Martine Bagot
email: martine.bagot@aphp.fr

MD Pierluigi Porcu

PhD Anne Marie-Cardine

PhD Maxime Battistella

MD Basem M William

Maarten Vermeer

Sean Whittaker

PhD Federico Rotolo

MD Caroline Ram-Wolff

MD Michael S Khodadoust

Prof Martine Bagot

Prof. Pierluigi Porcu

Prof Maarten Vermeer

Prof Sean Whittaker

PhD Armand Bensussan

PhD Carine Paturel

PhD Cecile Bonnafous

PhD Helene Sicard

MD Hatem A Azim

Prof H Youn

Prof. Y H Kim

Prof M Vermeer

IPH4102, a first-in-class anti-KIR3DL2 monoclonal antibody, in patients with relapsed or refractory cutaneous T-cell lymphoma: an international, first-in-human, open-label, phase 1 trial

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

NCT02593045).

Findings: From November 2015 -November 2017, 44 patients were enrolled (median age: 69years). 35 patients (80%) had SS, 8 (18%) had mycosis fungoides and 1 (2%) had primary cutaneous T-cell lymphoma, not-otherwise specified. Median prior systemic therapies was 3. In the dose-escalation, no dose-limiting toxicity was identified and the trial's safety committee recommended a flat dose of 750mg for the cohort-expansion, corresponding to the maximum administered dose. Most common adverse events (AEs) were peripheral oedema (27%), and fatigue (20%). Lymphopenia was the most common grade 3-4 AE (7%). One patient developed fulminant hepatitis following IPH4102 discontinuation and subsequently died with evidence of HHV-6B infection. In the efficacy population (n=44, 100%), median follow-up was 14•1months (IQR : 11.3-20.5). Confirmed global overall response rate (ORR), duration of response (DOR) and progression-free survival (PFS) were 36•4% [95% CI: 23•8% -51•1%], 13•8 [95% CI: 7•2%

-NR] and 8•2 months [95% CI: 7•1% -17.2], respectively. . In the SS subset (n=35, 80%), confirmed global ORR, median DOR and PFS were 42•9% [95% CI: 28•0% -59•1%], 13•8 [95% CI: 7•2 -NR] and 11•7 [95% CI: 8•1 -NR] months, respectively. Confirmed ORR in skin, blood and lymph node compartments were 51.4%, 55.9% and 11.1%, respectively, with 26.5% of patients experiencing complete response in the blood. Marked improvement in QOL and pruritus scores was observed. To date, 7 SS patients (20%) are still receiving IPH4102.

Interpretation: IPH4102 is safe and shows encouraging clinical activity in relapsed/refractory SS.

If confirmed, IPH4102 would emerge as a novel treatment option for these patients. Further studies are underway.

Funding: Innate Pharma

Research in context

Evidence before this study Cutaneous T-cell Lymphoma (CTCL) is an uncommon and incurable form of non-Hodgkin lymphoma. Sézary Syndrome (SS) represents around 5-10% of CTCL, and is considered its leukemic and most aggressive form with median survival hardly exceeding 4 years. These patients typically suffer devastating pruritus, frequent infections, and body disfigurement resulting in very poor quality of life. In 2018, two novel agents; brentuximab vedotin and mogamulizumab were approved for the treatment of subsets of patients with CTCL who received at least one prior systemic therapy. However, only mogamulizumab included SS patients in its pivotal trial. In more refractory patients (i.e. who received at least two prior systemic therapies), no agents are proven to be effective particularly in SS. Vorinostat is the only approved agent in the US showing in a recent trial an overall response rate of 2.3% in Sézary Syndrome and progression free survival in the range of 3 months. KIR3DL2 (CD158k) is a member of the highly polymorphic family of killer-cell immunoglobulin like receptors (KIRs). It is widely expressed in CTCL, particularly SS in more than 85% of patients and was recently proposed as the most sensitive diagnostic and prognostic marker for SS patients.

We searched the scientific literature to identify reports of patients with CTCL, SS and KIR3DL2.

We searched MEDLINE for studies published in English until December 31, 2018. Search items included "Cutaneous T-cell lymphoma", "KIR3DL2", and Sézary Syndrome".

Added value of this study

This is the first reported trial of the anti-KIR3DL2; IPH4102 in the literature. Unlike the very few previous studies focused on patients with refractory CTCL who received at least two prior systemic therapies, this study uses the current international consensus response criteria incorporating skin, blood, lymph node and visceral responses. This study shows impressive activity of IPH4102 in SS patients who received at least two prior systemic therapies, as shown by a confirmed global response of 42•9%, duration of response of 13•8 months and progression free survival of 11•7 months. The treatment was very well tolerated with no identified doselimiting toxicity in the dose escalation portion of the study. IPH4102 also resulted in the improvement of the quality of life of the majority of patients treated. These results represent a new paradigm shift in managing patients with refractory SS.

Implications of all available evidence

The study reports an exceptional activity of a novel targeted agent in a rare form of CTCL; SS with very high unmet medical need. These results led to the US Food and Drug Administration designating a Fast Track development program the investigation of IPH4102 for the treatment of adult patients with relapsed or refractory SS who have received at least two prior systemic therapies. A pivotal trial in SS is currently underway along with a phase 2 program investigating the role of IPH4102 in other T-cell malignancies that express KIR3DL2.

Introduction

Cutaneous T-cell lymphomas (CTCL) are a heterogeneous group of rare extra-nodal non-Hodgkin lymphomas, with approximately 3,000 new cases diagnosed in the US every year [START_REF] Criscione | Incidence of cutaneous T-cell lymphoma in the United States, 1973-2002[END_REF] . The most common subtype of CTCL is mycosis fungoides (MF) that accounts for 50 -60% of all cases [START_REF] Swerdlow | The 2016 revision of the World Health Organization classification of lymphoid neoplasms[END_REF] . Sézary syndrome (SS) is a rare leukemic subtype characterized by erythroderma, lymphadenopathy and high burden of neoplastic T-cells (Sézary cells) in the blood [START_REF] Wilcox | Cutaneous T-cell lymphoma: 2017 update on diagnosis, risk-stratification, and management[END_REF] . SS patients typically suffer devastating pruritus, frequent infections, and body disfigurement resulting in very poor quality of life (QOL) [START_REF] Wright | Prevalence and severity of pruritus and quality of life in patients with cutaneous T-cell lymphoma[END_REF] . Prognosis is dismal with median survival ranging from 2.5 -4 years [START_REF] Kubica | Sezary syndrome: a study of 176 patients at Mayo Clinic[END_REF][START_REF] Alberti-Violetti | Advanced-stage mycosis fungoides and Sezary syndrome: survival and response to treatment. Clinical lymphoma[END_REF] .

Recently, based on the results of two randomized trials, brentuximab vedotin and mogamulizumab were approved for the treatment of subsets of patients with CTCL who received at least one prior systemic therapy [START_REF] Prince | Brentuximab vedotin or physician's choice in CD30-positive cutaneous T-cell lymphoma (ALCANZA): an international, open-label, randomised, phase 3, multicentre trial[END_REF][START_REF] Kim | Mogamulizumab versus vorinostat in previously treated cutaneous T-cell lymphoma (MAVORIC): an international, openlabel, randomised, controlled phase 3 trial[END_REF] . Only mogamulizumab included SS patients in its pivotal trial. In more refractory patients (i.e. who received at least two prior systemic therapies), vorinostat is the only approved agent in the US with modest clinical activity in SS [START_REF] Kim | Mogamulizumab versus vorinostat in previously treated cutaneous T-cell lymphoma (MAVORIC): an international, openlabel, randomised, controlled phase 3 trial[END_REF] . KIR3DL2 (CD158k) is a member of the highly polymorphic family of killer-cell immunoglobulin like receptors (KIRs). It is widely expressed in CTCL, and particularly SS in more than 85% of patients [START_REF] Battistella | KIR3DL2 expression in cutaneous T-cell lymphomas: expanding the spectrum for KIR3DL2 targeting[END_REF] . KIR3DL2 was recently proposed as the most sensitive diagnostic and prognostic marker for SS [START_REF] Hurabielle | Usefulness of KIR3DL2 to Diagnose, Follow-Up, and Manage the Treatment of Patients with Sezary Syndrome[END_REF] suggesting that it could serve as an ideal therapeutic target for these patients.

IPH4102 is a humanized first-in-class monoclonal antibody designed to deplete KIR3DL2expressing cells via antibody-dependent cell-cytotoxicity and phagocytosis [START_REF] Viaud | IPH4102, a humanized KIR3DL2 antibody with potent activity against cutaneous T-cell lymphoma[END_REF] . It has shown antitumour activity in mouse xenograft models and ex-vivo autologous assays using patient-derived natural killer (NK) and Sézary cells [START_REF] Viaud | IPH4102, a humanized KIR3DL2 antibody with potent activity against cutaneous T-cell lymphoma[END_REF] . Here we report the results of the first-in-human phase 1 study evaluating IPH4102 in patients with relapsed/refractory CTCL.

Methods

Study design and participants

This was an international, open-label, phase 1, multicentre study evaluating IPH4102 in patients with relapsed/refractory CTCL. The study was composed of dose-escalation and cohortexpansion portions. It was conducted in five academic hospitals in the US, France, UK, and the Netherlands in accordance with the principles of the Declaration of Helsinki and the Good Clinical Practice guidelines. The study was designed by the Sponsor; Innate Pharma together with the study investigators. The study protocol was approved by the institutional review board at each participating site. All patients signed informed consent before being screened.

Eligible patients had relapsed/refractory histologically confirmed primary CTCL, aged ≥ 18 years, received at least two prior systemic therapies, and had an Eastern Cooperative Oncology group performance score ≤ 2.In the dose-escalation part, and based on a scientific advice from the European Medical Agency in November 2014, only patients who had at least 5% of infiltrating mononuclear cells expressing KIR3DL2 in the skin or 5% phenotypically aberrant circulating Tcells expressing KIR3DL2 were included. Two expansion cohorts were planned in the two CTCL subtypes known to express KIR3DL2 in the majority of patients [START_REF] Battistella | KIR3DL2 expression in cutaneous T-cell lymphomas: expanding the spectrum for KIR3DL2 targeting[END_REF] ; SS and MF with evidence of large cell transformation (LCT) with target recruitment of 15 patients in each cohort. A protocol amendment was performed in March 2017 to allow recruitment of patients irrespective of KIR3DL2 expression in the cohort-expansion. Further details regarding inclusion and exclusion criteria are provided in the Appendix (page 3).

