Pierre Trap
email: pierre.trap@univ-fcomte.fr

Michel Faure

Wei Lin

Romain Augier

Antoine Fouassier

Syn-collisional channel flow and exhumation of paleoproterozoic High Pressure rocks in the Trans-North China Orogen: the critical role of partial-melting and orogenic bending

Keywords: High-pressure rocks, Exhumation, Partial melting, Channel flow, Trans-North China Orogen

Within the paleoproterozoic Trans-North China Orogen, the High-Pressure Belt (HPB) is made of high-pressure (~15 kbar) mafic granulites hosted in migmatitic gneisses. In this contribution, we document a set of structural analyses acquired over the whole HPB. We also proposed a morphological subdivision of the partially molten rocks that compose the HPB according to changes in melt fraction. A compilation of the P-T and radiochronological data carried out over the last 15 years is presented. The results highlight the concurrent effect of oroclinal bending and partial-melting in controlling the exhumation of the deeply buried continental crust.

During ongoing compression of the thickening orogenic root, onset of partial-melting at peak metamorphism is responsible for a first strength drop that enhanced an eastward lateral flow. Radiometric ages show that the deep crust was partially molten over a 50 Ma lasting period during which it evolved in a diatexite core mantled by metatexites. This was responsible for a second strength drop with strain concentrated along the diatexite/metatexite boundaries, as exemplified by the newly documented Datong-Chengde Shear Zone, a ~400 km-long normal shear zone with a sinistral strike-slip component that accommodated the final uprise of the high-pressure rocks.

Introduction

Paleoproterozoic high-pressure metamorphic rocks buried to depth exceeding 50 km, and exhumed to shallow crustal levels are extremely rare all over the world [START_REF] O'brien | High pressure granulites: formation, recovery of peak conditions and implications for tectonics[END_REF]. Such old high-pressure rocks are very precious since the understanding of their structural and metamorphic evolution brings insights about orogenic processes during the Paleoproterozoic, and more generally about flow and exhumation mechanisms of thickened orogenic continental crust. Unfortunately the mechanisms responsible for the exhumation of such rare old high-pressure rocks are quite difficult to settle since the structural and metamorphic evidences have commonly been reworked during subsequent younger orogenies.

For the purpose of our study, the High-Pressure Belt (HPB) of the Trans-North China Orogen (TNCO) is of particular interest because (1) high-pressure mafic granulites (including retrograded eclogites) with isothermal decompression paths have been largely reported along the whole belt (e.g. [START_REF] Zhang | High-pressure mafic granulites in the Trans-North China Orogen: Tectonic significance and age[END_REF], (2) younger reworking processes are weak in this area of the North China Craton, (3) outcrop conditions allow a detail geometric and kinematic study over the entire HPB, and (4) the regional architecture and evolution of the TNCO are presently relatively well understood.

As for numerous high-pressure belts over the world, the TNCO High-Pressure Belt is mainly made of partially-molten rocks (migmatites) within which retrograded eclogites and HP-granulites occur. Partial-melting changes rock rheology and density, and is therefore a critical phenomenon in exhumation of deep-seated crust. In particular, the viscosity drop commonly attributed to partial-melting is responsible for continental crust to flow since it can no longer support the weight of the wedge [START_REF] Vanderhaeghe | Evolution of orogenic wedges and continental plateaux: Insights from crustal thermalmechanical models overlying subducting mantle lithosphere[END_REF]. This concept is well known as channel flow [START_REF] Beaumont | Himalayan tectonics explained by extrusion of a low-viscosity crustal channel coupled to focused surface denudation[END_REF][START_REF] Beaumont | Crustal channel flows: 1. Numerical models with applications to the tectonics of the Himalayan-Tibetan orogen[END_REF][START_REF] Beaumont | Channel flow, ductile extrusion and exhumation in continental collision zones[END_REF][START_REF] Jamieson | Crustal channel flows: 2. Numerical models with implications for metamorphism in the Himalayan-Tibetan orogen[END_REF][START_REF] Jamieson | Provenance of the Greater Himalayan Sequence and associated rocks; predictions of channel flow models[END_REF][START_REF] Grujic | Channel flow and continental collision tectonics: An overview[END_REF]. Recently, [START_REF] Vanderhaeghe | Migmatites, granites and orogeny: flow modes of partially-molten rocks and magmas associated with melt/solid segregation in orogenic belts[END_REF] inventories the various modes of flow of partially-molten orogenic continental crust and distinguishes the vertical channel flow driven by plate tectonic related forces and the horizontal channel flow related to the gravity force associated with lateral change in crustal thicknesses. A large number of conceptual models have been proposed to account for channel flow and exhumation of lower crust in collisional orogens [START_REF] Beaumont | Himalayan tectonics explained by extrusion of a low-viscosity crustal channel coupled to focused surface denudation[END_REF][START_REF] Beaumont | Crustal channel flows: 1. Numerical models with applications to the tectonics of the Himalayan-Tibetan orogen[END_REF][START_REF] Beaumont | Channel flow, ductile extrusion and exhumation in continental collision zones[END_REF][START_REF] Jamieson | Crustal channel flows: 2. Numerical models with implications for metamorphism in the Himalayan-Tibetan orogen[END_REF][START_REF] Jamieson | Provenance of the Greater Himalayan Sequence and associated rocks; predictions of channel flow models[END_REF][START_REF] Gervais | Testing modes of exhumation in collisional orogens: Synconvergent channel flow in the southeastern Canadian Cordillera[END_REF][START_REF] Rey | Limit of channel flow in orogenic plateaux[END_REF]. In each model a particular tectonic setting is advocated such as, for instance, upper-crustal extension, active erosion, retreat of the foreland, under-thrusting or orogenic wedge shortening. Overall, mode of flow and exhumation of lower crust comes from a balance between gravity and boundary forces, which is specific to each orogenic belt.

