof and evidence (e.g., the everyday scientific reasoning scale, [START_REF] Golumbic | Establishing an everyday scientific reasoning scale to learn how non-scientists reason with science[END_REF].

C.1.1.b Research

The Merriam-Webster dictionary provides the following definition: "investigation or experimentation aimed at the discovery and interpretation of facts, revision of accepted theories or laws in the light of new facts, or practical application of such new revised theories or laws6 ."

C.1.1.c Discipline

Simply said, a discipline is a field of study 5 . Ferris (2004) said that science and discipline could be seen as interchangeable when they describe a particular means of knowing. But, to be less general, an academic discipline can be seen as a subject matter of teaching and research (e.g., Biglan, 1973a) or as, noticed by [START_REF] Krishnan | What are academic disciplines? Some observations on the disciplinarity vs. interdisciplinarity debate[END_REF], a branch of science which has most of the following characteristics: a particular object of research (e.g., society) even though it can be in common with another discipline; a body of specialist knowledge referring to the object of research; theories and concepts which organize the accumulated knowledge; specific terminologies or a specific technical language adjusted to the object of research; specific research methods; and institutional manifestation (teachings, academic departments, professional associations).

Academicians tend to perpetuate the belief of a dichotomy between hard and soft sciences, which does not correspond to the spirit of the categorization by subject matter in academic areas proposed by Biglan (1973a[START_REF] Biglan | Relationships between subject matter characteristics and the structure and output of university departments[END_REF]. Indeed, the studies that he carried out among scholars from a university and a small college of North America to judge academic areas show that these areas could be characterized along three main dimensions which are the following:

i/Existence vs. absence of a clearly delineated paradigm (a paradigm referring to a body of theory to which all members of a field adhere according to Biglan who cited Thomas Kuhn7 ). This dimension was the most prominent (in terms of explanatory variance), it distinguishes areas such as physical and biological sciences on one hand of the axis from areas such as humanities and education sciences, on the other hand; hence Biglan's differentiation between hard, paradigmatic academic areas and soft, nonparadigmatic areas.

ii/Concern with application is a pure-applied dimension distinguishing disciplines that are concerned with practical application of their subject matter (e.g., education sciences, engineering sciences) from academic areas that are "pure" (e.g., mathematics, zoology).

iii/Concern with living systems as objects of study such as psychology and botany on one hand, vs. nonlife systems such as astronomy and computer science, on the other hand.

Disciplines have also cultural, at least, community-based dimensions; the persistent idea of hard vs. soft science based on a hypothetical order of value is one example, for instance, hard is good, soft is bad (see the review of [START_REF] Shapin | Hard science, soft science: A political history of a disciplinary array[END_REF]; the similar idea of science vs. nonscience to demarcate academic areas is also an example of the cultural dimension of disciplines (see [START_REF] Zimring | What Science is and how it Really Works[END_REF], for his brief history of science vs. nonscience).

C.1.1.d Interdisciplinarity

Tackling complex real-world problems (e.g., energy crisis, famine, pandemics, marine pollution, cyber-criminality, etc.) requires researchers to adopt a holistic view, cross the borders of are brought together at the end, for example, in the form of separate chapters in a report.

 Interdisciplinarity means that scientists work jointly (they interact, coordinate, etc.) but research is still disciplinary specific based.

 Transdiciplinary work implies that scientists developed a shared approach and a common conceptual framework to solve the research problem that they have defined together.

Transdisciplinarity provides a more comprehensive level of understanding (see [START_REF] Lawrence | Deciphering interdisciplinary and transdisciplinary contributions[END_REF]. It may include non-academic, societal actors (see [START_REF] Lawrence | Characteristics, potentials, and challenges of transdisciplinary research[END_REF].

According to the above categorization, it is obvious that the best way for science to deal with major environmental and societal issues and contribute achieving the 17 sustainable development goals8 is transdisciplinarity.

C.1.1.e Technology and Innovation

The Collins dictionary 5 says that "technology refers to methods, systems, and devices which are the result of scientific knowledge being used for practical purposes." Not only science and technology are therefore interdependent, but also they are interdependent with innovation [START_REF] Brooks | The relationship between science and technology[END_REF]). An innovation is "an idea, practice, or object that is perceived as new by an individual or other unit" [START_REF] Rogers | Diffusion of Innovations[END_REF], and innovation is often associated with development (e.g., [START_REF] Silvestre | Innovations for sustainable development: Moving toward a sustainable future[END_REF] or prosperity (e.g., EIC, 20229 ). We said earlier that the students of today will be the innovators of tomorrow10 ; in fact, even though not all of them will be inventors, Aeronautics and Space Administration (NASA) to assess the evolution of an idea from the first thought to the full deployment of a product 15 . Since then, the scale has been improved and formalized to provide a useful tool in R&D in general, it has even inspired the development of other scales (see Bruno et al., 2022 and[START_REF] Sprenkeling | Bridging social and technical sciences: Introduction of the Societal Embeddedness Level[END_REF]. Indeed, technology readiness alone is not sufficient to assess the maturity of the technology. Even though TRL and SRL are close when innovations are technological, they do not overlap, they remain two models of maturity (Bruno et al., 2022), while the examination of societal embeddedness cannot be done independently of the level of technological readiness [START_REF] Sprenkeling | Bridging social and technical sciences: Introduction of the Societal Embeddedness Level[END_REF].

C.1.2 The Basics

Science is about gathering facts, constructing explanations, and building knowledge. In that sense, it is obvious that most of academic disciplines fall under science and are thus concerned with the scientific démarche 18 .

C.1.2.a The Steps in Research

Whatever the discipline, scientific research generally follows the following path: observation of an issue or need to understand some phenomena or facts; definition of the research question; collection of data from experimentations, focus groups, surveys, computer-based simulations 19 , etc.; data analysis; interpretation; conclusions with regard to the research problem; return to knowledge and facts (in the form of new knowledge or new facts); new questions (Figure 4). It is worth noting that not only the results should be made public, but also the methodology used and, when possible, the data collected; the former contributes to increasing knowledge, the latters to enabling others to reproduce the study or carry out further analyses (we will come back to this in Section D). Hence the necessity to write up the methodology without leaving out a single detail.

18 https://www.collinsdictionary.com/dictionary/english/demarche 19 For example, the four-color conjecture of Francis Guthrie, formulated in 1952 (in the form that "every map drawn on a sheet of paper can be colored with only four colors in such a way that countries sharing a common border have different colors", Appel & Haken, 1977, p. 108), was proven to be true in 1976, by a computer with a program written and many times modified by Appel and Kaken since 1972

C.1.2.b Exploration or Hypotheses

Research can be characterized in many ways: 2017) who used qualitative analyses (multidimensional scaling, cluster analysi s) of quantitative data (verbal statements who were sorted and rated) in a participatory study that aimed to identify the organizational actions required to ensure patient -centred care 21 Induction refers to "a form of reasoning, also called empirical induction, in which a general law or principle is inferred from particular instances that have been observed" (Colman,p. 373), whereas in deduction a particular conclusion is drawn from a set of premises (Blackburn, 2016, p. 122) 22 According to Jackson and Christensen (2014), "theory often refers to a generalization or set of generalizations that are used systematically to explain some phenomenon" 23 Also, the qualitative approach is not confined to soft sciences ("soft" in accordance with the definition of Biglan, 1973a[START_REF] Biglan | Relationships between subject matter characteristics and the structure and output of university departments[END_REF], e.g., observational techniques are used in ethology (i.e., a branch of biology); and the quantitative approach is not reserved to hard sciences, e.g., hypothesis testing is often used in psychology



C.1.2.c Research Question

The research question helps the researcher along the path of the scientific démarche of which it is a part. Developing a good research question is even the most important part of the research process [START_REF] Lipowski | Developing great research questions[END_REF].

According to [START_REF] Cummings | Conceiving the research question and developing the study plan[END_REF] o use open-ended questions, i.e., that do not provide a set of responses.

Source:pixabay.com  Research questions and hypotheses in quantitative research refer to relationships among variables. For example, a research question could be "Can the theory of planned behaviour (e.g., [START_REF] Ajzen | The theory of planned behavior[END_REF] explain the relationship between pedestrians' self-confidence and their behaviour with regard to basic safety rules for crossing railway lines?"; a resulting hypothesis could be "The higher the level of pedestrians' perceived self-confidence, the quicker the decision to cross the railway line." Creswell and Creswell (2018, pp. 137-) recommend to:

o Define the goal of the studies, both research questions and hypotheses depending on that goal: either i/comparing groups on an independent variable to see the impact on a dependent variable or ii/relating variables, i.e., relating one or more independent variables to one or more dependent variables, and iii/describing responses to the independent, mediating, or dependent variables. See below for more details on variables.

o Use the same pattern of words' order in research question and hypotheses to ease the identification of major variables.