A safety data-monitoring committee constituted of study investigators and representatives from the sponsor convened at regular intervals to overview the safety of trial subjects, and particularly inform on dose-escalation decisions, declaration of dose limiting toxicities (DLTs), the maximum tolerated dose (MTD) and the recommended phase 2 dose.

Procedures

The first tested dose was 0•0001 mg/kg and intra-patient dose escalation was allowed. In the cohort-expansion, all patients were treated with the recommended dose based on the results of the dose-escalation part. Treatment was administered as one-hour infusion weekly for the first month, every two weeks x 10 administrations, and then every 4 weeks until disease progression or unacceptable toxicity. No dose reductions were allowed. Dose interruption due to an adverse event (AE) was allowed up to a maximum of 4 weeks. The protocol recommended permanent discontinuation of IPH4102 in case of severe infusion related reaction (IRR), unresolved grade 3 liver toxicity, or other AEs requiring discontinuation according to the investigator's assessment.

AEs were graded according to the National Cancer Institute Common Terminology Criteria for

AEs, version 4.0 [START_REF]Common Terminology Criteria for Adverse Events (CTCAE)[END_REF] . Overall response was evaluated using the global composite response score based on response in each compartment, as described in the international consensus criteria (Appendix, page 6) [START_REF] Olsen | Clinical end points and response criteria in mycosis fungoides and Sezary syndrome: a consensus statement of the International Society for Cutaneous Lymphomas, the United States Cutaneous Lymphoma Consortium, and the Cutaneous Lymphoma Task Force of the European Organisation for Research and Treatment of Cancer[END_REF] ; with skin response evaluated using the modified Severity Weighted Assessment Tool (mSWAT) [START_REF] Olsen | Phase IIb multicenter trial of vorinostat in patients with persistent, progressive, or treatment refractory cutaneous T-cell lymphoma[END_REF] . In the dose-escalation, either flow cytometry or cytomorphology was used to evaluate blood response based on investigator's preference. In the cohort-expansion, only flow cytometry was used. Skin and blood compartments were evaluated every 4 weeks throughout the study. Lymph node and visceral involvement were evaluated at baseline using MRI, CT or PET scan at the discretion of the investigator. If positive, follow-up imaging was performed at week 5 and then every 12 weeks thereafter. QOL was evaluated with each IPH4102 infusion using Skindex-29 [START_REF] Chren | Skindex, a quality-of-life measure for patients with skin disease: reliability, validity, and responsiveness[END_REF] and pruritus visual analogue score (VAS) [START_REF] Reich | Visual analogue scale: evaluation of the instrument for the assessment of pruritus[END_REF] .

KIR3DL2 was evaluated by immunohistochemistry (IHC) using an anti-KIR3DL2 antibody (clone 12B11, mouse IgG1 isotype). Another antibody was used for assessment by flow cytometry (clone 13E4, mouse IgG1 isotype). Both antibodies bind to KIR3DL2 on different epitopes than IPH4102. Detection of antidrug antibodies (ADA) was based on electrochemoluminescence via a bridging format that uses a mix of biotin-labelled IPH4102 and SULFO-TAG-labelled IPH4102. KIR3DL2 expression and histological evaluation of LCT were performed centrally at Saint Louis Hospital (Paris, France). Pharmacokinetics (PK)/immunogenicity, IHC and minimal residual disease (MRD) were performed by Quality Assistance (Donstiennes, Belgium), Histalim (Montpellier, France), and Adaptive Biotechnologies (Seattle, Washington, US), respectively, under the paid supervision of the sponsor. Immunomonitoring was performed centrally at Saint Louis Hospital for European sites and in the US at ABL (Rockville, Maryland) during the doseescalation and Caprion Biosciences (Montréal, Canada) during the cohort-expansion.

Outcomes

The primary endpoint was the occurrence of DLTs during the first two weeks of treatment, defined as: grade ≥3 toxicity lasting for ≥8 days, except lymphopenia; or grade ≥4 symptoms judged to be consistent with an IRR/ cytokine release syndrome without premedication; or grade ≥3 symptoms judged to be consistent with a recurrent IRR/cytokine release syndrome despite premedication; or grade ≥3 tumour lysis syndrome. Secondary endpoints are detailed in the Appendix (page 4) and included PK, immunogenicity and QOL endpoints in addition to several efficacy endpoints like overall response rate (ORR), duration of response (DOR) and progression free survival (PFS).

Exploratory objectives comprised the characterization of pharmacodynamics biomarkers in skin (by IHC) and blood (by flow cytometry), through monitoring of KIR3DL2-expressing cells before and during treatment. MRD was assessed using high throughput sequencing of the clonal TCR rearrangements of neoplastic T-cells in the skin and blood. Other exploratory biomarker analysis were evaluated but will be reported elsewhere and included evaluation of NK cell, macrophage infiltration, other immune receptors, cytokine release, and gene expression pattern.

Statistical Analysis

In the dose-escalation, an accelerated 3+3 design was adopted to determine the MTD [START_REF] Penel | Classical 3 + 3 design" versus "accelerated titration designs": analysis of 270 phase 1 trials investigating anti-cancer agents[END_REF] . One patient was treated at each of the first three dose levels, and subsequently three patients were treated per dose level until the maximal administered dose (MAD) of 10 mg/kg. Cohort expansion was designed to confirm the safety of the recommended dose and investigate clinical activity without a priori assumption regarding sample size. Safety data were summarized for the safety population; patients who received at least one dose of IPH4102. Efficacy analysis was performed according to CTCL subtype (i.e. SS, MF) for the efficacy population; patients who received at least one dose of IPH4102, and had a baseline disease assessment and at least one subsequent scheduled disease assessment. Response was assessed between the first administered dose until end of treatment. In order to have a best global response, patients had to have a confirmatory response assessment no sooner than 4 weeks after the initial documentation of response [START_REF] Olsen | Clinical end points and response criteria in mycosis fungoides and Sezary syndrome: a consensus statement of the International Society for Cutaneous Lymphomas, the United States Cutaneous Lymphoma Consortium, and the Cutaneous Lymphoma Task Force of the European Organisation for Research and Treatment of Cancer[END_REF] . DOR and PFS were estimated using the Kaplan-Meier method and were censored at the latest disease assessment. QOL analysis is detailed in the Appendix (page 5). The association between exploratory biomarkers, evaluated on weeks five and 14, and clinical activity was evaluated using descriptive statistics. All statistical analyses were performed using SAS 9.3 and R 3.5.

The study is registered with clinicaltrials.gov number: NCT02593045.

Role of the funding source

The funder; Innate Pharma and the trial safety committee members jointly designed the trial. The investigators and the funders collected and interpreted the data. Data analysis was performed by the Sponsor. All authors including representatives from the Sponsor contributed to the development of the manuscript and approved the final version for submission. MB, FR and HAA and that the MTD was not reached, the study safety committee recommended using the MAD for the cohort expansion, which corresponded to a flat dose of 750 mg.

Table 2 summarizes AEs that occurred in at least 10% of patients and all grade ≥ 3 AEs. Most common AEs were peripheral oedema (n=12, 27%), and fatigue (n=9, 20%), which were all grade 1-2. Lymphopenia was the most frequent IPH4102-related AE and occurred in six patients (14%). IRR were observed in three patients (7%) at different dose levels. Six grade 3-4 possiblyrelated AEs were reported in five patients: grade 4 sepsis (n=1), grade 3 transaminase increase (n=1), grade 3 lymphopenia (n=3), and grade 3 hypotension (n=1). No immune-mediated reactions related to IPH4102 were reported. In total, only 4 patients permanently stopped IPH4102 for an AE.

A total of two patients experienced ≥ grade 3 liver toxicity including one patient who developed fulminant hepatitis six weeks after discontinuing IPH4102 that lead to death. This 75 year-old patient received 4 lines of cytotoxic chemotherapy among other systemic therapies prior to starting IPH4102, and had several associated comorbidities. He had had partial response to IPH4102, lasting for one year before developing disease progression. He had normal liver function and lymphocytic count throughout the treatment course. Investigations revealed positive human herpes virus-6B (HHV-6B) serology confirmed by PCR in both serum and liver biopsy.

The second patient experienced isolated grade 3 AST increase while on treatment, which recovered two weeks later. Liver function parameters of all the remaining patients were otherwise uneventful (Appendix, page 9).

At the data cut-off date of October 15, 2018, median follow-up for the whole population was Compliance to QOL questionnaires was high; 97% and 95% of the VAS and Skindex questionnaires were completed, respectively. Treatment with IPH4102 was associated with a decrease in pruritus (Figure 3A) and Skindex global (Figure 3B) as well as symptoms, emotional and functional scores (Figure 3C-E) overtime.

IPH4102 serum levels remained below the lower limit of quantification (100 ng/mL) at the 0•0001 and 0•001 mg/kg dose levels. The PK profile of IPH4102 was linear and dose-proportional from 0•75 to 6 mg/kg, with slight accumulation occurring at 10 mg/kg during the weekly schedule (Appendix, page 11). In the dose-escalation, IPH4102 concentration exhibited a classical two-phase exponential decrease following each infusion as of the 0•05 mg/kg dose-level (Appendix, page 17). In the cohort-expansion, IPH4102 serum concentration remained >20 µg/mL in all patients, irrespective of the frequency of dosing. Further details are provided in the Appendix (page 17).

Four patients (9%) were positive for ADA, one in the dose-escalation and three in the cohortexpansion, of whom only one was considered treatment-related. This patient developed ADA on In skin, no clear correlation was observed between the degree of KIR3DL2 expression at baseline and response to IPH4102 (data not shown). Pre-and post-treatment biopsies were obtained in 31 out of 35 patients (88.5%). A post-hoc analysis showed that at least 50% reduction of KIR3DL2expressing cells in skin or MRD in blood at week five was associated with numerically higher global ORR and longer PFS (Appendix, page 14). Similar trends were observed on week 14 for MRD and KIR3DL2 expression in both skin and blood compartments (Appendix, page 15).