In spite of numerous petrological and geochronological studies conducted on the highpressure granulites and surrounding rocks of the TNCO, the tectonic processes, and especially the crustal structure and flow pattern involved in the exhumation of the high pressure and partially-molten rocks remain unclear and constitute the topic of this paper. For the first time, we document a set of structural analyses acquired on the entire High Pressure Belt. This was conducted together with recognition of morphological subdivisions of the partially molten rocks according to changes in melt fraction. In addition, we present a new compilation of the available Pressure-Temperature paths and geochronological data. A synthetic model allows us to discuss the unroofing processes of the High-Pressure Belt (HPB) and to highlight the critical role of partial-melting and oroclinal bending in triggering and controlling lateral extrusion through channelized flow and exhumation of the deeply buried continental crust.

The High-Pressure Belt within the Trans-North China Orogen

Tectonic outline of the Trans-North China Orogen within the North China Craton

A long-established three-fold subdivision describes the North China Craton (NCC) as composed of the two Archean-Paleoproterozoic Eastern and Western Blocks separated by the ~1.85 Ga Trans-North China Orogen, also named Central Orogenic Belt (Fig. 1; Zhao et al., 2001a-b). Thoroughly, the Western Block is composed of two discrete sub-blocks labelled the Ordos and Yinshan Blocks welded together along the Khondalite Belt around 1.95-1.92 Ga [START_REF] Zhao | Late Archean to Paleoproterozoic evolution of the North China Craton: key issues revisited[END_REF][START_REF] Zhao | Single zircon grains record two Paleoproterozoic collisional events in the North China Craton[END_REF][START_REF] Santosh | Extreme crustal metamorphism during Columbia supercontinent assembly: evidence from North China Craton[END_REF]Santosh et al., , 2007a,b;,b;[START_REF] Yin | Metamorphic evolution and tectonic implications of the Qianlishan-Zhuozishan Complex of the Palaeoproterozoic Khondalite Belt in the Western Block, North China Craton[END_REF][START_REF] Yin | LA-ICPMS U-Pb zircon ages of the Qianlishan Complex: constrains on the evolution of the Khondalite Belt in the Western Block of the North China Craton[END_REF][START_REF] Yin | U-Pb and Hf isotopic study of zircons of the Helanshan Complex: Constrains on the evolution of the Khondalite Belt in the Western Block of the North China Craton[END_REF]. The Eastern block is divided in the Southern Block and the Anshan Block that welded together along the Jiao-Liao-Ji mobile belt at ~1.9 Ga (Faure et al., 2004;[START_REF] Li | SHRIMP U-Pb zircon geochronology of the Liaoji granitoids: constraints on the evolution of the Paleoproterozoic Jiao-Liao-Ji belt in the Eastern Block of the North China Craton[END_REF].