C.1.2.d Hypothesis

In a general way, a hypothesis is "a proposition as a supposition, rather than asserted that serves a tentative of explanation of certain facts. A hypothesis is "a prediction about a specific event or relationship between variables" (Creswell & Creswell, 2018, p. 52). Before going further, some clarifications about variables are provided by :

 The independent variable (IV)-also named the experimental variable (which is varied or manipulated by the experimenter)-influences or affect the outcome of an experimental study. The dependent variable (DV) is the outcome or result of the influence of IV. A predictor or antecedent variable is used to predict an outcome of interest in a survey method study. An intervening or mediating variable transmits the effect of an IV on a DV 24 . A moderating variable is a predictor variable that impacts on the relationship B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH between IV and DV (demographic variables such as age and gender are often considered as moderating variables instead of major independent variable).

Also referring to Creswell and Creswell (2018, p. 137):

 A null hypothesis "makes a prediction that in the general population, no relationship or no significant difference exists between groups on a variable"  If the null hypothesis is rejected (i.e., the statistical test does not show relationship or significant difference between groups) then the alternative hypothesis is considered:

o The directional alternative hypothesis (one-tailed) makes a directional prediction (e.g., higher, lower, more, less, etc.);

o The nondirectional hypothesis (two-tailed): the direction is not specified.

C.2 Doing Science

This chapter described three types of research approaches -qualitative, quantitative, and mixed methods -more in detail than in the previous chapter. Let us (i) emphasize that one or other of these approaches is adopted at almost each phase of the process of designing human-centred technologies and human-centred socio-cyber-physical systems (see Figure 2); and (ii) recall that human-centrality is one of the pillars of Industry 5.0 (the others are sustainability and resilience) (see [START_REF] Breque | Industry 5.0: Towards a Sustainable, Human-Centric and Resilient European Industry[END_REF][START_REF] Renda | Industry 5.0, a Transformative Vision for Europe: Governing Systemic Transformations Towards a Sustainable Industry[END_REF].

The choice of an approach mainly depends on the goal of research and the research question, rather than on the researcher's discipline. Nevertheless, the choice may also depend on the researcher's worldview, which is often attached to a discipline or a particular branch of a discipline, a worldview being a general philosophic orientation about the world, composed of beliefs and values acquired and shared through communities' memberships (e.g., Creswell & Creswell, 2018;Duffy & Chenail, 2011;[START_REF] Yilmaz | Comparison of quantitative and qualitative research traditions: Epistemological, theoretical, and methodological differences[END_REF].

For example, the postpositivist worldview relies on a deterministic philosophy 25 , hence the (positivist) researcher aims to "identify and assess the causes that influence outcomes" (Creswell 25 Stanford Encyclopedia of Philosophy (https://plato.stanford.edu/). "Determinism: the world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law". T here is the belief that "every event is necessitated by antecedent events and conditions together with the laws of nature."

B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH & Creswell, 2018), for instance through experimental designs. Another example of worldview is the constructivism: the researcher adopts the view that individuals and groups construct their own reality and knowledge, the key point is thus the meaning they make of their experiences and world; the goal of the researcher is then to "rely as much as possible on the participants' views of the situation being studied" (Creswell & Creswell), for instance through interviews with open-ended questions, i.e., that do not provide a set of responses, the participants responding with their own words. Finally, mixed methods research that combines or mixes ideas from both qualitative and quantitative research [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF] is rather a matter of pragmatism, that is, "what is important and justified or 'valid' is what works in particular situations in practice" [START_REF] Johnson | Educational Research. Quantitative, Qualitative, and Mixed Approaches[END_REF], the focus being on the research problem and the approaches to understand it (Creswell & Creswell, 2018). However that may be, the choice of data collection techniques may just depend on the availability of financial/time/human resources.

Each approach is described below with the data collection techniques that we think to be relevant to human-centred design (but some techniques are utilizable in qualitative and quantitative research, e.g., questionnaires).

C.2.1 Qualitative Research

C.2.1.a Purpose

Researchers who wish to have a deep understanding of a particular phenomenon or experience within a specific context are likely to adopt qualitative research, more precisely qualitative analysis of data (see Table 2). It can be characterized as follows:

 In-depth examination of the experience or perceptions of individuals, group/society phenomena, expectations, interests, indifference, hostility, etc. within a specific context, in short, any subject that may give rise to attitudes and behaviours in that context, which the researcher wants to understand without concern for generalization [START_REF] Aspers | What is qualitative in qualitative research[END_REF]Creswell & Creswell, 2018;[START_REF] Flick | The SAGE Handbook of Qualitative Data Analysis[END_REF][START_REF] Ravitch | Qualitative Research. Bridging Conceptual, Theoretical, and Methodological[END_REF]Thomas & Malgivy, 2011).

And according to Creswell and Creswell:

 Mainly in natural settings;

 Open-ended forms of data;

 Focus of the participants' meanings;

 Researchers' concern for how their personal background, culture and role may shape the direction of the study;

 Holistic perspective on the research problem.

C.2.1.b Data Collection Techniques

Data collection techniques for qualitative are almost always used in face-to-face interaction with the study community and the study participants, they focus on data collection at the sociocultural collective level and individual level, and through two possible ways: observation or interviewing that is, data are what the researcher sees or what is told to the researcher, respectively (Given, 2008, p. 520).

Focus Group

The focus group technique (FG) can be used at almost all levels of the human-centred design process (Figure 2).

-Need analysis (i.e., identification of the needs and expectations of the stakeholders involved in the design and deployment of the technology, they include the end users). For example, see [START_REF] Cano | Needs analysis to design an English blended learning program: Teachers' and administrators' voices. Profile: Issues in Teachers' Professional Development[END_REF];

-Specifications (i.e., activity that includes the transcription of the needs and expectations into technical specifications). For example, see [START_REF] Demiris | Facilitating interdisciplinary design specification of 'smart' homes for aging in place[END_REF];

-Tests and evaluations of concepts and prototypes; for example, see [START_REF] Kinnaird | Focus groups for functional InfoVis prototype evaluation: A case study[END_REF].

The goals of focus group discussions are to understand questions related to social interaction process, attitudes, opinions and experiences in specific groups and contexts, how knowledge and ideas develop and operate in a given cultural or group context (Ravitch & Carl, 2020, pp. 147-148). Exchanges and interactions enable them to debate controversial topics, for example, ethical issues of technologies (ethics being a questioning of moral standards26 ) or other debatable topics.

Discussions within focus groups are conducted by a skilled interviewer (also named moderator or facilitator) whose role is to ask questions, prompt answers and manage the flow of talk (Scott,p. 252) A focus group is relatively a small group: in addition to the moderator, it involves from three to about ten participants; the more sensitive the topic of discussion and/or the more vulnerable the participants, the more appropriate the smallness of the group size (e.g., [START_REF] Barbour | Doing Focus Groups[END_REF][START_REF] Ravitch | Qualitative Research. Bridging Conceptual, Theoretical, and Methodological[END_REF][START_REF] Smithson | Focus groups[END_REF]. Focus groups are not appropriate when the topics may be seen as personal or sensitive by the participants [START_REF] Smithson | Focus groups[END_REF].

Focus group discussions are audio-or video-recorded (video-recording also records the nonverbal aspects of a discussion), then transcribed, then coded (at least one coder to limit interpretation biases and errors) -for example with NVivo qualitative data analysis software27 -and analysed.

The use of a software to process qualitative data "enables a researcher to demonstrate the integrity, robustness, and therefore, trustworthiness of an investigation" (Given, 2008, p. 563), the latter being often questioned, especially by positivist researchers (e.g., [START_REF] Shenton | Strategies for ensuring trustworthiness in qualitative research projects[END_REF] (and yet it is the trustworthiness of both qualitative and quantitative research that is challenging).

Vandemeulebroucke et al. ( 2019) provide an example of analysis of focus group discussions about the ethical issues of socially assistive robots as perceived by older adults (target users). [START_REF] Duboz | Exploring the acceptance of connected and automated vehicles: Focus group discussions with experts and non-experts in transport[END_REF] used the technique of focus group for online discussions on the acceptance of connected and automated vehicles (also interesting, their paper provides in an annexe the script for the moderators).