Discussion

This study evaluated the safety and efficacy of IPH4102 in relapsed/refractory CTCL patients.

IPH4102 showed a favourable safety profile and was associated with high rate of durable global response and improvement of QOL in the SS subset, which represented the majority of patients included in this trial.

No DLTs or IPH4102 immune-related AEs were observed and only four patients stopped treatment due to an AE. This compares very favourably to the safety profile of available systemic therapies for CTCL patients. One patient developed a possibly IPH4102-related hepatitis six weeks after treatment discontinuation, which subsequently lead to death. However, this patient had positive viral load of HHV-6B in both serum and liver tissue, which have been previously

shown to result in fatal outcomes, particularly in immunocompromised patients [START_REF] Charnot-Katsikas | Fulminant hepatic failure attributed to infection with human herpesvirus 6 (HHV-6) in an immunocompetent woman: A case report and review of the literature[END_REF][START_REF] Hill | Hepatitis due to human herpesvirus 6B after hematopoietic cell transplantation and a review of the literature. Transplant infectious disease : an official journal of the[END_REF] .

Acknowledging the limited on-treatment liver function changes reported in this study and considering the profile of the included patients being elderly and heavily pre-treated, we believe that the observed hepatic safety profile of IPH4102 is rather reassuring.

Six patients (14%) developed lymphopenia of which 50% were grade 3-4, yet none resulted in opportunistic infections. KIR3DL2 is expressed on around 30% of NK cells 20 ; however we did not find that IPH4102 reduces the count of KIR3DL2-expressing NK cells (data not shown). It is plausible that the observed lymphopenia is a result of IPH4102 reducing the CD4 neoplastic lymphocytosis thus unmasking an underlying lymphopenia caused by the disease, a phenomenon that is common in CTCL [START_REF] Yawalkar | Profound loss of T-cell receptor repertoire complexity in cutaneous T-cell lymphoma[END_REF] .

In SS, IPH4102 showed a high global and blood response of 42•9% and 55•9%, respectively.

Importantly, these responses were long-lived with median DOR and PFS of approximately one year. Only four out of 35 SS patients experienced progressive disease as best response, which indicates that more than 85% of patients derived benefit. In earlier settings, extracorporeal photopheresis is widely used with an ORR around 43% [START_REF] Zic | The treatment of cutaneous T-cell lymphoma with photopheresis[END_REF] . More recently, mogamulizumab received regulatory approval in MF/SS patients who received at least one prior systemic therapy, showing a response rate of 37% in the SS subgroup [START_REF] Kim | Mogamulizumab versus vorinostat in previously treated cutaneous T-cell lymphoma (MAVORIC): an international, openlabel, randomised, controlled phase 3 trial[END_REF] . In the current study, IPH4102 demonstrated highly comparable clinical activity, yet in more refractory patient population with very favourable toxicity profile. Of note, vorinostat is the only FDA-approved agent in managing CTCL patients who have received at least two prior systemic therapies, a population similar to the one treated in the current trial [START_REF] Olsen | Phase IIb multicenter trial of vorinostat in patients with persistent, progressive, or treatment refractory cutaneous T-cell lymphoma[END_REF] . In a recent phase 3 trial, it showed an ORR of only 2% in SS patients [START_REF] Kim | Mogamulizumab versus vorinostat in previously treated cutaneous T-cell lymphoma (MAVORIC): an international, openlabel, randomised, controlled phase 3 trial[END_REF] . Thus, the observed clinical activity with IPH4102, if confirmed, could represent a new paradigm shift in managing relapsed/refractory SS patients.

Responses appeared to be restricted to patients without LCT. These results need to be interpreted with caution as only six SS patients had evidence of LCT at baseline. LCT is a histological feature observed in 10-20% of patients at diagnosis and has been shown to be associated with poor outcomes [START_REF] Scarisbrick | Cutaneous Lymphoma International Consortium Study of Outcome in Advanced Stages of Mycosis Fungoides and Sezary Syndrome: Effect of Specific Prognostic Markers on Survival and Development of a Prognostic Model[END_REF] . Of note, patients with LCT were excluded from the recently reported trial that led to the approval of mogamulizumab in MF/SS patients who received at least one prior systemic therapy [START_REF] Kim | Mogamulizumab versus vorinostat in previously treated cutaneous T-cell lymphoma (MAVORIC): an international, openlabel, randomised, controlled phase 3 trial[END_REF] . A post-hoc analysis showed that IPH4102 has clinical activity in mogamulizumab pre-treated patients comparable to that observed in the whole population suggesting that prior treatment with mogamulizumab may not affect responses to IPH4102.

Further confirmation of IPH4102 activity in mogamulizumab pre-treated patients in future studies is warranted.

Quality of life represents a major concern for CTCL patients, particulary SS in whom nearly 90% of patients suffer severe debilitating pruritus [START_REF] Wright | Prevalence and severity of pruritus and quality of life in patients with cutaneous T-cell lymphoma[END_REF] with profound impact on employment, relationships and social well-being [START_REF] Demierre | Significant impact of cutaneous T-cell lymphoma on patients' quality of life: results of a 2005 National Cutaneous Lymphoma Foundation Survey[END_REF] . In the current trial, the majority of included patients experienced marked improvement in various QOL parameters, including itching.

Only eight MF patients were treated in this study, of whom four (50%) had no evidence of KIR3DL2 expression. Thus it is hard to reliably estimate the potential magnitude of benefit of IPH4102 in these patients. Future studies are planned to better characterize the activity of IPH4102 and the value of KIR3DL2 testing in MF patients.

This study has some limitations that should be taken into account. While the observed clinical activity of IPH4102 and its impact on QOL in SS patients is very promising, this study was not powered to provide definite conclusions on these fronts and thus these findings require further confirmation. In addition, we could not draw conclusions on the dose-response relationship as intra-patient dose-escalation took place in the majority of patients in the dose-escalation part of the study.

In conclusion, this study provides preliminary encouraging evidence showing that IPH4102 could emerge as a very promising treatment option in patients with relapsed/refractory SS. Based on these results, the FDA has granted on January 17, 2019 Fast Track designation for IPH4101 in managing these patients. A phase 2 study (TELLOMAK, clinicaltrials.gov: NCT03902184) is currently underway to confirm the clinical activity in SS and evaluate the potential of IPH4102 in other T-cell malignancies that express KIR3DL2.

14• 1 8 [

 18 months (interquartile range: 11•3 -20•5) and seven patients were still ongoing treatment. All patients had at least one post-baseline assessment. In the efficacy population (n=44), confirmed global ORR, DOR and PFS were 36•4% [95% CI: 23•8% -51•1%], 13•8 months [95% CI: 7•2% -NR] and 8•2 months [95% CI: 7•1% -17.2], respectively. In the SS subset (n=35, 80%), IPH4102 showed a confirmed global ORR of 42•9% [95% CI: 28•0% -59•1%] (Figure 2A). Response by compartment is detailed in the Appendix (page 10). Median DOR (Figure 2B) and PFS were 13•8 months [95% CI: 7•2 -NR] and 11•7 months [95% CI: 8•1 -NR] (Figure 2C, 21 events), respectively. Clinical activity according to the initially administered dose-level is provided in the Appendix (page 16). Post-hoc analysis according to the presence of LCT at baseline and prior treatment with mogamulizumab was performed. No responses were observed in the 6 SS patients who had evidence of LCT at baseline. Seven SS patients were previously treated with mogamulizumab of whom three showed global OR (42•9%) and only one showed progressive disease as best response. Median DOR and PFS were 13• 95% CI: 7•2 -NR] and 16•8 [95% CI: 8•1 -NR] months, respectively. Only nine patients (20%) were diagnosed with other CTCL subtypes, of whom eight had MF and five had evidence of LCT. One patient developed confirmed global response that lasted for 6•9 months. The remaining MF patients had stable disease as best global response. Median PFS (8 events) was 3•9 months [95% CI: 3•0 -NR]. One patient had CD4+ primary cutaneous peripheral T-cell lymphoma, not-otherwise-specified. He experienced stable disease as best global response and progressed on week 18.

  week 10 and subsequently developed several episodes of grade 2 IRR resulting in treatment discontinuation on week 36. In the three other patients: one was tested positive before starting therapy while the two others were positive at a single time point only. None of these patients exhibited any significant change in IPH4102 PK profile and none developed IRR, hence they were considered un-related to IPH4102 exposure. At baseline, aberrant Sézary cells ranged from 459 to 17,410 cells/µL (median: 2,984 cells/µL) in the dose-escalation and from 150 to 10,301 cells/µL (median: 1,234 cells/µL) in the cohortexpansion. The specific Vbeta was assessed for all SS patients at baseline. It was identified in 19 patients (54%), and subsequently monitored by flow cytometry throughout treatment. The median percentage of clonotypic cells expressing KIR3DL2 was 89% and 57% in the dose-escalation and cohort-expansion, respectively. Available clonotypic information is provided in the Appendix (page 12) In blood, descriptive analysis showed that treatment with IPH4102 resulted in early reduction in the level of aberrant Sézary cells and circulating KIR3DL2 expressing CD4+ T-cells (Figure 4A-B).

Figure 1 :Figure 2 :

 12 Figure 1: Study flow chart

Figure 3 :

 3 Figure 3: Impact of IPH4102 on quality of life of all patients included in the trial (N=44). A:

Figure 4 :

 4 Figure 4: A: Mean count of Aberrant Sézary cells (CD7 -or CD26 -CD4 + ) per µL blood,

Table 1 :

 1 Patients' characteristics Patients included in both dose-escalation and cohort-expansion parts ** Romidepsin and /or vorinostat ^ One patient had history of being stage IVB SS but had limited blood involvement at study entry (B1). As per protocol, patient was considered as SS ^^ One patient had a protocol violation, received only one line of prior systemic therapy

	Figure 4
											Complete or partial response		25000										Complete or partial response Stable disease
											Stable disease Progressive disease		20000										Progressive disease
															15000
															10000 10000
	Number of CD7 -CD26 -CD4 + T cells/µL													Number of KIR3DL2+ CD4+ T cells/mL	5000 7500
															2500
															0
															0	8		1 6		2 4	3 2		4 0		4 8	5 6
																		Weeks after the 1st administration
	Weeks	0	4	9	17	25	31	35	39	43	47	51	55	Weeks		0	4	9	17	25	31	35	39	43	47	51	55
	Complete or partial response (N)	15	15	12	12	13	7	8	3	3	3	3	2	Complete or partial response (N)	15	15	12	12	13	7	8	3	3	3	3	2
	Stable disease (N)	15	13	10	11	7	5	5	3	3	2	0	0	Stable disease (N)	15	13	10	11	7	5	5	3	3	2	0	0
	Progressive disease (N)	4	3	2	0	0	0	0	0	0	0	0	0	Progressive disease (N)	4	3	2	0	0	0	0	0	0	0	0	0

IQR: interquartile range, SS: Sézary Syndrome, MF: Mycosis Fungoides, NOS: not otherwise specified, N: Number, NA: not applicable *

Acknowledgments

This study was funded by Innate Pharma.