The High-Pressure Belt lies within the 1200km long and 100-300km wide Trans-North China Orogen (TNCO) (Fig. 1). According to different schools of thought, the TNCO resulted from (1) continental collision at ~1.85 Ga after an eastward subduction of the Western Block below the Eastern Block (Zhao et al., 2001a(Zhao et al., -b, 2004[START_REF] Zhao | Late Archean to Paleoproterozoic evolution of the North China Craton: key issues revisited[END_REF][START_REF] Wilde | Archean to Paleoproterozoic evolution of the North China Craton[END_REF]Kröner et al., 2005aKröner et al., -b, 2006;;[START_REF] Zhang | High-pressure mafic granulites in the Trans-North China Orogen: Tectonic significance and age[END_REF], (2) a westward subduction with final collision to form the NCC at ~2.5 Ga [START_REF] Kusky | Paleoproterozoic tectonic evolution of the North China Craton[END_REF][START_REF] Polat | Geochemistry of Neoarchean (ca. 2.55-2.50 Ga) volcanic and ophiolitic rocks in the Wutaishan greenstone belt, central orogenic belt, North China craton: implications for geodynamic setting and continental growth[END_REF][START_REF] Polat | Geochemical and petrological evidence for a suprasubduction zone origin of Neoarchean (ca. 2.5 Ga) peridotites, central orogenic belt, North China craton[END_REF]Kusky et al., 2007;[START_REF] Li | A late Archean foreland fold and thrust belt in the North China Craton: implications for early collisional tectonics[END_REF] or at ~1900-1800 Ma (Wang, 2009) and otherwise (3) a collision after a double-sided subduction [START_REF] Santosh | Assembling North China Craton within the Columbia supercontinent: The role of double-sided subduction[END_REF]. [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF] and [START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF][START_REF] Trap | Contrasted tectonic styles for the Paleoproterozoic evolution of the North China Craton. Evidence for a ~2.1 Ga thermal and tectonic event in the Fuping Massif[END_REF]Trap et al. ( , 2009aTrap et al. ( , 2009b) ) proposed a model in which the building of the TNCO involved three continental blocks, two westward subduction zones and associated two collisional events. The eastern positioned suture is called the Zanhuang suture (Faure et al., 2009, Trap et al., 2009) that resulted from westward subduction of the Eastern (Yanliao) Block under the Fuping Block (Fig. 1B; [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF]Trap et al., 2009). [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF] propose that the amalgamation of the Fuping Block and the Eastern Block occurred at ~2.1 Ga. The western suture, called the Trans-North China Suture that crop out in the Lüliangshan massif, marked the closure, at around 1880 Ma, of an oceanic domain called the Lüliang Ocean (Fig. 1B; [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF][START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF]Trap et al., , 2009a-b)-b).

This suture is the main lithospheric boundary along which ophiolitic and continental crustderived nappes, displaced to the East or South-East, are rooted, resulting in the edification of the Trans-North China Orogen (TNCO) where HP rocks crop out.

The TNCO consists of several tectonic and metamorphic units (Fig. 1B; [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF], Trap et al., 2007). At the top of the litho-tectono-metamorphic pile, the Hutuo Supergourp [START_REF] Sbgmr | Regional Geology of Shanxi Province[END_REF][START_REF] Tian | Geology and Gold Mineralization of Wutai -Hengshan Greenstone Belt[END_REF] consists of unmetamorphozed or weakly metamorphosed, locally highly deformed sedimentary series of conglomerate, sandstone, mudstone, and carbonates with subordinate intercalations of volcanic rocks. It unconformably cover the Low-Grade Mafic Unit (LGMU) that represents greenschists facies klippen of mafic magmatic and sedimentary rocks emplaced from the NW to the SE upon the Orthogneiss and Volcanite Unit (OVU) made of magmatic and volcanic-sedimentary rocks metamorphosed under amphibolite to MP-granulite facies conditions. The OVU tectonically overlies a para-autochtonous unit that corresponds to the basement of the Fuping Block. The last unit recognized in the Trans-North China Orogenic wedge, and that is the focus of the present contribution, is the high-pressure rocks unit, referred as the High-Pressure Belt.

[ Figure 1 ]

Geological setting of the High Pressure Belt (HPB)