Interviews

Focus group discussions is a form of interview, except that in the three forms of interview described in this chapter the interviewer addresses only one person, which is thus appropriate when dynamic between stakeholders is not essential or when there is no interest in group norms (e.g., [START_REF] Mack | Qualitative Research Methods: A Data Collector's Field Guide[END_REF]. The goal of interviewers is to try eliciting information or expressions of opinion or belief from the participant, face-to-face or remotely, e.g., by telephone (e.g., [START_REF] Brinkmann | The interview[END_REF]. It is emphasized in the Sage encyclopedia of qualitative research methods [START_REF] Given | The SAGE Encyclopedia of Qualitative Research Methods[END_REF]) that interviewing cannot be used in thinking that it would be the easiest way to do research, but it is a mistake; the qualities that interviewers should have are interest in the perspectives of other people and the skill of listening [START_REF] Patton | Qualitative Research & Evaluation Methods: Integrating Theory and Practice[END_REF]. Whatever the form of interview, a document directs the interviewer, it is the interview guide (used in focus group discussions too), see [START_REF] Given | The SAGE Encyclopedia of Qualitative Research Methods[END_REF] and [START_REF] Patton | Qualitative Research & Evaluation Methods: Integrating Theory and Practice[END_REF]; it is also useful for the collection of reliable, comparable qualitative data [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF]. The interview guide (or agenda) includes the questions or at least the topics to be explored during the interview, as well as instructions. The research question drives an interview, the goal of the set of questions is therefore to provide answers to the research question: the researcher has to iii/conversational interviews are time consuming. Nevertheless, this form of interview can be used to characterize the context of use of a technology and identify users' needs, as well as during the test and evaluation phase, complementary to quantitative analysis. For example, see: [START_REF] Demirbilek | Universal product design involving elderly users: A participatory design model[END_REF]; [START_REF] Prange | User requirements for assistance of the supporting hand in bimanual daily activities via a robotic glove for severely affected stroke patients[END_REF].

 Relatively structured interviews: the questions are exactly those of the interview guide and they are asked in the same standardized way for all respondents, which leads to answers that can be compared, even quantified (see [START_REF] Brinkmann | The interview[END_REF]. The interviewer cannot improvise, which is suitable when the researcher and the interviewer are not the same person, see Wood et al. (2003) who conducted a study comparing structured interviews with children conducted by a human interviewer vs. a robot interviewer. Structured interviewing is appropriate when the range of replies of the participants is well-known, when it is not the case, semi-structured interviews are better [START_REF] Maguire | Methods to support human-centred design[END_REF]. and should lead the participant to concrete descriptions rather than abstract reflections; [START_REF] Given | The SAGE Encyclopedia of Qualitative Research Methods[END_REF] adds that concrete descriptions are obtained with "what" and "how" questions (rather than with "why"). The interview guide specifies the order of questions (or topics) to be covered [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF], preferably moving from more public questions to more personal matters [START_REF] Willig | Introducing Qualitative Research in Psychology (3 rd edition)[END_REF]. Willig wrote that restating the participant's comments showed that the interviewer had listened; besides, it is an opportunity to check mutual understanding. The master's thesis of Navarrete describes the use of semi-structured interviews for user requirement elicitation in the human-centred design process [START_REF] Navarrete | User requirements elicitation: A comparison between generative techniques and semi-structured interviews[END_REF].

Many authors (e.g., [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF]Johnson & Christensen, 2004;[START_REF] Mack | Qualitative Research Methods: A Data Collector's Field Guide[END_REF][START_REF] Ravitch | Qualitative Research. Bridging Conceptual, Theoretical, and Methodological[END_REF] consider that recording interviews (with permission) is very important and taking notes also. Recording involves transcription, essential for those who intend to carry out a non-superficial analysis of data: consider therefore the costly step of transcription before drawing the research design. In addition to audio-or video-records of the interview, taking notes (of participants' behaviour, contextual cues, etc.) -when it is possible and when it does not distract the participants may be useful for the debriefing that follows an interview, even more for data coding and analysis.

The above-mentioned work of Navarrete ( 2020) is very useful to understand how to prepare semistructured interviews, code and analyse data.

Questionnaires

According to de [START_REF] De Leeuw | Self-administered questionnaires and standardized interviews[END_REF], self-administered questionnaires mainly differ from interviews by i/the absence of the interviewer (therefore no encouragement regarding motivation to answer and no extra-explanation) and ii/the fact that the respondents see the questions (which requires a particular attention regarding the formulation and presentation of the questions).

Moreover, interviews transcripts are qualitative (text), whereas questionnaires can deal with both qualitative and quantitative data and analysis; questionnaires are less costly (time and resource), a great deal of information can be collected in a short period of time from a lot of people, and they are appropriate for sensitive questions. But, along these advantages, [START_REF] Ravitch | Qualitative Research. Bridging Conceptual, Theoretical, and Methodological[END_REF] notice some disadvantages, among them: responses can be inaccurate because of the bias of social desirability28 ; it may happen that not many thought goes into the responses, which can affect their accuracy; understanding of the questions may differ from the researcher's point of view.

A

Observation

According to the Sage encyclopedia of qualitative research methods, observation implies that the researchers (whether their research is qualitative or quantitative or between the extremes) collect impressions using their senses, especially looking and listening, in a systematic way to learn about a phenomenon of interest (Given, 2008, p. 573). Concretely, observation consists in watching observations were carried out). Combined with observation, the think-aloud technique may be useful in the evaluation phase of the human-centred design process; it consists in asking the participant to think aloud-i.e., "to verbalize his or her thoughts and why he or she is performing certain actions" while interacting with or using the object of evaluation [START_REF] Burnes | Human-centred design[END_REF]

C.2.2 Quantitative Research

According to [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF], the concept of 'quantitative' in research refers to quantitative data (i.e., quantifiable, countable, measurable) or quantitative analysis (e.g., statistical analysis) or both (see Table 2). This chapter focuses on quantitative analysis of both qualitative and quantitative data.

C.2.2.a Purpose

The purpose of carrying out research with quantitative analysis is to describe situations or phenomena, establish relationships between variables 30 , or attempt to explain causal relationships between variables (Mertler, 2016, p. 108), which can be translated into the following types of research question: descriptive, comparative, associative relationship, and causal relationship questions (see Creswell & Creswell, 2018;[START_REF] Onwuegbuzie | Linking research questions to mixed methods data analysis procedures[END_REF].

The focus on only some variables makes quantitative research different from the holistic nature of qualitative research.

Figure 5 recaps that the research question determines the appropriate method: globally, surveys enable the researchers to answer their questions about "a quantitative description of trends, attitudes, and opinions of a population, or tests for associations among variables of a population, by studying a sample of that population", while experiments 31 enable the researcher to answer questions about the impact of manipulated variables on outcomes of interest after having kept all other variables constant (Creswell & Creswell, 2018, p. 147). In any quantitative research statistical procedures are used for data analysis and interpretation [START_REF] Mertler | Introduction to Educational Research[END_REF]: descriptive studies consist of the summary of quantitative and qualitative data (mean, standard deviation, frequency distribution, etc.) and graphics, whereas the others include inferential statistics that allow the researcher to make generalizations about the population from which a sample is selected [START_REF] Gravetter | Essentials of Statistics for the Behavioral Sciences 10 th ed[END_REF].  True experiments with experimental group(s) and control group, and random assignment of the participants to groups; depending on authors, true experiments also include random selection, i.e., "the process of choosing, in random fashion, individuals for participation in

The so-called Likert scales are ordinal scales responses that can be ranked or ordered; but it is not possible to measure the distance between the values, the intervals between values cannot thus be presumed to be equal, which implies that means cannot be calculated, which limits inferential statistical procedures to non-parametric tests such as Chi-square or Mann-Whitney U tests (Allen Seaman, 2017;[START_REF] Jamieson | Likert scales: How to (ab) use them?[END_REF]. The use of a visual analog scale enables the researcher to measure perceptions, it is more practical in terms of data analysis and provides unambiguous results.

The study of [START_REF] Tsironis | Comparative usability evaluation of three popular MOOC platforms[END_REF] about the evaluation of MOOC platforms is an example of gathering data of both objective and subjective nature in an experimental study:

-Goal: to evaluate the usability of MOOC platforms; The study of Shangavi, Zhang, and Jeon (2023) is another example:

-Goal: to examine the impact of auditory display urgency and the driver's affective state on driving task performance and quality in semi-automated cars with a study with a simulator.

-IVs:

o Affect: induced anger vs. neutral affect (between-group),

o Auditory warning of requested take over, with various frequencies and numbers of repetitions, i.e., a total of 9 alerts (within-group).

-DVs:

o Take over performance and quality through: speed, deceleration, steering angle, lane change direction (driving task data) and eye-tracking data regarding the use of mirrors (number of glances, gaze duration), o Scores at an affective state questionnaire (7-point Likert-type scale).

addition of qualitative date to a quantitative design: integration or combination rather addition is the main characteristics of mixed methods research [START_REF] Creswell | A Concise Introduction to Mixed Methods Research[END_REF].

According to Creswell & Creswell (2018), the research question directly addresses this mixing, that is, a mixed method study ideally contains at least a qualitative research question, a quantitative question and a mixed methods question, the latter addressing the integration or combination of the qualitative and quantitative data, at least in convergent mixed methods

C.3 Conclusion

Section C is a view over the concepts of science and research which are useful to the students who wish to deal with the design of human-centred technologies and services, not only for designing inclusive mobility, but also all human-centred technologies and services at the time of Industry 5.0.