The authors would like to thank the patients who participated in this study and their families, as well as the staff that worked on the trial. This research was funded by Innate Pharma.

Jr had access to the raw data. MB and YHK had final authority over the manuscript and the decision to submit for publication.

Results

From November 4, 2015 through November 20, 2017, a total of 54 patients with relapsed/refractory CTCL were screened of whom 44 patients were enrolled and received at least one dose of IPH4102 (Figure 1). Twenty-five patients were included in the dose-escalation. In the cohort-expansion, recruitment was restricted to 15 SS and four MF with LCT due to shortage in drug supply.

Main patient characteristics are summarized in table 1. Median age was 69 years (interquartile range: 58 -76) and nearly 80% (n=35) of patients had SS and stage IV disease. As per protocol, all patients received at least two prior systemic therapies except for one patient, which was documented as a protocol violation. Seventeen patients (39%) received IPH4102 as the 5 th line of systemic therapy or more.

Flow cytometry assessment of SS patients showed that 27 (77%) had the CD3+CD4+CD26phenotype while 7 (20%) had the CD3+CD4+CD7-phenotype. One patient displayed a CD26+CD7+ phenotype of his Sézary cells, thus they were alternatively identified and followedup using the individual clonotypic surface TCR (Vbeta 2).

Ten dose-levels of IPH4102 were investigated, ranging from 0•0001 to 10 mg/kg. No DLTs were observed and the MTD was not identified. Summary of AEs per dose level are provided in the Appendix (page 7). Among the 22 patients included in the first 9 dose-levels, intra-patient dose escalation and escalation to the MAD of 10 mg/kg occurred in 86% (n=19) and 44% (n=11) of patients, respectively. Taking into account IPH4102 PD and PK profiles, the absence of DLTs


Théo Dezert
email: theo.dezert@ifsttar.fr

Sergio Palma Lopez
email: sergio.lopes@ifsttar.fr

Yannick Fargier
email: yannick.fargier@ifsttar.fr

Philippe Cote
email: philippe.cote@ifsttar.fr

S Palma Lopes

P Côte

Combination of geophysical and geotechnical data using belief functions: Assessment with numerical laboratory data

Keywords: Data fusion, belief functions, geophysical data, geotechnical data, experimental test bench, electrical resistivity tomography. I

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2 may lead to the complete rupture of the levee [START_REF] Foster | The statistics of embankment dam failures and accidents[END_REF]. Such a section characterization, with associated confidence indexes, could be included in failure hazard models. The use of belief functions [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF][START_REF] Dempster | Upper and lower probabilities induced by a multivalued mapping[END_REF] and different information combination rules to combine geotechnical and geophysical data is proposed. This makes it possible to take into account at the same time the uncertainties, inaccuracies and incompleteness of data related to each method. In the field of geosciences, belief functions have already been used and provide interesting results for slope instability mapping [START_REF] Binaghi | Slope instability zonation: a comparison between certainty factor and fuzzy Dempster-Shafer approaches[END_REF][START_REF] Althuwaynee | Application of an evidential belief function model in landslide susceptibility mapping[END_REF], detection of precious metal [START_REF] Tangestani | The use of Dempster-Shafer model and GIS in integration of geoscientific data for porphyry copper potential mapping, north of Shahr-e-Babak, Iran[END_REF], groundwater [START_REF] Mogaji | Regional prediction of groundwater potential mapping in a multifaceted geology terrain using GIS-based Dempster-Shafer model[END_REF] or flood susceptibility mapping [START_REF] Tehrany | The application of a Dempster-Shafer-based evidential belief function in flood susceptibility mapping and comparison with frequency ratio and logistic regression methods[END_REF]. To our best knowledge, no work has been proposed, considering the combination of two sources of information with different spatial distribution (spatialized and punctual) and for an investigation campaign in the vertical section.

Here, an innovative method of information fusion to combine electrical resistivity tomography results and cone penetrometer test data is proposed. First, work on data obtained from synthetic models is displayed. The obtained results allow to conduct a comparative study, evaluating the effect of different parameters (like the data noise level) on the fusion result. The fusion methodology is then tested from data acquired on a test bench. In this work, the potential of such a methodology is shown by using insertion depth data, acquired by a laboratory penetration cone, and electrical resistivity data acquired by a mini Electrical Resistivity Tomography (ERT) device. The depth of penetration data corresponds to geotechnical information while the electrical resistivity data correspond to geophysical information. The main concern is to highlight the ability of this information fusion algorithm to characterize the interfaces between materials and to discriminate three different types of materials with variation in thickness of one of them, and to present the variation of the results according to the number and position of the simulated boreholes. The main contributions of this work are as follows. First, this new methodology makes it possible to take into account the uncertainties, inaccuracies and incompleteness associated with the different methods of investigation used, proposing a modeling of the Basic Belief Assignments (BBAs) specifically adapted to the problematic. Then, the proposed graphic representation is innovative since it allows both to present the different geological sets that would be present in the subsoil and their layout, while presenting the confidence associated with these results. This methodology is particularly suitable for the characterization of interfaces and anomalous zones, which may correspond to areas where the risk of instability is potentially the greatest. This work also allows the implementation of a small physical model to validate the fusion approach with real data. This article is organized as follows. In section II a presentation of the approach of fusion used in the methodology is given, which introduces the use of the evidence theory and the combination methods used here. In section III, a synthetic study will then present the fusion approach from artificial data. It will also present the comparative results associated to two parametric studies. Then, in section IV, a presentation of the investigation methods used in the introduced experiment (laboratory penetration cone and mini ERT device) is given. Finally, the test bench fusion results are presented in section V and discussed in section VI, in order to understand the interests, limitations and perspectives of such a methodology.

II. Fusion methodology 1) Belief functions and combination rules

The belief functions have been introduced by Shafer [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF] in 1976 in the development of his mathematical theory of evidence inspired by previous works of Dempster [START_REF] Dempster | Upper and lower probabilities induced by a multivalued mapping[END_REF]. Shafer's theory is also referred as Dempster-Shafer theory (DST) in the literature. This theory (proposes a method to) calculate(s) the belief and the plausibility of an event (here a soil material class) from distinct source of evidence (measured data). The practical advantage of using such a theory lies in its ability to manage information from different sources, associated with variable uncertainties and inaccuracies. In this work, only two sources of information will be considered: geotechnical and geophysical. Another advantage of this theory is its ability to assess the degree of conflict between sources (ex: contradictory information between data obtained from large scale geophysical campaign and from punctual geotechnical investigation). Uncertainties correspond to degrees of confidence that are given to a value, whereas inaccuracies correspond to intervals of values that can be directly associated with measurement errors related to the method. For example, the uncertainty of measuring a geotechnical parameter identical to the one measured in a borehole increases with the distance to that point. The inaccuracy can for its part, be associated with the error bar of the result. The belief functions allow to take into account the ignorance and incompleteness of the information. It is indeed possible to grant credit on all the possible results in order to quantify the ignorance. For the reader eager to learn more, the theory is detailed in [START_REF] Martin | General combination rules for qualitative and quantitative beliefs[END_REF]. A Bayesian approach as part of a subjective probability approach [19] could have been considered for geophysical and geotechnical data combination. However, the main limitation of such an approach is that probabilities essentially represent uncertainty and only very poorly the level of inaccuracy. Moreover, in the probabilistic modeling stage, the different decisions (events) are only represented on singletons (i.e. single events) and are necessarily considered exhaustive and exclusive. The exclusivity is implied by the assumption of the additivity of probabilities. However, this hypothesis may be too strong and limit the representation of the knowledge. Furthermore, with a Bayesian approach, it is difficult to model the lack of knowledge or the knowledge that is not expressed in probability distributions. In order to define and to use the belief functions, it is necessary (i) to set a frame of discernment, (ii) to assign belief mass values to the events of this framework (Basic Belief Assignments -BBAs), (iii) to choose a fusion rule for combining information; and (iv) to represent the combined information. The Frame of Discernment Θ (FoD) is made of all the possible events about the problem under concern, the elements of the FoD are exclusive and exhaustive, so that for n events: { } In the considered problematic, the possible events of the FoD correspond to intervals of values of geophysical and geotechnical parameters that can be associated with classes of geological materials (for example, θ 1 =clays, θ 2 =sands…). The space of belief mass functions, the set of all subsets of Θ, written 2 Θ , is fixed by all the disjunctions and by the possible conflict between the sources of information (written ∅) such that:

{∅ { } { } { } { } { } { } { } { }}
As in the probability theory, the belief mass function m j is defined, for a source of evidence S j (for j=1, 2), attributed to A (defined on 2 θ ) in [0, 1] such that the more m(A) tends to 1 and the more the confidence in A is important :

∑

The difference with the probability theory lies in the fact that A can represent the union of several events (for example, either OR ). It is therefore possible to model uncertainty and lack of knowledge. For instance, when no information is available about the achievement of an event member of Θ, one can set , avoiding the uniform distribution that would have been considered in a probabilistic scheme. Combination rules, as part of the belief functions theory, can thus take different levels of uncertainty and imprecisions into account according to the source of information. If only defined on singletons, the belief mass function is similar to a probability distribution. Smets fusion approach developed in his Transferable Belief Model (TBM) [20] (i.e. conjunctive fusion) allows the attribution of a mass of belief to the conflict, outside the FoD, so that (open-world assumption): ∅ Where m 12 (•) denotes the combined BBA resulting from the combination of information of sources 1 and 2. The belief mass resulting from the fusion of information from source 1 and 2 is written: ∑ And the level of conflict between the two considered sources of information can therefore be quantified by:

∅ ∑ ∅ With m 1 (X)
and m 2 (Y) the belief masses respectively attributed to events X and Y by sources 1 and 2.