In the Trans-North China Orogen, high-pressure mafic and felsic granulites (Figs. 2A and2B) crop out in a NE-SW trending unit of 150 km wide and 400 km long belt (Fig. 1B), referred as the High-Pressure Belt (HPB) that extends from the northern part of the Hengshan Massif (Zhao et al., 2001a;[START_REF] O'brien | The petrology of two distinct granulite types in the Hengshan Mts, China, and tectonic implications[END_REF], through the Datong-Huai'an area [START_REF] Zhai | Discovery and preliminary study of the Archean high-pressure granulites in the North China[END_REF][START_REF] Zhai | The discovery of Archaean retrograde eclogites in the North China craton[END_REF][START_REF] Guo | Early Precambrian Manjinggou high-pressure granulites melange belt on the southern edge of the Huai'an Complex, North China Craton: geological features, petrology and isotopic geochronology[END_REF][START_REF] Guo | High-pressure granulites in the Sangan area, North China Craton: metamorphic evolution, P-T paths and geotectonic significance[END_REF] and Xuanhua Massif [START_REF] Wang | Some evidence for the Late Archean collisional belt in the western Hebei Province[END_REF][START_REF] Guo | High-pressure granulites in the Sangan area, North China Craton: metamorphic evolution, P-T paths and geotectonic significance[END_REF], up to the Chengde Massif [START_REF] Li | Discovery of Late Archean high-pressure granulites in Luanping-Chengde area, Northern Hebei Province: tectonic implications[END_REF][START_REF] Mao | Isotopic ages and geological implications of high-pressure mafic granulites in the northern Chengde area, Hebei Province, China[END_REF]. Within the HPB, the average foliation strike progressively changes from N70E to the East to N45E to the West (Fig. 1B). Two major ductile shear zones, the Zhujiafang [START_REF] Li | Late Archean continental cratonization: evidence from Hengshan metamorphic terrain, North China Craton[END_REF]

and the

Datong-Chengde Shear Zones (this study) limit the HPB along its southern and northern boundaries, respectively (Fig. 3A). The high-grade metamorphic rocks of the HPB are unconformably covered by Meso-to Neoproterozoic and Jurassic-Cretaceous unmetamorphosed sedimentary or volcanic rocks and intruded by several generations of granitoids, mainly of Mesozoic age. Consequently, the western and eastern terminations of both shear zones and the structural relationships of the HPB with the southeastern orthogneiss-volcanite unit remain unknown.

[ Figure 2 ] The HPB consists mainly of anatectic rocks with granulitic boudins that recorded a clockwise P-T retrograde evolution, characterized by an isothermal decompression from 15 kbar to 5 kbar (e.g. [START_REF] Zhang | High-pressure mafic granulites in the Trans-North China Orogen: Tectonic significance and age[END_REF]. Lithological and metamorphic characters are presented in detail in the next sections.

Northwest of the HPB, high temperature Al-rich metasediments crop out that belong to the 'Khondalite series'of the Chinese literature which is considered to have developed in the passive continental margin of the Ordos Terrane of the Western Block [START_REF] Condie | The origin of khondalites: geochemical evidence from the Archean to early Proterozoic granulite belt in the North China Craton[END_REF][START_REF] Zhao | Thermal evolution of Archean basement rocks from the eastern part of the North China Craton and its bearing on tectonic setting[END_REF][START_REF] Zhao | Late Archean to Paleoproterozoic evolution of the North China Craton: key issues revisited[END_REF][START_REF] Kusky | The Paleoproterozoic North Hebei Orogen: North China Craton's Collisional Suture with the Columbia Supercontinent[END_REF]. To the east, these rocks are underlain by TTG rocks that form the northern domains of the Xuanhua and Chengde massifs, north of the DCSZ (Fig. 1B). Along the DCSZ and the northern boundary of the HPB, blocks of hornblendite, metagabbro, pyroxenite and serpentinite are exposed, well observed in the western Huai'an Massif and eastern Chengde Massif. In this last area, these mafic and ultramafic rocks are involved in the Datong-Chengde Shear Zone (Figs. 5 and7). Ophiolites are not cropping out in the Datong area and farther East. Nevertheless, the lithological, structural and metamorphic contrasts between the khondalite series and the high-pressure granulites suggest that this fault represents the northeastward extension of the Trans-North China suture east of Datong. These mafic and ultramafic rocks might be considered as the remnants of the Lüliang Ocean.

As a whole, the HPB appears as the deepest part of the thickened crust that was exhumed and that occupies a peculiar position in the core of an oroclinal bend experienced by the TNCO. Indeed, the orocline is well marked by the change in strike of the Paleoproterozoic planar fabrics that progressively turns from N20E to N70E, from the south-western Lüliang Massif toward the north-eastern Chengde Massif, respectively (Fig. 1B).