This section is far from being exhaustive. For example, validity has not been described earlier, even though both quantitative and qualitative research are concerned with validity (even though what the concept covers is different because the matter of generalization does not concern qualitative studies).

According to Mertler (2016, pp. 138-140), internal validity in quantitative research refers to "the degree to which measured differences on the dependent variable are a direct result of the manipulation of the independent variable, whereas external validity refers to "the extent to which results of particular study is generalizable, or applicable, to other groups or settings." [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF] provides a more global definition of validity, in social sciences, it refers to "the accuracy and trustworthiness of instruments, data, and findings" (p. 53). See also [START_REF] Whittemore | Validity in qualitative research[END_REF] for an in-depth discussion about validity in qualitative research.

Validity, trustworthiness, integrity, and so on, all have to see with ethical research, which is the topic of Section D-Ethical considerations.

  This document is a sequel to the working paper titled "Human-Centred Research & Design for Inclusive Mobility. Sections A & B" and published at HAL Science 1 , the French open-access repository. The whole work consists of five sections. Section A presents the French establishment Université Polytechnique Hauts-de-France (UPHF) 2 and the Laboratory of Industrial and Human Automation Control, Mechanical Engineering and Computer Science (LAMIH UMR CNRS 8201) 3 . The context of the work is described in terms of inclusive mobility, particularly regarding the human-centred design of technologies dedicated to human mobility and handicapped people. Section A also presents the technical and scientific equipment dedicated to mobility and transport at LAMIH. Section B explains two human-centred theoretical approaches to design technologies and services dedicated to human mobility in the time of Industry 5.0. As a reminder, according to the European Union, the European industry will serve society better by complementing the techno-economic vision of Industry 4.0 (digitalization, AI technologies, efficiency and flexibility of production) with the Industry 5.0 perspective which focuses on human centricity, sustainability and resilience.

Figure 2

 2 Figure 2 Human-centred design approach: the human (users, operators, stakeholders) is almost at all levels of the design process. Source: Rajaonah, 2022, p. 33

Figure 3

 3 Figure 3 Al-Khwarizmi (pixabay.com)

A

  human-centred perspective on R&D requires to consider the society, what Innovation Fund Denmark 16 did by creating the Societal Readiness Level (SRL) scale that assesses the adaptation of a social or technical innovation to the society, as well as the social acceptance of innovations. The Legal Readiness Level (LRL) scale proposed by Bruno et al. (2022) considers a specific aspect of this adaptation to the society through the examination of the compliance of innovations with legal, regulatory and ethical issues. Sprenkeling et al. (2022) go beyond the readiness of innovations by aiming for their embeddedness in society. They propose a four-level tool named Social Embeddedness Levels (SEL) which connects technological and societal dimensions in the assessment of innovations during the development process. Societal dimensions concern the impact on the environment, stakeholders' involvement, policy and regulations, and market and financial resources.

  Qualitative vs. quantitative research or mixed research. According to Creswell and Creswell (2018): o In qualitative research, the researcher aims to explore or understand "the meaning individuals or groups ascribe to a social or human problem"; o In quantitative research, the researcher aims to test "objective theories by examining the relationship among variables"; o Mixed research involves both.  Bernard (2006) clearly distinguished qualitative vs. quantitative data, and qualitative vs.quantitative analysis (Table2).

Figure 4

 4 Figure 4 Doing science in a few words

  , research questions are good if they can confirm, refute or extend previous findings, or provide new findings; and also they should be relevant to scientific knowledge and future research. Research questions emerge from observed problems, or findings in owns' or others' prior studies. It requires that the researcher master the published literature in the scientific areas of interest, as well as the new trends, ideas and techniques. Concretely, based on Creswell and Creswell (2018), research questions could be categorized into two categories:  Research questions in qualitative research refer strictly speaking to questions to be answered by the research, they are neither objectives nor a priori hypotheses based on established theories. They comprise central research questions (one or two questions) and subquestions (no more than five to seven subquestions) following each central question. An example of central research question could be "How the personality of rail users can shape their safety behaviour in railway stations?" Creswell and Creswell recommend to: o focus the central question on a single phenomenon or concept;o begin the research questions rather with "what" and "how" than with "why" to restrain the researcher from thinking in terms of cause-and-effect relationships; o use exploratory verbs (e.g., to report, to describe, to discover, to generate, to seek to understand, to explore a process) and use them as nondirectional words (examples of "directional" verbs used in quantitative research are: to affect, to influence, to impact, to determine, to cause, to relate);

  have that in mind not to lose sight of the research question, hence the usefulness of the interview guide (e.g., Willig, 2013). Three forms of interviews are usually distinguished:  Relatively unstructured interviews: suit to fieldwork where the interviewer cannot know in advance what is going to happen and who will be present, most of questions flow naturally like during a conversation from the immediate context (the participants may not even realize they are being questioned) i.e., they are not predetermined and vary with individuals and circumstances. Limits pointed out by Patton (2002) are i/the possible difficulty to organize and analyse the data, especially due to ii/the fact that this form of interview is the less systematic and comprehensive, and

  Source: Pixabay.com  Semi-structured interviews are the most often used. Good questions are brief, simple, open,

  qualitative questionnaire (i.e., with open-ended questions) is appropriate in a study involving a few participants; in case of a survey involving thousands of respondents, a particular attention should be devoted to the issue of dealing with open-ended questions, long before the choice of a research design, even though the survey combines open-ended and closed-ended questions. Rahimi and Tafazoli (2022) conducted a study with 12 participants to assess the usability of language massive open online courses; they used a qualitative questionnaire and their paper explains how they analysed the responses.

  people and recording what they do and say. It is carried out either in a natural setting (e.g., observing students in a classroom, pedestrians at a railway crossing, athletes during training) or in the laboratory (for example, to assess the usability of a prototype by observing participants interacting with it). The researcher either participates in the activity of the person-s being studied (participative observation) or does not participate (non participative observation)29 . See the study ofBeede et al. (2020) to understand the use of a large-scale participative observation within the framework of human-centred evaluation of a deep-learning-based system (in total more than 150

Figure

  Figure 5 Quantitative research, schematically

-

  IV: three types of MOOC platform (within-group design); -Collected data include: o Data collected automatically during the task: task duration, success at finding correct webpage and/or controlling to perform the required action, in order to derive measures of effectiveness and efficiency, the latters being DVs, o Responses from 0 to 100 to the ten items of the questionnaire of perceived usability (another DV) for each MOOC platform.

  research. Indeed, Creswell and Creswell distinguished three kinds of mixed methods:  Explanatory sequential mixed methods: quantitative research first, then qualitative research in order to explain the quantitative data;  Exploratory sequential mixed methods: qualitative research in first to explore the views of participants, the resulting information being used to design the quantitative research study, for example, to build an instrument that is appropriate to the sample under study or to specify variables;  Convergent mixed methods: quantitative and qualitative data are merged for a comprehensive investigation of the research problem. The research of Côté-Leclerc et al. (2017)which goal was to investigate how playing adapted sports did affect the quality of life of people with mobility limitations and which was carried out with 34 wheelchair users with paraplegiawas a mixed methods sequential explanatory study. The quantitative step consisted in comparing the perceived quality of life of wheelchair users playing an adapted sport with people without disabilities; the qualitative step included 10 individual semi-structured interviews (respondents were a sample of the 34 wheelchair users). The research of Schröder et al. (2018)which goal was to investigate the mobility behaviour of a rural population of Germany in terms of medical consultations-was a mixed methods exploratory study. The qualitative step consisted of four focus groups and one telephoneinterview (40 persons in total) dedicated to get in-depth opinion from representatives affiliated with mobility in the rural district under study; the quantitative step consisted in a survey questionnaire that was built from the results of the previous study, and distributed to a representative random sample of 1000 adults living in the district. B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH The research of Rouleau et al. (2022) -which goal was to quantitatively and qualitatively assess the acceptability of a virtual patient simulation used in nursing continuous educationwas a convergent mixed methods study. The first step was quantitative, based on an online 80-item survey completed after having consulted the virtual patient (N=27), while the second step was qualitative -but complementary to the surveybased on a focus group with five of the 27 nurses, both types of data being analysed independently; the third step consisted in integrating the quantitative and qualitative results to compare them. See the following references cited by Rouleau et al. to better understand the concept of integration: Fetters et al. (2013), Johnson et al. (2019), and Pluye et al. (2018).