According to Shafer's approach and unlike Smets' rule, Dempster-Shafer's rule (DS) does not allow the attribution of a mass of belief to the conflict (closed-world assumption):

The conflict is there reallocated through a classical normalization factor. The mass of belief in A, , resulting from the fusion of information from sources 1 and 2 is written:

∅ ∑
The disadvantage of this method is that the conflict between the sources is no longer represented and it is possible to obtain counterintuitive results if the conflict is important because of this normalization. Even more problematic, even if the distinct sources are both informative whatever the level of conflict is, Dempster-Shafer's fusion process can even not take into account the second source of information [START_REF] Dezert | On The Validity of Dempster-Shafer Theory[END_REF]. On the other hand, the PCR6 (Proportional Conflict Redistribution No. 6) rule of combination [START_REF] Smarandache | Advances and applications of DSmT for information fusion[END_REF][START_REF] Smarandache | Information fusion based on new proportional conflict redistribution rules[END_REF], considering two sources of information, only transfers the conflicting mass to the events that are actually implied in the conflict and in proportion with their individual masses in order to preserve the specificity of the information. In order to apply the PCR6 rule : i) the combination rule described in Eq (5) must be applied, ii) the total or partial conflicting masses have to be calculated and iii) the total of partial conflicting masses have to be redistributed proportionally on non-empty sets. So, for and ∀ A ∈ \{∅} :

∑ [ ] ∈ ∅ 2) Construction of BBAs from geophysical and geotechnical data Belief masses have to be assigned to each considered event of the FoD, for both sources of information. The combination of the belief masses can only be initiated after this stage. In the following, the geophysical source of information will be identified as source 1 and the geotechnical source of information as source 2. A 2D model assumption will be made, corresponding to the x and z spatial axes, since vertical sections of subsoil are considered.

Geophysical data

The discretization of the considered subsoil section, as well as the depth of investigation and the resolution, depend on the acquisition method used [START_REF] Kearey | An introduction to geophysical exploration[END_REF]. It is the user who sets, using the inversion tool used, the shape and dimensions of the discretization grid used. It is about starting from this discretization and being able to associate for each cell, masses of beliefs for each event of the FoD. The constitutive classes of the FoD are also fixed at the end of the inversion process by the geophysicist, with the help of a representation of the distribution of the set of inverted geophysical values, in the form of modal classes (Figure 1.a). The representation in this form makes it possible to highlight the centers, minima and maxima of the events considered in order to be able to fix the bounds of the intervals associated with the events of the FoD. The number of cells of the subsoil section are represented according to the geophysical parameter values. The infima and suprema must be fixed so that the intervals are of the same width in order to avoid the appearance of a bias when calculating Wasserstein distances (detailed under). To associate the belief masses with the FoD events, the intervals of inverted values of the physical parameter (in red, Figure 1.b) are considered. For some geophysical methods, these intervals can correspond to the value obtained at the end of the inversion with its associated inaccuracy. It is then necessary to associate belief mass values m 1 (.) corresponding to each element of , for each cell of the inverted section. The masses are obtained from the calculation of Wasserstein distances [START_REF] Tran | Comparison of fuzzy numbers using a fuzzy distance measure[END_REF], considering two geophysical intervals A = [ a 1 , a 2 ] and B = [ b 1 , b 2 ] with A and B belonging to R, A being the interval corresponding to an event of the FoD and B being an interval of inverted values (Figure 1.b), Eq. ( 10):

[( ) ( )] [( ) ( ) ]
(10) This calculation estimates the distance between two intervals according to their size and the distance between them. The Wasserstein distances are calculated (using a logarithmic scale if the geophysical parameter requires it) between the inverted values with estimated inaccuracies, and the intervals associated with each event, chosen by the geophysicist. Each cell is finally associated with a standardized BBA respecting Eq. ( 3). This way, the more the distance of a geophysical interval resulting from the inversion is "close" to one event of the FoD, the more the mass of belief associated is important, and reciprocally.

Geotechnical data

For the geotechnical part, the information proposed during an investigation campaign is spatially punctual (in the x-z plane) and often contained in vertical soundings made from the surface. It is about associating masses of belief with the different events of the FoD for each cell of the considered vertical soundings. For this, the values proposed at each depth are considered with the associated inaccuracy, corresponding to the measurement error that could be attributed to the measuring device (Figure 2.a). Thus, as for the geophysical part, intervals of values are obtained. The geotechnical mesh consisting of as many cells in depth as the number of geotechnical values (Figure 2.b) is generated. A mass of belief m 2 (.)=1 is assigned, in the drilling points, to the events corresponding to the measured geotechnical parameter. A value of 1 is set since we are very confident in the information inside the boreholes unlike the spatialized geophysical information. A new mesh is then constructed (Figure 2.c), according to the size and depth of the boreholes. In order to characterize the entire section of the model, as does the geophysical method, and to associate mass values to each new cell (BBA), an exponential lateral decay of the belief mass is imposed, from the drilling point to the nearest borehole so that the decay rate is a function of the values proposed by the nearby borehole. So that, for a specific depth, Eq. ( 11): With x being the distance from the considered cell to the reference borehole (x=0 in the borehole), k a decay factor fixed by the user to adjust the lateral decay rate, BBA(x) the belief mass values assigned to each event of the FoD for a position x, with BBA(0)=1. C v corresponds to the coefficient of variation expressed in Eq. ( 12), such as used in [START_REF] Phoon | Characterization of geotechnical variability[END_REF]: √ ∑ Where Q is the geotechnical value of the reference cell in the considered borehole and Q i the geotechnical value in the nearby borehole. For Figure 2.b, n mesh =3 has been considered. If n mesh = 5 or 7, the computation of the C v will take into account 5 or 7 cells in the nearby borehole. Indeed, for two consecutive boreholes with similar values, at similar depth, the decay of the confidence is slower than for two consecutive boreholes presenting radically different values. This decay of belief mass is carried out to the left and to the right, from each drilling.

Figure

2: Construction of a geotechnical discretization mesh from two vertical boreholes acquisition (SD1 and SD2). a) Representation of the geotechnical values for SD1 and SD2 according to the depth. b) The boreholes are divided in cells associated with belief mass equal to 1 for the considered event. c) Construction

of a new mesh according to the size and depth of the boreholes. If, between two boreholes, the mass of belief associated with a hypothesis A is less than 1 (m 2 (A) <1), then the remainder of mass to be allocated to satisfy Eq. ( 3), is reported on the proposition "any type of material" represented by the union of all events, such as Eq. ( 13): Considering n boreholes, from 1 to n from left to right: borehole 1 cannot be compared to any borehole to its left neither can borehole n be compared to any borehole to its right. Indeed, for a given depth, an equal C v is considered for left and right directions, for boreholes located at the beginning and at the end of the section.

3) Dimensioning of the mesh prior to the fusion Each source of information imposes its own mesh but in order to combine the belief masses from the geophysical information source (source 1) and the geotechnical source (source 2), it is necessary to have a common mesh containing, for each cell, the geophysical and geotechnical BBAs. In order to not alter the quality of the information, no interpolation is carried out. It is decided to superimpose the geophysical discretization grid resulting from the 2D inversion to the geotechnical division, depending on the number and the borehole positions. Thus, an irregular mesh is obtained but without any approximation (Figure 3).

III. Synthetic study

Below, a synthetic study based on artificial data is proposed in order to test this new proposed methodology. It is the opportunity to show the impact of different levels of noise on the geophysical information as well as the influence of the lateral decay factor k (Eq.11) on the results of the fusion in order to be able to choose a value for the use of such a methodology from real data. 1) Considered methods For this study, the electrical resistivity tomography (ERT) method stands for the geophysical information source and the Cone Penetrometer Test (CPT) method for the geotechnical information source. The basic principle of DC-resistivity methods consist in injecting an electric current of known intensity [A] by means of two "current" electrodes and measuring a voltage [V] between two "potential" electrodes. Depending on the electrode layout, the topography, the properties of the materials and their distribution, apparent resistivity values can be computed. The depth of investigation depends on the spacing of the electrodes, the configuration of the electrodes and the nature of the soil [START_REF] Loke | Tutorial 2-D and 3-D electrical imaging surveys[END_REF]. By generalizing this principle, a two dimensional (2D) ERT consists in aligning a series of electrodes and acquiring a large number of measurements based on four electrodes configuration. The apparent resistivity data acquired are then inverted using an inversion code or software to reconstruct a complete 2D-section of electrical resistivity [Ω.m]. Here the Res2Dinv software (ver 3.71.118) [START_REF] Loke | Tutorial 2-D and 3-D electrical imaging surveys[END_REF] has been used. In order to obtain an artificial resistivity section of subsoil, a two steps procedure is followed. First, resistivity data are simulated using the Res2Dmod software [START_REF] Loke | RES2DMOD ver. 3.01: Rapid 2D resistivity forward modelling using the finite difference and finite-element methods[END_REF], on the section that we want to consider. Second, apparent electrical resistivity values are inverted with Res2Dinv, considering a L1 norm [START_REF] Loke | A comparison of smooth and blocky inversion methods in 2D electrical imaging surveys[END_REF] and an extended model discretization, to obtain the synthetic inverted section of electrical resistivity. The CPT method consists in pushing rods into the soil, at a constant speed, with a conical tip at the end [30]. This test is often used for the determination of the soils mechanical resistance properties. The two measured parameters are the tip resistance q c [MPa] and sleeve friction f s [MPa]. Although the method uses two parameters, only q c will be considered as the study parameter.