The regional deformation history of the westernmost part of the HPB, has been investigated by [START_REF] Zhang | Extensional collapse and uplift in a polymetamorphic granulite terrain in the Archean and Paleoproterozoic of north China[END_REF] in the Datong-Huai'an area. These authors inferred a deep-seated low-angle ductile extensional detachment as the main structure responsible for the exhumation of the high-pressure granulites. Because of a lack of unequivocal kinematic indicators, [START_REF] Dirks | Exhumation of high-pressure granulites and the role of lower crustal advection in the North China Craton near Datong[END_REF] did not took into consideration such a detachement fault and suggested that the exhumation of the HP rocks was not accommodated by orogenic extensional tectonics. They rather advocated a dynamic interplay between solid-state vertical flow and horizontal flattening, in lower and upper structural domains, respectively. These two studies focused on the westernmost edge of the HPB (i.e. the Datong-Huai'an area), but no structural work has been done in the entire HPB. In particular, the geometric and kinematic features of the central and eastern parts of the HPB were not analyzed. Furthermore, the tectonic evolution of the HPB as a whole has never been considered. In order to get a general structural view of the HPB, the western Datong-Huai'an area, the central Xuanhua massif and the eastern Chengde massif were the targets of a detail structural analysis. In addition, we present a morphological subdivision of the HPB and its surrounding rocks based on observation of changes in melt fraction (mainly diatexite/metatexite distinction).

The HPB within the Partially Molten Zone (PMZ)

The HPB is mainly composed of partially-molten rocks (Fig. 2) and lies within a here defined Partially Molten Zone (PMZ). Within the PMZ, a four-fold subdivision from lower to upper structural level is recognized: These four anatectic subunits namely from bottom to top (1) The Lower Mafic Metatexite, (2) The Middle Diatexite, (3) The Upper Metatexite and (4) the Outer Metatexite. This subdivision is primarily a morphological one based on the melt fraction in the migmatitic rocks, mainly diatexite/metatexite disctinction. Metatexite and diatexite represent rocks with low and high melt fraction, respectively [START_REF] Sawyer | Atlas of migmatites[END_REF].

The Lower Mafic Metatexite

Structurally, the Lower Metatexite represents the deepest domain that crops out in the central part of the HPB, i.e. in the southern part of the Xuanhua Massif and the easternmost part of the Datong-Huai'an area (Fig. 5 and6). The lowermost part is composed of banded tonalitic and mafic granulite gneiss. The pre-melting structures of the protolith are well preserved and the weak amount of leucosome argues for a low melt fraction (Fig. 2A). This apparently low melt fraction might not be due to a low-melting rate but rather to melt loss, as suggested by low leucosome to peritectic garnet ratios [START_REF] Sawyer | Atlas of migmatites[END_REF].

The Middle Diatexite

The Middle Diatexite is composed of granitoids of various compositions. The lower part is dominated by orthopyroxene-bearing granitoids (charnokite-enderbite suite) with subordinate amounts of dioritic granitoids. The upper part of the Middle Diatexite is more felsic with predominant dioritic to granodioritic compositions. These granitoids are diatexites in the sense of [START_REF] Sawyer | Atlas of migmatites[END_REF] with leucocratic material enclosing boudins and rafts of retrograded HP granulites (Fig. 2B). Morphological aspects grade from scholen to schlieric diatexites (Figs. 2C and2D). Some felsic biotite-garnet and sillimanite-garnet metasedimentary rocks also occur as meter-thick paleosome lenses enclosed within leucocratic neosome. In addition, numerous K-feldspar rich granitoids are reported as cm to m-thick veins and sheeted dykes that intrude within the diatexite. Sometimes, such K-feldspar rich granitoids form 10-meters large bodies particularly in the highest structural level of the Upper Metatexite.

The Upper Metatexite

The Upper Metatexite is located in the uppermost part of the HPB, either in central position or along the DCSZ and the Zhujiafang Shear Zone. It mostly consists of partially molten TTG gneiss, mafic and felsic metavolcanites and sometimes Al-rich metapelites and metacarbonaceous rocks (Figs. 2E, 4A and4B).

The Outer Metatexite

These rocks crop out in two distinct areas, on each sides of the HPB (Fig. 8). North of the HPB, from Xuanhua area to Chengde area, TTG and migmatites widely develop. These partially melted rocks are metatexites developed from a khondalitic paleosome. Mafic and felsic metavolcanic rocks are also recognized as protoliths. The TTG and migmatites are conspiscuously intruded by numerous granitic dykes and sills. In the following, this unit will be referred to as the Northern Felsic Unit (Figs. 3 and8). At the scale of the entire TNCO, the Northern Felsic Unit corresponds to the deformed and partially molten margin of the Western Block. The relationships of this unit with the Khondalite Unit that crops out northeast of Datong are unclear since the contact is not exposed in the field. Furthermore, south of the Zhujiafang Shear Zone or North of the Chendge-Datong Shear Zone, HP granulites are no more observed. Patch metatexite [START_REF] Sawyer | Atlas of migmatites[END_REF] with a very low-melt fraction (Fig. 2F) marks the limit of the partially molten area.