.1.f Research & Development (R&D)

	technology and innovation were pillars of the United Nations 2030 agenda 11 -regrouped the  Research and experimental development 13 "comprise the creative and systematic work
	sustainable goals into macro-goals (see below), which shows that the goals are not independent undertaken in order to increase the stock of knowledge-including knowledge on
	each other, neither are the scientific disciplines that underlie them; it also shows that innovation humankind, culture and society-and to devise new applications of available knowledge."
	(i.e., new ideas, new practices or new technologies) is at all levels of sustainable development,  "R&D is found in the social sciences, humanities and the arts, as well as in the natural
	and therefore concerns all academic disciplines. sciences and engineering."
	 Goals 1-7 (i.e., no poverty, zero hunger; good health & well-being; quality education;  A R&D activity necessarily: aims at new findings (novelty); develops new concepts or
	gender equality; clean water & sanitation; affordable & clean energy) dedicated to the ideas that enhance existing knowledge (creativity); involves uncertainty about the final
	social pillars of sustainable development; outcome in terms of results, costs, and/or time; is "conducted in a planned way, with
	 Goals 8-12 (i.e., decent work & economic growth; industry; innovation & infrastructure; records kept of both the process followed and the outcome (systematic); is transferable
	reduced inequalities; sustainable cities & community; responsible consumption & and/or reproducible, that is, an R&D project should result in the potential for the transfer
	production) dedicated to the economy; of the knowledge, ensuring its use and allowing other researchers to reproduce the results
	 Goals 13-15 (i.e., climate action; life below water; life on land) dedicated to the as part of their own R&D activities."
	environment;
	 Goals 16 and 17 (i.e., peace, justice & string institutions; global partnerships for
	sustainable development) dedicated to governance.
	C.1The dictionary defines research and development (R&D) as being the "studies and tests that are
	done in order to design new or improved products" 5 or the "part of a commercial company's
	activity concerned with applying the results of scientific research to develop new products and
	improve existing one" 4 . But, regarding the definition of innovation, R&D is not only focused on
	technological products and processes.
	According to the Frascati Manual 2015 12 published by the Organisation for Economic Co-
	all, whatever their disciplines, could have a role in innovation, therefore on development and operation and Development (OECD):
	progress due to the mentioned above interdependencies. Precisely, with regard to the 17
	sustainable development goals, Walsh, Murphy and Horan (2020) -who asserted that science,
	B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH

 There are three types of R&D activities: o Basic research, i.e., theoretical or experimental work carried out to acquire new knowledge of the underlying foundation of phenomena and facts, without any application in view; o Applied research, i.e., original research undertaken to acquire new knowledge but primarily directed towards a specific, practical aim; or o Experimental development, i.e., "systematic work, drawing on knowledge gained from research and practical experience and producing additional knowledge, which is directed to producing new products or processes or to improving existing products or processes"; it is just a part of the product development process. There are relationships between these three activities as it is shown in the following example retrieved from the Frascati Manual 2015 (an excellent document that should be read by all students).  Example in language/linguistics: o Basic research: to study how different languages interact as they come into contact each another; B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH o Applied research: to analyse the underlying neurology of languages and language skills acquisition; o Experimental development: to develop a tool for autism diagnosis. C.1.1.

g Technology Readiness and Other Scales Some

  calls for project proposals -e.g., projects funded by Horizon Europe (the European Union's research and innovation framework programme for 2021-2027 14 ) -specify the required degree of development or maturity regarding the innovation of interest; it is often the Technology Readiness Level (TRL). This scale was invented in 1974 at the North American National

Table 1

 1 presents the nine levels of technological readiness (TRL), the nine levels of societal readiness (SRL), and the four levels of societal embeddedness (SEL).

Table 1 . Three scales to measure the degree of maturity of innovations

 1

	Technology Readiness Levels	Societal Readiness Levels	Societal Embeddedness Levels
	TRL	SRL	SEL
	TRL1-Basic principles observed	SRL1-Identification of problem and of societal readiness
	TRL2-Technology concept formulated	SRL2-Formulation of problem, proposed solution(s) and potential impact, and	SEL1-Exploration Societal aspects explored
	TRL3-Experimental proof of concept	identification of relevant stakeholders SRL3-Initial testing of proposed solution(s) together with relevant stakeholders
	TRL4-Technology validated in a lab	SRL4-Validation of proposed solution(s) through pilot testing in relevant environment
	TRL5-Technology validated in a relevant environment	SRL5-Validation of proposed solution(s) by relevant stakeholders in the area	SEL2-Development Societal aspects assessed
	TRL6-Technology	SRL6-Solution(s)
	demonstrated in a relevant	demonstrated in real world
	environment	environment, with relevant
	TRL7-System prototype demonstration in an operational environment	stakeholders to gain feedback SRL7-Refinement of project on potential impact and/or solution and, if needed, retesting in real world	SEL3-Demonstration
	TRL8-System complete and qualified	environment with relevant stakeholders SRL8-Proposed solution(s) as well as a plan for societal adaptation complete and	Societal aspects included in system
	TRL9-Actual system proven in an operational environment	qualified; society ready to adopt the solution SRL9-Actual solution proven in relevant environment	SEL4-Deployment Innovation proven in societal environment
	Bruno et al. (2020); European	Innovation Fund Denmark 17 ;	Sprenkeling, Geerdink, Slob, &
	Commission (2022)	Bruno et al. (2020)	Geurts (2022)

B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH

Table 2 . Qualitative vs. quantitative, the distinction with examples or explanations (Bernard, 2006, pp. 451-452)

 2

	Data
	Qualitative	Quantitative

o Confirmatory research aims to test a priori alternative hypotheses;

o In exploratory research, the researcher attempt to generate some a posteriori hypotheses from the data set.

 Inductive vs. hypothetico-deductive approach 21 . According to

[START_REF] Stebbins | Exploratory Research in Social Sciences[END_REF]

:

o Exploration is primarily inductive, while confirmation is primarily deductive; primarily, not exclusively, that is: when deductive thinking is used in exploratory research, it is rather within the researcher's "emerging theoretical framework" (not within established theory 22 ); and when inductive thinking is used in confirmatory studies, it is to confirm the researcher's "emergent generalizations," not to test a priori hypotheses.

o Qualitative research is thus not confined to exploration: qualitative research can also be confirmatory. In fact, research [in human and social sciences] can be described as qualitative exploratory, qualitative confirmatory, quantitative exploratory, or quantitative confirmatory 23 . 20 See, for example,

Ogden et al. (

  ; see[START_REF] Rose | Usability testing with teens: Adapting human-centered design and UX methods[END_REF] who used this technique with teens in usability testing. Like for focus group B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH discussions and semi-structured and informal interviews, data (participants' comments and behaviour, researcher's field notes) should be coded before analysis.

https://hal.science/hal-03726812

https://www.uphf.fr/en

https://www.uphf.fr/lamih/en Figure 1 Industry 5.0(Breque et al., 2021, p. 13)

https://www.merriam-webster.com/dictionary/research

B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH

Kuhn, T . S. (1962). The structure of scientific revolutions. University of Chicago Press: Chicago. https://psycnet.apa.org/record/1962-35001-000(accessed Jan. 23, 2023). Newtonian mechanics and Einstein's theory of relativity are paradigms of physics, the theory of evolution is a paradigm in biological sciences and behavior ism in psychology

Sustainable Development Goals: https://sdgs.un.org/goals

European Innovation Council (2022), EIC 2023 Work Programme, https://eic.ec.europa.eu/eic-2023-work-programme_en(accessed Feb. 03, 2023)

[START_REF] Rajaonah | Human-Centred Research & Design for Inclusive Mobility. Sections A & B[END_REF], Human-centred research & design for inclusive mobility. Sections A & B, https://hal.science/hal-03726812/

T he 2030 Agenda for Sustainable Development: https://www.un.org/sustainabledevelopment/development -agenda/

OECD (2015). Frascati Manual 2015: Guidelines for collecting and reporting data on research and experimental development. T he measurement of scientific, technological and innovation activities. Paris: OECD Publishing. http://dx.doi.org/10.1787/9789264239012-en

'Research and experimental development' and 'research and development' are here both abbreviated as R&D

https://innovationsfonden.dk/en/about -innovation-fund-denmark

For example, trust in automation can be considered as a mediating variable standing between the level of automation of an industrial robot (IV) and the working partner's reliance on the robot (DV)

See, for example: Ricoeur, 2000;[START_REF] Russ | La pensée éthique contemporaine[END_REF]

https://lumivero.com/products/nvivo/ (accessedMarch 24, 2023)

Piedmont, R.L. (2014). Social Desirability Bias. In: Michalos, A.C. (eds), Encyclopedia of quality of life and well-being research. Dordrecht, T he Netherlands: Springer. https://doi.org/10.1007/978-94-007-0753-5_2746

T he literature is not homogeneous regarding 'participative vs. non-participative observation' and 'participant vs. nonparticipant observation'

Research design is the outline, plan or strategy used to answer the research question[START_REF] Johnson | Educational Research. Quantitative, Qualitative, and Mixed Approaches[END_REF]

B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH a research study, such that every member of the population has an equal chance of being selected to be a member of the sample" (Mertler, 2016, p. 127).