2) FoD and considered model For this synthetic study, a two-layer model is considered, composed of materials that can be likened to silts for the upper layer and clays for the underlying layer. The FoD therefore contains three material class hypotheses, such as: { } With the event corresponding to the clayey material, to the silty material and to unknown materials. The latter is associated with the union of the geophysical and geotechnical value ranges that do not correspond to those associated with and . This event allows us in a certain way, to quantify the lack of knowledge of the environment since it does not include the two first sets. The construction of the BBAs then consists in associating the data of the two considered sources to the events of the FoD. Figure 4 shows the two-layer model based on events from the FoD, used for this synthetic study. 3) Construction of BBAs from geophysical and geotechnical data Geophysical data The electrical acquisition is simulated with a Wenner acquisition mode and with 96 electrodes interspaced from one meter. An electrical resistivity of 100 Ω.m is considered for the upper material and a resistivity of x z 30 Ω.m for the underlying one [START_REF] Palacky | Resistivity characteristics of geologic targets[END_REF] (Figure 4). Electrical acquisitions are simulated with different noise levels (5, 10 and 15%). The results of this inversion (with 10% noise, figure 5.a) allow to highlight the presence of two layers but the interface between these two layers is not perfectly identified. A variation of thickness in the center of the model is visible. The interface is not straightforward and anomalies are present on the surface even though they are not part of the initial model. From these inversion results, it is possible to define the ranges of electrical resistivities that will be associated with the different events considered for the fusion process. A distribution in modal classes is used to visualize the number of cells, in the discretized section of the 2D inversion, associated with specific range of resistivities (Figure 5.b). This distribution allows to highlight the two large material classes of the model. Thanks to it, the bounds of the considered events can thus be defined (in Ω.m), so that the intervals have the same length (in logarithmic scale):

[ ] [ ] [ [ ] [ ] ]
As explained in II.2., it is possible to associate belief masses with each cell of the mesh thanks to the values resulting from the inversion. As part of the construction of geophysical BBAs, the values presented Figure 6 are obtained. This figure highlights the association of the values of Figure 5.a with the events of the FoD, Eq. ( 15). The presence of a top layer ( ) and a base layer ( ) can be detected (Figure 6.a). It appears that there is a variation in the thickness of the layers in the center of the model, but the interface is not well characterized. Moreover, the intermediate values of electrical resistivity resulting from the inversion (Figure 5.a) between and layers induce the representation of a third material ( ) which has no reality in the model that has been fixed. The belief masses are maximum when the resistivity values correspond to the center of the resistivity classes set for each event (Eq.15).

Geotechnical data

Concerning the source of geotechnical information, the simulation of four vertical CPT soundings inter spaced from 19 meters is proposed (Figure 7). 20 cm wide and up to 15 m deep boreholes are considered, and a value of q c is recorded every 50 cm from the surface. An inaccuracy of 10 -2 MPa on the measurements is considered. For a fixed normalized friction ratio of 3%, a value of q c of 20 MPa is considered for the upper silty material and a value of 0.2 MPa for the underlying clay material, as proposed in the Robertson diagram [START_REF] Robertson | Use of piezometer cone data[END_REF].

Figure 7: 2D section of subsoil displaying true ER distribution with boreholes positions in black and associated tip resistance vertical profiles in white. In order not to have uniform values of q c for the materials and to try to represent the noisy reality of an acquisition in the field, values are drawn following a normal distribution defined for each event. Mean q c values of 0.2 and 20 MPa are respectively used to define the normal distributions of the material classes. Standard deviation values equal to 10% of the mean values are associated, echoing the 10% noise used for the geophysical data. Keeping the minimum and maximum values, these random draws, make it possible to define the limits, in MPa, of the intervals associated with the elements (i.e. material classes) of the FoD:

[ ] [ ] [ [ ] [ ] ]
The minimum and maximum values are fixed at 0.1 and 100 respectively because they are the minimum and maximum values in Robertson's diagram [START_REF] Robertson | Use of piezometer cone data[END_REF]. There are two types of sounding results according to their position (Figure 8). Once the values associated with the meshes of the sounding are obtained, it is possible to associate masses of belief to the whole section by extending the geotechnical information, as explained in II.2. In the framework of the construction of geotechnical BBAs and for k = 0.1 (Eq.11), the obtained values are proposed in Figure 9. This figure highlights the fact that the confidence is maximum in the soundings. This method allows us to characterize the material on the first 5 meters of the model and the material from 10 to 15 meters deep. ). For the model base area, this can be explained by the fact that the soundings stop at 15 meters depth. Regarding the areas between 5 and 10 meters to the right and left of the first and last sounding, this is related to the fact that for these two soundings, the closest soundings propose different values at the same depths, the confidence attributed to the presence of therefore decreases very quickly laterally. This decay is also high towards the edges of the model because no other sounding is present at the ends to constrain the information. We examine in this part the results of the fusion of belief masses established for the proposed synthetic model by varying the noise level of the geophysical information, as well as the value of the lateral decay factor k (Eq.11) influencing the lateral decay rate of geotechnical information.

Figure 10 shows the fusion results with different values of k (10 -2 , 5.10 -2 , 10 -1 , 5.10 -1 and 1) for a simulated noise of 10% on the acquired geophysical information. Noise was set at 10% since the electrical resistivity classes of the FoD were defined from the modal classes of the inverted 10% noise image, The increase of k implies that for two soundings offering similar values at the same depth, the confidence associated with the corresponding type of material will tend to decrease. On the other hand, for two soundings proposing different values at the same depth, the increase of k will hardly have any impact on the belief masses associated with the selected events (e.g. between 5 and 10 m of depth between the boreholes 1 and 2, Figures 10.d). With regard to the material classes identified after the fusion process, the more k increases, the more the quantity of conflict decreases (in red, Figures 10.a). This is explained by the fact that when there is little trust in the geotechnical data, there is little conflict with the geophysical data. In the meantime, an increase in the proportion of θ 3 is observed (Figures 10.c) close to the interface. This observation is explained by a larger mass attributed to the union of events and by geophysical data which propose intermediate values at the interface level. In the following of this work, an intermediate value of k will be retained, equal to 0.1. With such parameter value, a good confidence in information repeating between two successive soundings is obtained, but it also leaves room for doubt by having enough unknown material (θ 3 ) at the interfaces. The obtained fusion results with different noise levels added to the geophysical information (5, 10 and 15%) are shown in Figures 10.iii A greater number of anomalies are also present when the noise level increases. The noise level finally impacts the level of inaccuracy associated with the geophysical data used in the fusion process. Larger data inaccuracies induce wider value ranges considered for calculating Wasserstein distances, which in turn can bring to consider belief masses on more events of the FoD. Since the classes associated with FoD elements were fixed from the values with 10% noise (section III.3 and Figure 4.b), it is "reasonable" to have a higher confidence (higher belief masses) on these results than on the results with 5% and 15% noise (Figures 11.c, 11.e, 10.iii.b, 10.iii.d). The fusion process allows to override the noise effects, whether the noise level is 5 or 15%. This can be imputed to the computation of Wasserstein distances, taking into account the data inaccuracies and considering all geophysical classes. IV.

11: a) Subsoil section displaying inverted electrical resistivity values from i) 5% noise and ii) 15% noise data acquisition. Representation of the events having the highest belief mass in b) and d) and their associated mass values in c) and e). Figures on the left

Setting up a test bench for real geotechnical and geophysical acquisitions A. Materials In order to be able to assess the validity of the developed fusion methodology, two methods of data acquisition were retained: (i) a mini-ERT device acting as the geophysical source of information and (ii) a laboratory penetration cone acting as the geotechnical source of information. Before setting up the test bench, it was necessary to select the materials that could be put in place in a tank in order to carry out the study. This selection implies that the materials used meet several conditions in order to validate the methodology: they must have (i) distinct electrical resistivity ranges, (ii) distinct penetration depths and (iii) a certain homogeneity in the space to limit uncontrolled anomalous values.

1) Mini ERT device Expressly for the purposes of this study, a mini ERT device (Figure 12) has been set up. This device consists of 48 electrodes of 6 mm length, positioned at regular intervals of one centimeter. It can be moved along the test bench to make multiple acquisitions and to cover a longer section.

Figure 12: Mini ERT device with 48 electrodes spaced 1 cm, adjustable height, used for electrical acquisitions in the test bench. 2) Laboratory penetration cone

The laboratory penetration cone method is described in the French standard NF P 94-052-1 [START_REF] Nf P | Sols : reconnaissance et essais -Détermination des limites d'Atterberg -Partie 1 : limite de liquidité -Méthode du cône de pénétration[END_REF]. It consists in measuring a penetration depth of a cone, in millimeters, subjected to its own weight (Figure 13). The materials are tested individually, repeatedly, to determine an average value and a standard deviation of penetration depth for each material. These values can be used later in the study to simulate different drilling positions within the test bench. This method can be likened to the CPT method which is one of the most popular in situ geotechnical tests. Figure 13: Laboratory penetration cone

3) Test bench and used materials For the validation of the methodology, we wanted to build a test bench that could be easily set up and controlled, with two or three layers and variation of the interface positions. Fast-hardening natural finegrained plaster as well as Hostun fine sand [START_REF] Flavigny | Note technique: le sable d'Hostun «RF[END_REF] are the retained constituents. These two materials meet the three conditions listed above. They were placed in a transparent PVC tank of 100 × 30 × 17 cm 3 as shown in Figure 14 with an underlying layer of 5 cm of plaster (setting time = 69 h) overlaid by a layer of 2.5 cm of water saturated sand.