Structural analysis

Although in some places, the Meso-and Neoproterozoic sedimentary sequences are folded, or deformed by brittle faulting [START_REF] Davis | Mesozoic tectonic evolution of the Yanshan fold and thrust belt, with emphasis on Hebei and Liaoning provinces, northern China[END_REF], no syn-metamorphic deformation younger than the Paleoproterozoic Trans-North China Orogeny can be documented in the study area, expect some reworking along portions of the western part of the DCSZ. Therefore, the ductile high-grade deformation described below can be confidently attributed to the Paleoproterozoic.

The HPB bulk geometry is an elongate asymmetric antiform with a gently northwarddipping northern limb, bounded by the Datong-Chengde shear zone, and a sub-vertical to steeply southward-dipping southern limb, limited by the Zhujiafang shear zone. The foliation pattern shows that the hinge zone of the antiform is curved in map view from E-W to NE-SW, and also in the vertical plane, with the eastern and western pericline terminations dipping toward the east and the west, in the Datong-Hua'ian and Chengde Massifs, respectively (Fig. 3). As a consequence, the central part of the HPB exposes the lower structural domain whereas the upper structural domain is observed in the eastern and western pericline terminations and along the two northern and southern bounding (Fig. 8).

Structural analysis yielded to the recognition of four main structural stages (labeled hereafter D 1 -D 4 ), responsible for the structuration of the HPB and the Partially Molten zone as a whole. Details of each deformation stage are given below.

D 1 Deformation stage

Within the HPB rocks, the D 1 fabric is an amphibolite facies gneissic foliation (S 1 ) recognized within the paleosomes. A L 1 mineral lineation is often obliterated by a pervasive static recrystallisation. In diatexite, a pre-partial-melting S 1 relictual fabric is preserved within the scattered schollen of paleosomes. In metatexite, S 1 and a syn-anatectic S 2 foliations are mingled in a S 1-2 fabric, the geometry of which defines the D 2 finite strain pattern (see below).

The D 1 fabric remains preponderant in the units that surround the PMZ, where partial-melting did not occurred, i.e. along the northern and southern limits of the PMZ, respectively. There, the conspicuous D 1 fabric is a gneissic foliation S 1 that trends NE-SW to E-W, on which a NW-SE trending mineral and stretching lineation, L 1 , marked by a preferred alignment of sillimanite, biotite or amphibole crystals develops (Fig. 3B). Along L 1 , a prominent top-to-the SE sense of shear is indicated by classical kinematic indicators, such as sigma-type porphyroclast systems or pressure shadows. In the commonest cases, reworking by the following D 2 to D 4 events led to the folding and scattering of the D 1 fabric trend.

[ Figure 3]

D 2 Deformation stage

D 2 strain features

The D 2 stage is the most prominent deformation stage developed in the PMZ, coevally with amphibolite to granulite facies metamorphism and crustal melting. D 2 can be considered as a syn-anatectic deformation, in other words, the D 2 migmatitic layered fabric was generated by in-situ melting and segregation of leucocratic material under a regional strain (Figs. 4A and4B). As mentioned above, the S 2 foliation is defined by leucocratic material that formed parallel to the early gneissic layering S 1 . Thus, the syn-anatectic foliation within metatexite has to be considered as a S 1-2 fabric.

Within the Lower Mafic Metatexites, S 2 is defined by the planar alignement of leucocratic melt pockets develop parallel to peritectic minerals as well as around retrograded matrix minerals. In some granitoids, such as the Huai'an anatectic charnokite (G.C. [START_REF] Migmatitic Leucosome Hpb Faure | ± 9.8 (a) M22 Anatectic charnokite (Huai'an charnokite) HPB Zhao et al[END_REF], the S 2 foliation is represented by the preferred orientation of leucocratic orthopyroxene or clinopyroxene-bearing anorthositic veins [START_REF] Dirks | Exhumation of high-pressure granulites and the role of lower crustal advection in the North China Craton near Datong[END_REF]. In the Middle Diatexite, S 2 is defined by biotite-amphibole schlierens and the preferred orientation of mafic restites (Figs. 2C and3E).

The L 2 mineral lineation is commonly marked by the linear preferred orientation of aggregates of peritectic minerals such as garnet, biotite or orthopyroxene. In leucocratic material, the L 2 lineation is represented by stretched mm-to cm-scale biotite or amphibole aggregates. However, the clearest and unambiguous observations of L 2 in migmatites are made at the outcrop scale, where the stretching direction is defined by meter-scale boudinage of competent mafic paleosomes or melanosomes (Figs. 2C and2D). Stretching is also documented by the orientation of tension gashes filled with granitic or charnokitic melt.