 Quasi-experimental design with control and experimental groups, and partial or total lack of random assignment;  Pre-experimental design with no control group;  Single-subject design (N=1) for which the behaviour of a single individual is observed over time;

 Between-group design: comparison of two or more groups;  Within-group design: repeated measures for different conditions at different times within a group.

Survey Designs

Survey research can be characterized as following, according to Mertler (2016, pp. 112-116):

 Use of a probability sampling technique 33 to ensure that the sample represents the population as accurately as possible;

 Descriptive surveys to describe the characteristics of a sample at one point in time;

 Cross-sectional surveys to examine the characteristics of and differences among several samples measured at one point in time;

 Longitudinal surveys to study the same group of participants at different points in time.

C.2.2.c Data Collection in Quantitative Research

Data are collected from the measurement of dependent variables in order to obtain data of objective nature. Besides, many techniques of data collection mentioned for qualitative research can be used to collect data of subjective nature to be analysed quantitatively (after having coded qualitative data into quantity if necessary). Exploiting data of subjective nature is fundamental in the process of human-centred design. This is how the use of questionnaires is frequent in experimental studies that assess human and technology interactions; indeed, the nature of the information gathered with a questionnaire is subjective even though the responses are in terms of numbers. 33 See, for example, Cumming, 1990;[START_REF] Goodman | Controlled selection-a technique in probability sampling[END_REF] B. Rajaonah Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH To recap, in the two above-mentioned studies the data collected were of both objective and subjective nature, but both data were quantitative. However, even though both quantitative and qualitative data are produced in a study, it is not necessarily a mixed methods study .

C.2.3 Mixed Methods Research

To recap the two previous chapters, quantitative research most often focuses on a few factors, even one factor, and aims to generalize to populations the objective (outsider) look at of samples of these populations, while qualitative research focuses on groups of individualseven on one individualwho construct their own reality and knowledge, and aims to investigate this subjective reality (without a goal of generalization). The mixed research paradigm combines or mixes perspectives of both qualitative and quantitative research [START_REF] Bernard | Research Methods in Anthropology. Qualitative and Quantitative Approaches[END_REF]; it is neither the simple gathering of quantitative data nor the simple


Abdul-Hamid Soubra

Three

Keywords:

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

INTRODUCTION

Over the past twenty years, tunneling in cohesionless soils has been made possible due to recent technological advances including the pressurized shield. Face stability analysis of shallow circular tunnels driven by the pressurized shield requires determination of the pressure to be applied by the shield to ensure the tunnel's face stability and limit environmental impact of tunneling. This pressure must avoid both the collapse (active failure) and the blow-out (passive failure) of the soil mass near the tunnel face. Active failure of the tunnel is triggered by application of surcharge and self weight, with the tunnel face pressure providing resistance against collapse. Under passive conditions, these roles are reversed and the face pressure causes blow-out with resistance being provided by the surcharge and self-weight.

In this paper, the collapse and the blow-out failures are investigated by the upper-bound theorem of the limit analysis theory using respectively collapse and blow-out mechanisms. These mechanisms allow the slip surface to develop more freely in comparison with the available mechanisms given by [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF]. It is to be noted that the upper-bound theorem gives unsafe estimates of the collapse and the blow-out loads. The aim of this work is to improve the available solutions by increasing (respectively reducing) the best available upper-bound solutions given in the collapse (respectively blow-out) case.

KINEMATICAL APPROACH TO THE FACE STABILITY ANALYSIS

The problem can be idealized, as shown in figures 1 and 2, by considering a circular rigid tunnel of diameter D driven under a depth of cover C. A surcharge σ s is applied at the ground surface and a constant retaining pressure σ t is applied to the tunnel's face.

To obtain upper-bound solutions for the collapse and blow-out problems, kinematically admissible failure mechanisms must be considered. According to the normality condition for an associated flow rule Coulomb material, for a kinematically admissible failure mechanism, the velocity along a plastically deformed surface must make an angle φ with this velocity discontinuity [cf. [START_REF] Chen | Limit analysis and soil plasticity[END_REF]].

Failure Mechanisms [START_REF] Davis | The stability of shallow tunnels and underground openings in cohesive material[END_REF] used the upper bound method in limit analysis and developed solutions for the collapse problem in the analysis of tunnel face stability. These authors considered the case of a Tresca material (φ=0°) and their mechanism was composed of two truncated cylinders. Later, [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF] adapted this mechanism to the case of a Coulomb (c, φ) material by replacing the cylinders with cones to respect the normality condition imposed by the upper-bound method of the limit analysis theory. These authors presented solutions for collapse and blow-out problems in the analysis of tunnel face stability. The results they presented showed significant differences with the lower bound solutions presented by [START_REF] Leca | Application du calcul à la rupture à la stabilité du front de taille d'un tunnel[END_REF]. In the current paper, two failure mechanisms M1 and M2 are considered for the tunnel face stability. For both mechanisms, when the total rate of energy dissipation and the total rate of external work are equated, the pressure σ t can be expressed as follows:

s s c t N cN DN σ γ σ γ + + = ( 1 )
Where γ N , c N and S N are non dimensional parameters. They represent respectively the effect of soil weight, cohesion and surcharge loading. Notice that:

0 1 tan = - + s c N N φ ( 2 )
Hence, in the following, only the N γ and N s coefficients will be presented; the N c coefficient can be obtained using (2).

Collapse Mechanism M1

M1 is an improvement of the collapse two-block mechanism presented by [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF]. It is composed of a shearing zone OAB sandwiched between two rigid truncated cones OACD and OBE (Figure 1). The geometrical construction of this mechanism is similar to that of [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF]. The upper rigid cone O'OA with a circular cross-section is truncated by the plane π. This cone is called 'Block I'. It will or will not intersect the ground surface depending on the C/D value. On the other hand, the lower rigid cone O''OE with a circular cross-section is truncated by the plane π' and by the vertical tunnel face. This cone is called 'Block III'. It has an axis inclined at an angle of π/2-β with the horizontal direction and thus, the intersection of this cone with the vertical tunnel face is an ellipse. This is in conformity with the experimental observations in centrifuge tests as mentioned by [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF]. Finally, the shear zone OAB is bounded by a threedimensional discontinuity surface that is a log-spiral curve AB in the vertical median plane of the tunnel. The equation of the curve, in polar coordinates is D(θ)=D 1 .exp ((θ-α).tanφ) where D(θ) is the radius of the log-spiral at an angle of θ, D 1 and D 3 are the radii of the log-spiral at A and B respectively and the center of the log-spiral is O. Note that the cones O'OA and O"OE considered in this mechanism have an opening angle equal to 2φ . We will now describe the velocity field for this O'' mechanism. M1 is a translational mechanism. The different blocks of this mechanism move as rigid bodies. The upper and lower rigid truncated cones OACD and OBE move with the velocities V 1 and V 3 respectively. These velocities are collinear with the cones' axes. This satisfies the condition imposed by the normality condition for an associated flow rule Coulomb material since the velocity jump vector is inclined at an angle φ to the discontinuity surface. The shearing zone OAB is composed of infinitely small-truncated rigid cones with circular cross-sections and an opening angle equal to 2φ. These rigid cones translate with velocities of different directions, which are collinear with the cones' axes and make an angle φ with the discontinuity surface. The velocity of each small cone is determined by the condition that the relative velocity between the cones in contact has the direction that makes an angle φ with the contact surface. It can be easily shown that the velocity V of each cone is V(θ)=V 1 .exp ((θ-α).tanφ). Notice that the log-spiral curve AB is assumed to be tangent to the upper and lower cones at points A and B respectively ; thus, there are no velocity discontinuities along OA and OB. As shown in figure (1), this mechanism is completely defined by two angular parameters α and β. We will now present the work equation for this kinematically admissible mechanism. The external forces contributing to the rate of external work consist of (i) the self-weight of the upper and lower truncated rigid cones (Block I and III) and of the shear zone OAB; (ii) the surcharge loading σ s (in case of outcrop of the upper rigid block) and (iii) the pressure σ t at the face of the tunnel. The rate of energy dissipation occurs along the lateral surfaces of the upper and the lower rigid cones. It also occurs along the lateral surface and the radial planes of the radial shear zone. By equating the total rate of external work to the total rate of internal energy dissipation, one obtains an equation, which has the same form as equation ( 1).

Blow-out Mechanism M2

Even though safety against collapse is a major concern during tunneling, the blow-out mechanism may be of interest for very shallow tunnels bored in weak soils, when the pressure σ t can become so great that soil is heaved in front of the shield. Such phenomenon has been observed during tunneling projects [START_REF] Clough | Measured soil response to EPB shield tunneling[END_REF]. M2 is a blow-out mechanism (cf. figure 2). It represents the passive case of the former mechanism. It is composed of three zones. Zones 1 and 3 are two rigid blocks (Blocks I and III respectively) consisting of two truncated rigid cones moving upward with velocities V 1 and V 3 respectively. The radial shear zone (Zone 2) is limited by a log spiral in the vertical symmetrical plane of the tunnel. With reference to M1, the M2 mechanism presents an upward movement of the three zones, thus, the cones with an opening angle 2φ are reversed and the log spiral's radius increases with the θ-decrease. Consequently, the velocity along the log-spiral of the shear zone is given by:

( ) ( ) φ θ β θ tan exp ) ( 1 - = V V
. Contrary to M1, the present mechanism always outcrops. It is completely defined by two parameters α and β as shown in figure (2). As for the M1 mechanism, by equating the total rate of external work to the total rate of internal energy dissipation, one obtains an equation, which has the same form as equation ( 1).