Figure 14: Transparency view of the test bench

A formwork was made during the placement of the plaster so that a 20 cm long anomaly could be inserted in. Saturated sand of 7.5 cm thickness is present instead of plaster. The contact between the materials and the bottom of the tank is at the origin of an interface that will be interesting to detect with the help of the methodology. 16 kg of plaster were mixed with 8 kg of water to obtain the material finally put in place. The electrical resistivity of the plaster was measured before and after the placement of the saturated sand to verify that the presence of water had a negligible impact on the electrical properties of the plaster. For the Hostun sand, 15.82 kg were pluviated in 5.8 kg of water, above the plaster to reach saturation. Trials had been carried out in advance to determine the proportions of water and sand required to achieve such a state as well as to validate the repeatability of such installation by pluviation. The values of electrical resistivities and penetration depths are displayed in Table 1. B. FoD and BBA modeling 1) FoD and target model A FoD consisting of four elements (material classes) is considered so that:

{ } With θ 1 the element corresponding to the plaster material; θ 2 corresponding to saturated sand; θ 3 corresponding to the hard and electrically insulating bottom of tank simulating a substrate and θ 4 corresponding to unknown materials, being the union of the ranges of values not corresponding to those associated with the 3 previously described materials. Figure 15 presents the target model in the form of events constituting the FoD, following the disposition of the materials within the test bench. Although the tank used is 1 m long, the ERT acquisition only covered a 83 cm long section, on the central line of the model, and allowed us to image up to 18 cm of depth. Figure 15: Scheme of the idealized section model (with vertical exaggeration), including the FoD constituent events associated with the materials of the test bench 2) Construction of BBAs from geophysical and geotechnical data The electrical acquisition was carried out on 83 cm long, on the central line of the model, with a first acquisition on 47 cm, and three next acquisitions done after respective displacements of 12 cm (roll along method). The results obtained from the inversion of the acquired data are displayed in Figure 16.a. These results make it possible to highlight the existence of three distinct sets, at depths relatively close to the target model (Figure 15) but presenting vertically slightly shifted interfaces, gradual rather than sharp. In addition, the variation in saturated sand thickness is poorly evaluated. Indeed, the anomalous zone is recognized but associated here, in its lower part, with values of electrical resistivities much larger than what they really are. The proposed values, although in the same order of magnitude, do not exactly match the ranges of values measured on the materials independently (Table 1). In order to characterize the events (materials) of the FoD, a distribution in modal classes (Figure 16.b) is used to visualize the number of cells of the discretized section for the 2D inversion, associated with their corresponding ranges of resistivities. This distribution makes it possible to highlight the three large sets of materials in the model. Thanks to it, the bounds of the events considered can thus be defined, in Ω.m, so that the intervals are the same length, as presented Eq. ( 18):

[ ] [ ] [ ] [ [ ] [ ] [ ] ]
In contrast to information from the geophysical source, geotechnical data were obtained beforehand by laboratory penetration cone testing, and then numerically simulated prior to fusion. Several simulations proposing various positions of survey points were carried out. In order to simulate drilling points, the associated mean depth values (mm) and associated standard deviations (Table 1) were used to draw values, following a normal distribution defined for each event. An average penetration depth value of 0 mm is used for θ 3 (bottom of tank) and an associated standard deviation of 0.01 mm, meaning that negative values may be drawn. These random draws, make it possible to define the limits, in mm, of the intervals associated with the events of the FoD as presented Eq. ( 19):

[ ] [ ] [ ] [ [ ] [ ] [ ] ]
Thus, 2 mm wide boreholes are simulated, down to 15 cm and acquiring every 5 mm with an associated inaccuracy of 0.01 mm. The values of penetration depth obtained can then be associated with the different materials of the model. Fusion results analysis and discussion Different rules of combinations Let us discuss and compare the results obtained by the 2 different combination rules used in an 8-boreholes simulation (Figure 17.i). In the framework of a model as rich in geotechnical information, the section proposed by the PCR6 method (Figure 17.i.c) is very close to the target model set up (Figure 15). The three sets are well characterized and the interfaces at 2.5 cm deep (sands-plaster) and at 7.5 cm deep (plaster-PVC tank and sand-PVC tank) are much better defined than by ERT alone (Figure 16.a). Moreover, thanks to this geotechnical information, the sand thickness anomaly could be correctly characterized as saturated sands (θ 2 ) and not as a more resistive anomaly, in continuity with the insulating material from below, as suggested by the results of the inversion. The lateral extension of this anomaly is, moreover, well estimated (20 cm). The combination of Smets highlights the significant conflict existing between the two considered sources of information (Figure 17.i.a) concerning the two first layers. Whatever method is used, the presence of a hypothesis θ 4 is found at the vertical and horizontal interfaces (Figures 17.i showing that the confidence granted to such a material remains quite relative. An overall confidence drop is also observed from 15 cm depth. This corresponds to the maximum depth reached by the simulated boreholes. As confidence is extended laterally, the belief masses are constrained only by geophysical information to such a depth and therefore rely only on one source of information.

Influence of the number of boreholes and positions

The first intuition would be to assume that the more the number of boreholes decreases, the more the method should be put in difficulty to properly characterize the section of the set up test bench. Although this is partly true, the quality of the results is not based as much on the number as on the positions of the drillings. Indeed, the anomaly of saturated sands contained between the two banks of plaster (Figure 15) is as well characterized in terms of lateral extension with three or five soundings (Figures 17.ii The explanation of such results lies in the fact that being in the presence of consecutive boreholes, informing about the occurrence of different materials, at an equivalent depth, induces a rapid decrease in the confidence attributed to the boreholes. Therefore, more credibility is given to the geophysical information source, explaining the greater presence of θ 4 , which reflects the gradual transitions in electrical resistivities. The masses associated with this event, however, remain relatively small. On the other hand, if two consecutive boreholes have the same geotechnical values, for a specific depth, the lateral decay rate will be low and no priority can be given to a different material existing between these two boreholes. That is why the sand anomaly in the center of the model does not appear in the results fusion with two soundings (Figures 17.iv.c) : no borehole pass through the anomaly and the geophysical source is unable to characterize this material as saturated sand. The strength of these results is that they suggest the presence of θ 4 in this location, suggesting that the survey campaign should be reinforced (with a new borehole position for example). The conflict presented by Smets combination (results in Figures 17.i.a, ii.a, iii.a and iv.a) is neither a function of the number of geotechnical soundings. In this study, the cases of fusion bringing the highest amount of conflict are in fact the ones with eight and two soundings. Nor is it to be confused with a lack of knowledge of the subsoil. Conflict zones highlight contradictory information between the two sources. These zones are generally between two consecutive boreholes providing the same information, but going against the available geophysical information. These are therefore potentially anomalous zones where the geophysical information must be considered carefully, in particular if the belief mass associated with the event retained after normalization is too low.

Important considerations and potential in the application

It is important to consider that the effectiveness of this fusion methodology has been assessed by comparing the fusion results with a target model (Figure 15). However, this remains an idealized representation of the test bench set up and could be, in some places, quite far from reality (real interfaces not perfectly horizontal or vertical, materials not perfectly homogeneous, 3D effects neglected ...). The approach is different from the one of the synthetic study (Figure 4) where the model shown corresponds to the true model. In order to control the effectiveness of the fusion methodology, it was envisaged to carry out ex post verifications of the constituent materials. Unfortunately, for practical reasons, this could not be done (reworking of materials modifying their physical properties, interaction with water, delicate cutting and extraction ...). Regarding the fusion methodology developed, two aspects are debatable. First, the choice to set a mass of belief equal to 1 on the geotechnical information in the boreholes. Second, the effect of different random draw results on the fusion results. The choice of a maximum punctual confidence (m=1) in boreholes is defended in order to give a full and local confidence to geotechnical information as it is currently done during investigation campaigns. Excessive risks are not taken since the test bench is relatively well known and the synthetic model is perfectly well known. Thus, it is sure that simulated borehole values refer to the right materials. Furthermore, a value of m=0.99 instead of m=1, for instance, does not significantly change the results and does not change the interpretation and the resulting discussion. Regarding the effect of random draws, these draws were done following a normal distribution, the variations from one draw to another are minimal and the results of fusion differ little. Such an information fusion algorithm, dedicated to the combination of data from geophysical and geotechnical sources, should prove useful for processing of data acquired during investigation campaigns for many different kinds of issues. It is possible to envisage its use with a larger number of materials, but also, and especially, with a larger number of data types from geophysical methods (seismics, ground penetrating radar) and geotechnical testing methods (penetration cone, core sampling with laboratory identification, permeability tests ...) associated. In the framework of a recognition campaign, the conflict zones, or zones with a low associated confidence, would make it possible to specify the locations where the investigation must be reinforced. The ultimate goal is to obtain a more robust and cost-effective diagnosis of the investigated structure, more targeted for geotechnical investigation. This methodology has particularly shown its ability to correctly characterize interfaces, which corresponds to areas where the risk of instability is potentially the greatest. For a levee embankment issue, for example, the results from such a methodology could come to feed into models of breakage risks (ex: CARDigues [START_REF] Apel | Flood risk assessment and associated uncertainty[END_REF]).

VII. Conclusion In this work, a new methodology has been presented, based on belief functions to take benefit and to combine two different and complementary kinds of information: geophysical and geotechnical. Each one having its own spatial distribution and related uncertainties and inaccuracies. A new representation of the information has been proposed, taking into consideration two different investigation methods, associated with degrees of belief. This representation is more informative than data superposition of different physical parameters. In the first place, this new approach has been validated with a synthetic study, simulating data acquired by ERT and a CPT method, considering a 2D model with two layers and thickness variation. The results were obtained with different noise ratios applied to the geophysical data and different values of lateral decay coefficient for the geotechnical information. The most appropriate value to pick up for the coefficient has been pointed out and it has been showed that this approach was able to manage the noise ratio, thanks to the use of Wasserstein distances. In order to address the problem of combining information acquired by geophysical and geotechnical methods during investigation campaigns, and to acquire values from real devices, a test bench composed of plaster and saturated sands was set up. The methods used to characterize such a physical model were the ERT method (geophysical) and the laboratory penetration cone method (geotechnical). While the data has been acquired by a dedicated small scale ERT device, on the surface and on the central line of the complete model, borehole were simulated respecting the penetration depth ranges previously established. Fusion results were proposed following 2 combination rules (Smets and PCR6) as well as for four different simulations of number and positions of boreholes. The results highlighted the ability of this fusion approach to correctly characterize the test bench materials as well as to specify the positions of the interfaces (vertical and horizontal) between the materials. Moreover, for each result, thanks to a graphical representation, the associated confidence is proposed. Further research should include cases of material mixtures and cases of different materials sharing common ranges of physical properties in order to test the ability of this methodology to differentiate them. We also wish to test this new methodology in real investigation campaigns in order to improve the available knowledge and strengthen the characterization. The level of confidence associated with the proposed results may be very relevant for decision support (eg models of failure hazards). The results of such a methodology should make it possible to propose the most relevant borehole positions (that are a function of conflictual and anomalous areas), in order to make the quality of the information more cost-effective.

Acknowledgments

We would like to thank Quiterie Forquenot de la Fortelle and Gautier Gugole for their precious help throughout the experimental phase and also would like to thank the Région Pays de la Loire for their financial support.