Along the L 2 stretching direction, kinematic patterns are contrasted. A non-coaxial strain regime is deduced from the observation of kinematic criteria such as asymmetric boudinage, asymmetric sigma-type porphyroclast systems around peritectic minerals, or shear band. In addition, symmetric boudinage argues for coaxial flow. Over the entire PMZ, the D 2 finite strain pattern can be subdivided into four spatially distinct areas: (1) the central part characterized by 10-50 km wide SW-NE trending domes deformed by a E-W coaxial flow;

(2) the geometrically higher rim of the central part, (3) the western part of the HPB, that are both characterized by non-coaxial regime and (4) the folded outer metatexite in the Hengshan Massif.

[ Figure 4 ] 4.2.2. SW-NE to E-W trending coaxial flow and doming Within the HPB, the S 2 geometry defines regional-scale dome structures that vary in size from 10 to 40 km in length and 5 to 20 km in width (Figs. 5,6 and 7). Usually, S 2 trends E-W in the central and eastern part of the HPB and NE-SW in its western edge (Fig. 3C). The attitude of the S 2 foliation varies from nearly horizontal to vertical in the dome top and margins, respectively. However, neither vertical nor steeply dipping foliation occurs at dome terminations but only along the NE-SW to E-W trending dome limbs (Fig. 5).

Across the PMZ, the L 2 lineation is preferentially E-W trending with a shallow to moderate plunge (Figs. 3C, 3D and3E). Within the HPB, both in the top of the domes where the foliation is flat-lying, or along the steeply dipping foliation in the domes flanks, N-S striking subvertical melt-filled veins perpendicular to the maximum flattening plane, represented by the S 2 foliation, argue for vertical shortening and E-W horizontal stretching. Thus, at the regional scale, orientation of the dilational sites is consistent with layer-parallel syn-anatectic stretching.

Folded nebulitic diatexites that suggest turbulent flow are not widespread and mainly located in the inner part of the HPB, in the core of the diatexite domes (Fig. 4C). More commonly, four types of fold can be distinguished owing to their geometry and their distribution pattern within the large-scale domes:

(i) In the top of the domes, cm to m-scale tight folds with horizontal axial-planes resemble ptgymatitic folds (Fig. 4D).

(ii) Meter-scale upright folds with vertical axial plane that are preponderant along the E-W trending synformal keel that surrounds the domes, some larger 100-500 m-scale upright folds might be inferred from S 2 orientation changes.

(iii) Along dome limbs, where S 2 is moderately to steeply dipping, cm-to m-scale recumbent folds verging away from the dome culmination are observed in diatexite.

(iv) Intrafolial folds are the commonest ones that range in size from ten centimetres to few meters with axes parallel the L 2 stretching direction (Fig. 4E).

Within diatexites, the progressive isoclinal folding of melanocratic layers accounts for transposition of an earlier disrupted compositional migmatitic S 2 foliation to a new one here denoted as S 2n (Figs. 4D and4E). Such a transposition is frequently observed in the central and upper parts of the domes where the migmatitic foliation is flat lying to moderately dipping. In some outcrops, [START_REF] Dirks | Exhumation of high-pressure granulites and the role of lower crustal advection in the North China Craton near Datong[END_REF] recognized at least six overprinting foliationforming and folding events. At the whole HPB scale, transposition is mainly observed in the upper part of the Middle Diatexite where steeply dipping S 2 is progressively changed in an horizontal one (Fig. 8). In addition, some high strained domains concentrated as highly stromatitic migmatites occur along vertical or steeply dipping foliation that delimitate dome in the Middle Diatexite (Fig. 4F).

[ Figure 5 ]

[ Figure 6 ] [ Figure 7 ] [ Figure 8 ] 4.2.3. Westward non-coaxial regime
In the western part of the HPB, the domal architecture turns gradually to a flat-lying structure defined by a relatively constant S 2 foliation that preferentially dips westward (Figs. 3A and3C). The D2 finite strain is heterogeneous with high strain domains concentrated along cm-to dm-scale shear zones where in-source leucosome or leucocratic vein commonly occur. The L 2 lineation conspicuously plunges W or SW (Figs. 3C, 5 and6). Kinematic indicators attest for a top-to-the W and SW normal shearing. This kinematic record is in agreement with previous work [START_REF] Zhang | Extensional collapse and uplift in a polymetamorphic granulite terrain in the Archean and Paleoproterozoic of north China[END_REF][START_REF] Dirks | Exhumation of high-pressure granulites and the role of lower crustal advection in the North China Craton near Datong[END_REF].