NUMERICAL RESULTS AND DISCUSSIONS

By equating the total rate of external work to the total rate of internal energy dissipation for both the M1 and M2 mechanisms, one obtains the N γ and N s factors as function of the two angles α and β. To obtain the critical γ N and N s corresponding to the blow-out case (respectively the collapse case), one has to minimize (respectively maximize) these factors with respect to the α and β-angles.

As mentioned before, [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF] have considered a collapse failure mechanism composed of two rigid cones and forced the upper cone to remain vertical. We present in figures ( 3) and ( 4) the γ N and N s values given by the present analysis (Mechanism M 1 ) and the ones given by Leca and Dormieux. It is clear that N γ increases with C/D ; then, it becomes constant for larger values of C/D corresponding to the condition of no-outcrop of the upper block. However, N s decreases with the C/D-increase and vanishes beyond a certain value of C/D corresponding to the outcrop condition. In this case, the surcharge loading will have no influence on the critical N s value. These conclusions conform to those of [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF]. It should be mentioned that the present failure mechanism gives greater upper-bound solutions than the best available upper-bound solutions proposed by [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF]. The improvement of the solution is about 8% for the N γ factor when φ=20° and C/D>0.55.

For the blow-out case, [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF] have considered a mechanism composed of a single rigid cone moving upward. The upper-bound solutions presented by them are compared with the ones corresponding to the present M2 mechanism in figures ( 5) and (6). The M2 mechanism is better than the one presented by Leca and Dormieux since the present upperbound solutions are smaller. For the N γ values, the reduction is very significant and it is of 41% when φ=30° and C/D=1.4. For the N s values, significant reductions are also obtained with regard to the results presented by Leca and Dormieux. For example, when φ=30° and C/D=1.4, the reduction attains 51%.

On the other hand, centrifuge tests have been carried out in Nantes (France) to study the face stability of tunnels in case of collapse [START_REF] Chambon | Stabilité du front de taille d'un tunnel faiblement enterré: modélisation en centrifugeuse[END_REF]. Two soil conditions were examined. A loose sand (γ=15.3kN/m 3 ) and a dense sand (γ=16.1kN/m 3 ). Shear tests on these soils has shown that c'=2.3kPa, φ'=35.2° for the loose sand, and c'=1.1kPa, φ'=38.3° for the dense sand. The results obtained by [START_REF] Chambon | Stabilité du front de taille d'un tunnel faiblement enterré: modélisation en centrifugeuse[END_REF] are presented in Table ( 1) and compared to those given by the present analysis. Note that the σ t given by the present analysis is calculated from direct maximization of this pressure (i.e. there is no error induced by the application of the superposition effect in equation 1). In order to be rigorous, no comparison is made with [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF] in the present section ; the calculation of their σ t value from the corresponding N factors may lead to approximate results due to superposition effect which may err any conclusion. As we can see, there is good agreement between experimental and theoretical results.

CONCLUSIONS

The analysis of translational failure mechanisms has shown that the present mechanisms give better results than the ones considered by Leca and Dormieux. The comparison of our results with those given by [START_REF] Leca | Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[END_REF] has shown that the present theoretical model improves N γ factor by 8% in case of collapse when φ=20° and C/D>0.55 ; the improvement attains 41% in the blow-out case when φ=30° and C/D=1.4. On the other hand, the comparison with the results given by centrifuge tests has shown good agreement.

Figure 1 :

 1 Figure 1 : Failure Mechanism M1 (Collapse)

Figure 2 :

 2 Figure 2 : Failure Mechanism M2 (Blow-out)

Figure 3 :

 3 Figure 3 : Comparison of Present N γ (thick lines) with that of Leca and Dormieux (1990) (thin lines) [Collapse]

Figure 5 :

 5 Figure 5 : Comparison of Present N γ (thick lines) with that of Leca and Dormieux (1990) (thin lines) [Blow-out]

Table 1 : Comparison between the present results and those of the centrifuge tests

 1

	C/D	γ [kN/m 3 ]	σ t [kPa]	σ t [kPa]
			(Present analysis)	(Centrifuge tests)
	2	15.3	3.5	4.4
	2	16.1	4.6	4.1

Professor, IUP Génie Civil et Infrastructures, L.G.C.N.S.N., Bd. de l'université, BP 152, 44603 Saint-Nazaire cedex, France. Formerly, E.N.S.A.I.S.,

24, Bd. de la Victoire, 67084 Strasbourg cedex, France.


M El Gonnouni

Y Riou

P Y Richer

Uncertainty analysis in the assessment of settlements caused by urban work

The aim of this study is to assess the influence of the tuwcertainties related to the soil variability in the numerical modelling of settlements caused by underground work. Based on a great number of in situ tests, a geostatistical method (kriging) applied to the subsurface is justified and applied in order to determine • the mean. position of the soil layers and their estimation variances. This uncertainty is then interpreted in terms of calculated surface settlements.

\

INTRODUCTION

The construction of underground engineering projects (tunnels, opened trenches, subways, underground passages) in urban sites causes settlements which can affect existing buildings and provoke environmental harm. Disorders of this kind can be estimated by deterministic geotechnical analysis, especially numerical methods based on : discretization. But in spite of their complexity, such •modelling contains some serious deficiencies : lack • of information on the physical and mechanical characteristics of the soil and its initial state, limited control of actions • . ,caused at different stages of construction, etc.

•

The aim of this study is a sensitivity analysis on the error caused by the natural variability of the subsurface in urban sites, and caused by the linear regression technique used to define a set a cross sections in the numerical modelling. With this in mirid, it was decided to resort to a geostatistical method in order to characterise statistically the composition of the soil (estimation of the mean position and estimation variance of elevation of interfaces). This uncertainty is then applied to the surface settlement calculation taking into account the boring of the underground work. So this uncertainty is expressed in terms of variation of settlement trough, a typical concern for geotechnical engineers.

The aim of this study is to supply engineers in charge of a underground work in urban sites with some information on the number of tests required for geometrical characterisation, and on the error in settlement calculations. This study has a practical interest, so, it refers to a particular site and tunnel project likely to cause surface settlement. This is the D line extension subway in the city of Lyon, a site subject to a important geotechnical investigation program, leading to ntuverical modelling and an initial statistical approach (Riou et al., 2000)

INPUT DATA FOR GEOSTATISTICAL ANALYSIS

This study concerns a 1 OOO meter long and 200 meter wide section located on the extension D line of the subway of Lyon between Gorge-de-Loup and gare de Vaise. The geotechnical report contains data from in situ and laboratory tests. All over this section, the geotechnical study includes 90 drillings, destructive and non-destructive testing, in-situ tests in boreholes, Standard Penetration Tests, conventional pressuremeter tests and scissometers (Bernat, 1998). In this study, the measurements are supposed to be reliable and the geotechnical analysis proposed by the Centre d'Etude des TUnnels (CETU) relevant. So, the subsurface provided by this analysis for each drilling point should be in agreement with some reality.

The three-dimensional representation of the drilling points with their subsurface elevation is shown on figure 1. This figure provides a qualitative information of the sampling density.

STATISTICAL CHARACTERISATION OF THE INTERFACES

The kriging was used in this study to obtain at any point of the soil an estimate of the position of the soil layer roof, in particular in an unsampled zone, and to define a variance of this estimate. The estimate is . established by a weighting of the meastuxements taken in the vicinity of the studied point. Optimal weighting, namely • ; the one that proves to be most realistic to estimate the elevation, is based on the variogr�. This basic statistical tool gives a structural interpretation of the phenomenon, i.e. in the present case, the similarity of the elevation of tuso points according to the distance which separates them.

The method used in this document is the ordinary kriging. This method is based on a hypothesis of stationarity of the random function that gathers a set of random variables representing the natural variability at any point. Considering the site section following the axis of the tunnel, this hypothesis seems to be justified in the whole support (900m), at least with regard to the four first layers (ochre silt, grey silt, sandy silt and sand gravel 1 : figure 2). We note in particular here that the fluctuations are more important than the drift. One the other hand, the two deepest layers (clay and sand gravel 2), along the support, display a «carrier», not uniform but likely to call into question the technique of estimate and the evaltuution of the variance. The geostatistical study was also applied to• the two zones (0-600m) 'Uld (600-900m) in order not to integrate the who le depression (500m-800m) in natural variability. All the data concern the elevations of each layer at different points, so it seemed natural to use this rough information in order to characterise the subsurface. However, the profile provided by the kriging of these data is not realistic. Due to the drift of the clay and sand gravel 2 layers, the estimate variance exceeds the thickness of clay layer. So the geostastical analysis leads to extreme lies with no clay layers. An overlapping of layers occurs in some areas. In order to avoid this pattern, a variogram model dealing with mean positions and thickness of soil is proposed here. These data provide a more realistic representation of subsurface profile.