[1] Caris, J. P. T., & Van Asch, T. W. (1991). Geophysical, geotechnical and hydrological investigations of a small landslide in the French Alps. Engineering Geology, 31 [START_REF] Chambers | Geophysical-geotechnical sensor networks for landslide monitoring[END_REF][START_REF] Abidin | Integral analysis of geoelectrical (resistivity) and geotechnical (SPT) data in slope stability assessment[END_REF], 249-276.

[2] Merritt, A. J., Chambers, J. E., Murphy, W., Wilkinson, P. B., West, L. J., Gunn, D. A., Meldrum, P.I.,

Figure 1 :

 1 Figure 1: a) Model classes' distribution of the geophysical parameter values from the considered subsoil section, allowing the selection of the geophysical classes in b). The red interval corresponds to an interval of inverted values, from one cell of a 2D section of subsoil, used for Wasserstein distances' calculation.Geotechnical dataFor the geotechnical part, the information proposed during an investigation campaign is spatially punctual (in the x-z plane) and often contained in vertical soundings made from the surface. It is about associating masses of belief with the different events of the FoD for each cell of the considered vertical soundings. For this, the values proposed at each depth are considered with the associated inaccuracy, corresponding to the measurement error that could be attributed to the measuring device (Figure2.a). Thus, as for the geophysical part, intervals of values are obtained. The geotechnical mesh consisting of as many cells in depth as the number of geotechnical values (Figure2.b) is generated. A mass of belief m 2 (.)=1 is assigned, in the drilling points, to the events corresponding to the measured geotechnical parameter. A value of 1 is set since we are very confident in the information inside the boreholes unlike the spatialized geophysical information. A new mesh is then constructed (Figure2.c), according to the size and depth of the boreholes. In order to characterize the entire section of the model, as does the geophysical method, and to associate mass values to each new cell (BBA), an exponential lateral decay of the belief mass is imposed, from the drilling point to the nearest borehole so that the decay rate is a function of the values proposed by the nearby borehole. So that, for a specific depth, Eq. (11):

Figure 3 :

 3 Figure 3: Example of a geophysical mesh (in black) and a geotechnical mesh (in red) superimposed to propose a new irregular mesh to carry out the combination calculations and present the fusion results.III. Synthetic study

Figure 4 :

 4 Figure 4: Representation of the events of the FoD in the imposed model of subsoil of the synthetic study.3) Construction of BBAs from geophysical and geotechnical data Geophysical dataThe electrical acquisition is simulated with a Wenner acquisition mode and with 96 electrodes interspaced from one meter. An electrical resistivity of 100 Ω.m is considered for the upper material and a resistivity of

Figure 5 :Figure 6 :

 56 Figure 5: a) Subsoil section displaying inverted electrical resistivity values from 10% noise data acquisition and b) model classes' distribution of the cells presented in a), according to the electrical resistivity values (Ω.m).

Figure 8 :

 8 Figure 8: Examples of the two types of simulated soundings with tip resistance values according to the investigation depth. a) corresponds to borehole n°1 and 4 on figure 7 while b) corresponds to borehole n°2 and 3 on figure 7.

Figure 9 :

 9 Figure 9: a) Representation of the events having the highest belief mass according to the BBA construction from geotechnical data and b) the associated belief mass values. The borehole positions are in dashed lines while the black line represent the position of the interface. The greater thickness of the material in the center of the model is also well characterized. On the other hand, a great doubt appears in yellow (Figure 9.a) in certain areas, not allowing the determination of a specific material (). For the model base area, this can be explained by the fact that the soundings stop at 15 meters depth. Regarding the areas between 5 and 10 meters to the right and left of the first and last sounding, this is related to the fact that for these two soundings, the closest soundings propose different values at the same depths, the confidence attributed to the presence of therefore decreases very quickly laterally. This decay is also high towards the edges of the model because no other sounding is present at the ends to constrain the information.4) Effect of lateral decay factor and noise level on the fusion results

4 )

 4 Figure 9: a) Representation of the events having the highest belief mass according to the BBA construction from geotechnical data and b) the associated belief mass values. The borehole positions are in dashed lines while the black line represent the position of the interface. The greater thickness of the material in the center of the model is also well characterized. On the other hand, a great doubt appears in yellow (Figure 9.a) in certain areas, not allowing the determination of a specific material (). For the model base area, this can be explained by the fact that the soundings stop at 15 meters depth. Regarding the areas between 5 and 10 meters to the right and left of the first and last sounding, this is related to the fact that for these two soundings, the closest soundings propose different values at the same depths, the confidence attributed to the presence of therefore decreases very quickly laterally. This decay is also high towards the edges of the model because no other sounding is present at the ends to constrain the information.4) Effect of lateral decay factor and noise level on the fusion results

Figure 5 .

 5 b. For each value of k, Figures 10.a and 10.b represent the results obtained by Smets fusion whereas Figures 10.c and 10.d represent the results obtained by PCR6 fusion. While Figures 10.a and 10.c show the material classes having the greatest mass of belief at the end of the fusion process, Figures 10.band 10.d correspond to the values of these respective belief masses, between 0 and 1. These figures, display the events (materials) potentially present within the section, as well as their attached level of confidence.

Figure 10 :

 10 Figure 10: Representation of the events having the highest belief mass in a) and c) and their associated mass values in b) and d), considering a 10% noise. In i) k=0.01, ii) k=0.05, iii) k=0.1, iv) k=0.5 and v) k=1. Figures on the left side are results for Smets fusion while figures on the right side are results for PCR6 fusion. The sounding positions are in dashed lines while the black line represent the position of the interface. The higher the value of k is, the higher the rate of confidence in geotechnical information is. This can be seen, for example, from the last borehole to the right end of the section (Figures 10.b) or between the 2 nd and

  and 11 with k = 0.1.

Figure

  Figure 11: a) Subsoil section displaying inverted electrical resistivity values from i) 5% noise and ii) 15% noise data acquisition. Representation of the events having the highest belief mass in b) and d) and their associated mass values in c) and e). Figures on the left side are results for Smets fusion while figures on the right side are results for PCR6 fusion. The sounding positions are in dashed lines while the black line represent the position of the interface.

  Figure 11: a) Subsoil section displaying inverted electrical resistivity values from i) 5% noise and ii) 15% noise data acquisition. Representation of the events having the highest belief mass in b) and d) and their associated mass values in c) and e). Figures on the left side are results for Smets fusion while figures on the right side are results for PCR6 fusion. The sounding positions are in dashed lines while the black line represent the position of the interface.

  amount of noise is, the less clear the interfaces proposed by the inversion are (Figures 5.a, 11.i.a, 11.ii.a).

Figure 16 :Figure 17 :

 1617 Figure 16: a) inverse model resistivity section obtained by roll along acquisitions in the central line of the model and b) model classes' distribution of the cells presented in a), according to the electrical resistivity values (Ω.m). V. Test bench data fusion results The results of the geophysical and geotechnical information fusion, are proposed in Figure 17. The simulations were carried out according to four distinct vertical drill positioning configurations, represented in dashed lines in the figures and at regular intervals: i) 8 holes inter-spaced of 10 cm (Figure 17.i) (x = 10; 20; 30; 40; 50; 60; 70; 80 cm), ii) 5 holes inter-spaced of 18 cm (Figure 17.ii) (x = 4, 22, 40, 58, 76 cm), iii) 3 holes inter-spaced of 25 cm (Figure 17.iii) (x = 15, 40, 65 cm) ), iv) 2 holes inter-spaced of 50 cm (Figure 17.iv) (x = 15, 65 cm). The fusion results carried out are presented, respecting i) the hypothesis of Smets (Figures 17.a and 17.b), ii) the hypothesis of a closed-world (section II.1) with PCR6 rule (Figures 17.c and 17.d). Figures 17.b and 17.d represent the belief mass values associated with events having the largest mass, represented respectively in Figures 17.a and 17.c. The fusion results are analyzed and discussed in the next section.

  Figure 17: Representation of the events having the highest belief mass in a) and c) and their associated mass values in b) and d). For i) 8 boreholes, ii) 5 boreholes, iii) 3 boreholes, iv) 2 boreholes are considered. For each case, (a,b) figures are results of Smets fusion, while (c,d) figures are results of PCR6 fusion. The borehole positions are in dashed lines. VI.Fusion results analysis and discussion Different rules of combinations Let us discuss and compare the results obtained by the 2 different combination rules used in an 8-boreholes simulation (Figure17.i). In the framework of a model as rich in geotechnical information, the section proposed by the PCR6 method (Figure17.i.c) is very close to the target model set up (Figure15). The three sets are well characterized and the interfaces at 2.5 cm deep (sands-plaster) and at 7.5 cm deep (plaster-PVC tank and sand-PVC tank) are much better defined than by ERT alone (Figure16.a). Moreover, thanks to this geotechnical information, the sand thickness anomaly could be correctly characterized as saturated sands (θ 2 ) and not as a more resistive anomaly, in continuity with the insulating material from below, as suggested by the results of the inversion. The lateral extension of this anomaly is, moreover, well estimated (20 cm). The combination of Smets highlights the significant conflict existing between the two considered sources of information (Figure17.i.a) concerning the two first layers. Whatever method is used, the presence of a hypothesis θ 4 is found at the vertical and horizontal interfaces (Figures 17.i.a, i.c). This hypothesis does not correspond to any material set up in the test bench. The belief masses attributed to such a hypothesis, highlight the transition zones not conform to reality, proposed by the inversion of the electrical resistivity data (Figure 16.a). In comparison to the belief masses associated with the other hypotheses of the model, the belief masses associated with θ 4 are the lowest (Figures 17.i.b, i.d),

  .c, iii.c). It also has an equivalent associated trust (Figures 17.ii.d, iii.d). It turns out that the belief masses associated with the event θ 1 (plaster) are even smaller for a fusion including three soundings (Figures 17.iii.d) than for a simulation of only two (Figures 17.iv.d).

Table 1 :

 1 Values of electrical resistivity and depth of penetration of the materials set up within the test bench

		Plaster before	Saturated
		pluviation	Hostun sands
	Electrical resistivity
	(Ω.m)
	Mean	31.28	78.15
	Standard deviation	3.23	11.18
	Number of measures	12	52
	Penetration depth (mm)
	Mean	0.11	17.31
	Standard deviation	0.04	1.61
	Number of measurements	8	10