The representation of the experimental variogram depends on the lag distance. A sensitivity study was achieved in order to obtain a variogram associating precision and regularity smoothing the disturbance due to a lack of data. A 25m step fit the best compromise (figure 3). The variograms related to the first four layers are bounded (figure 4). This confirms, for these layers, the stationary hypothesis-expressed previously. The clay and sand gravel 2 variograms show the typical profile of a -signal with a drift. Nevertheless, it was decided to use these variogram structures and to validate them on the kriging results in comparison with the observations. These variograms show some variations (hole effect), due to . the lack of information, recurrent problem in geotechnical study. But these variations are smaller in cohesive material layers (embankment, ochre si_It and grey silt) than in sandy material layers, except for the clay layer located between the two sand-gravel layers. So, when the interfaces is related 2 ) characterize the sandy layers. These ranges justify here the method to assess the subsurface profile and its variance. So, it seems there are two different spatial structures, depending on the nature of soil. No geological interpretation of this phenomenon is proposed here. That concerns a particular site. It would be useful to compare these results with similar analyses carried out on other.urban sites.

Kriging

For the purpose of kriging, correlation structures are determined by fitting typi�al variogram shapes : mathematical models assuming a positive estimation. Spherical and exponential models were applied in this study : tables l. From cross validation tests, the spherical_ model is preferred to the other one for all soil layers : table 2.

Elevations and estimation variance of layers in a 600m zone

On the basis of the previous results, a "likely interface zone" is then defined as the intersection of zones indicated in figure 5.

This process does not take into account the mean position variance that would lead to a greatest interface zone and to some subsurface without clay layer. On basis of the geotechnical analysis (figure 2), this possibility cannot be justified. Other convenient processes likely to propose a subsurface profile a11d its variability, can be probably applied. However, this process has been selected on account of the results in conformity with the observations (figure 7). Contrary to the process dealing with interface data, all the observed layers are represented. •.Figure 7 : Measures and geostatistical subsurface Some measurements are located outside the "likely interface zone". This is due to the process and the kriging that, as for most interpolators, smooths the •profiles resulting •from measurements. So, this zone has to be considered as a 'likely' zone. We notice here that the elevation variability is probably underestimated because of the extent of measured area exceeding the tunnel zone. A weighting of measurements located in this zone would be probably more realistic.

VARIANCE OF SURF ACE SETTLEMENTS

From the previous geostatistical subsurface, 19 cross sections have been defined in a 540m long profile, each section including the tunnel position, as indicated in figure 7. So, a two-dimensional numerical modelling of the boring can be carried out every 30m, a distance corresponding to the third of the smallest range. In this study, only three numerical results related to the sections located respectively at the 240m, 480m and 720m are presented. In ea ch cross section, the interface is supposed to •be horizontal. This . hypothesis can be justified by the diameter of the tunnel (6m) representing only one tenth of the weakest range.

• For each of these cross sections, and for all extreme positions (lower and upper limits) of the interface,. a numerical calculation of sur face settlement has been carried out. The numer ical modelling is defined as follows : The assessment of the A rate is based on a comparison of the numerical results with the measurements in a reference section 2 . 'A was calculted here to be 32.5%.

1 The heave at the tunnel invert depends on this distance when the Mohr Coulomb model is used with a constant Young'modulus,. So this distance is fixed. 2 As mentionned in the introduction, the aim of this study is a sensitivity analysis on the error caused by the natural variability of the subsurface in urban sites. With this in mind, A is fixed

The lower and the upper limits of the surface settlement in the three sections are shown in figure 8. These calculated values are to be compared with the recorded surface settlements ranging from 2 to 11 mm. But it should be noted that this range encompasses more . than subsurface uncertainties: mechanical parameters and the implicit uncertainty in the construction of the tunnel were also included.

CONCLUSION

A method based on a geostatistical process and • FEM software is presented and applied to an urban tunn el project in order to evaluate the reliability of the calculated surface settlement. This method dealing with the interface locations, provides a subsurface variability consistent with the recorded measurements. The FEM code provides a surface settlement variability from this previous variability.

For the case history in Lyon, and for the total settlement, at the end of the stage 2, the calculated discrepancy ranges from 26 to 55 %. It ranges from 9 to 34 % for the stage 1 •prior to the lining laying.

These values depend on the position of tunn el in regard to the subsurface and especially on the number of layers crossing the tunn el. These values provide some useful information to geotechnical engineers involved in a tunnel project. But we suggest applying this method on other urban sites in order to validate it.

Further calculations are now intended every 30m, along the studied zone. These calculations aim at the assessment of a spatial correlation structure of the calculated settlement. This result will be then analysed to direct exploration at the position of greatest estimation variance. A similar study dealing with mechanical parameters of each soil layers and Stochastic Finite Element Method, remains to be investigated.

6.ACKNOWLEDGEMENTS

The work described in this paper is in part supported by the Programm e Ville du Ministere de !'Education Nationale, de la Recherche et de la Technologie.

Figure 1 :

 1 Figure 1: Drilllngs and subsurface provided by the geotechnical analysis

Figures 2 :

 2 Figures 2 : Subsurface profile of the site in the studied zone Projection on the vertical plane passing by the axis of the tunnel

Figure 3 :

 3 Figure 3 : V ariogram from sand gravel 1 layer

  to a cohesionless material layer or a layer with a sandy part, the elevation variogram indicates a sharp profile, a smaller range and a higher sill. The two silt layers have a mean position range varyin� from 70 to .130m and a sill varying from 0.4 to 0.5 m . A smaller range (approximately 60-70m) and an important variability (maximal sill of 1 to 2m

Figure 4 :

 4 Figure 4: Variogram of mean position and thickness of the layers

Figure 5 :

 5 Figure 5 : Assessment of "likely interface zone"

  at the outside line of the tunnel up to 'A rate (no lining) 3 steps • stage 2: complete force release with lining application of tunnel weight (-3,2 kN/m 3 ) 7 steps

Figure 8 :

 8 Figure 8 : Variation of surface settlement in the three sectionsThe sensitivity analysis based on the calculated surface settlements gives a maximum discrepancy of 55% (34%, if stage 1 is only taken into consideration).Co�ceming the stage 1, this discrepancy is in relation with the number of soil layers crossed by the tunnel. This result seems consistent as the unloading acts mainly on these layers. The discrepancy of the complete surface settlements (end of stage 2) cannot be simply analysed because of the tunnel upheaval due to hydrostatic pressure acting on the lining and accordingly on upper layers. The variation of the three calculated surface settlements along the 480 m zone combines unn atural variability, tunnel position governed by practical requirements, and subsurface considerations. This first variability has been introduced in this study because the subsurface structure generally controls the tunnel design.

  1996. Mode/isation du creusement. d'un tunnel en terrain meuble. Qualification sur chantier experimental, Rapport de These, Ecole Centrale de Lyon, France. Riou Yvon, Emeriault Fabrice, Breysse Denys, Cambou Bernard 2000 Evaluation des desordres /ors d'un creusement de tunnel en site urbain : quel/e jiabilite dans /es modelisations numeriques ? Xlleme Colloque Franco Polonais de Mecanique des sols et des Roches Appliquees, Paris, 2000.

Table I

 I .a: Sets of models tested for mean position variograms

	Soil layer	diagram	range (m)	sill (m")
	embankment
	ochre silts	S+E	70-130	0.4
	grey silts	S+E	70 -130	0.3
	sandy silts sand gravels r	S+E S+E	60-70 60-70	0.85 1.65
	clay	S+E	60-70	2.00
			30-50	0.5
	grey silts	S+E	30-50	0.5
	sandy silt sand gravels 1	S+E S+E	50-60 100 -120	2.3 4.2
	clay	S+E	30-50	0.40

S = Sphencal model, E = Exponential model Table l .b: Sets of models tested -for thickness variograms Soil layer diagram Range (m) sill (m"') embankment ochre silts S+E S = Spherical model, E = Exponential model

Table 2 :

 2 Results of the cross validation

	soil layer	Select models	Errors	Error
				estimate m	Variance m 2
	Ochre silts	model s	range (m) 90	0.021	0.164
	Grey silts Sandy silts Sand gravels I	s s s	80 60 60	0.036 0.0215 0.006	0.13 0.41 0.88
	Clay	s	70	0.027	I
	Sand gravels 2	s
	3.3