Sinistral strike-slip shearing

In the westernmost edge of the HPB, S 1-2 is steeply dipping with a L 2 lineation that plunges weakly to moderately toward the southwest along which a sinistral strike-like movement with a normal component is observed (Figs. 3A and3C). This sinistral strike-slip shearing is transitional in space with the westward one. A sinistral strike slip deformation is also observed in the northeastern edge of the PMZ, along the Longhua shear zone, north Chengde Massif, whereas few kinematic indicators attest for syn-anatectic dextral shearing along the hangingwall of the DCSZ, in Damiao village area (Fig. 3A).

Northward verging syn-anatectic folding in the Hengshan Massif

In the Hengshan Massif (southern PMZ), the S 1-2 foliation is folded by open to tight, north verging, recumbent folds. Leucosomes concentrate in shear bands developed along the limbs and axial surfaces of the folds that constitute dilatants sites where melt preferentially migrate into. This fold axial plane is considered as a S 2n since the S 1-2 is folded. This synanatectic north verging folding is mainly observed south of the Zhujiafang Shear Zone, outside of the HPB (Fig. 9A).

[ Figure 9 ]

D 3 Deformation stage

The D3 deformation stage developed under subsolidus conditions. The E-W trending flow is also recognized in a subsolidus state during D 3 . In the central part of the HPB, S 3 is flat lying and parallel to S 2 . Along the L 3 mineral lineation, symmetric pressure shadows or porphyroclast systems argue for a coaxial regime (Fig. 9B). In some outcrops, a symmetric D 3 boudinage (Fig. 9C) is also in agreement with a D 3 coaxial flow, even if sometimes, a synanatectic D 2 fabric is still preserved within the lenses. In the western part of the HPB, D 3 shows a SW to W directed shearing that appears as parallel to the D 2 strain.

The most prominent manifestation of D 3 is the Datong-Chengde Shear Zone (DCSZ) that appears as a km-scale ductile normal shear zone (Figs. 3A and3F). In its eastern part, the shear zone separates into a northern branch, the Longhua shear zone (LSZ) and a southern branch, the Damiao shear zone (DSZ; Fig. 3). S3 is a NW to N dipping mylonitic foliation that contains a NW plunging L 3 stretching lineation (Figs. 10A, 10B and 10C). East of Chengde, between Sangou and Wutache, the S3 mylonitic foliation becomes near horizontal.

Kinematic indicators show a top-to the NW displacement (Figs. 10D and10E). Thus, in its present geometry, the DCSZ has a normal plus left-lateral kinematics. The sinistral strike-slip component is more pronounced in the western part of the DCSZ (Figs. 3 and7).

The D 3 mylonitic fabric developed at the granulite/amphibolite facies transition as evidenced by destabilisation of Opx porphyroblasts dynamically recristallized in an assemblage of orthopyroxene + amphibole + plagioclase (Fig. 10D). It is noteworthy that the DCSZ mainly developed in the footwall of the Middle Diatexite of the HPB. Along the eastern part of the DCSZ, some segments may have been reactivated during Paleozoic as expressed by the brittle-ductile steeply dipping Shangyi-Chicheng Fault [START_REF] Hu | The 40 Ar/ 39 Ar geochronology constraint and geological significance of mylonites in Shangyi-Chicheng fault belt on the north of the North China Craton[END_REF].

D 4 Deformation stage: the late Zhujiafang strike-slip shearing

In the northern part of the Hengshan massif, the flat-lying to SW-dipping S 2 is continuously deflected into an E-W trending steeply dipping orientation as approaching the Zhujiafang Shear Zone (ZSZ). The ZSZ is characterized by a subvertical to southward steeply dipping (>70°) mylonitic to ultramylonitic foliation that holds a horizontal to shallowly plunging stretching lineation along which a sinistral kinematics is observed [START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF][START_REF] Wang | Reply to the comment by Zhao et al. on: "Tectonic evolution of the Henghsan-Wutai-Fuping complexes and its implicaion for the Trans-North China Orogen[END_REF]. However, dextral component has been reported in the vicinity of the Zhujiafang shear zone [START_REF] Kröner | Zircon geochronology and metamorphic evolution of mafic dykes in the Hengshan Complex of northern China: evidence for late Palaeoproterozoic extension and subsequent high-pressure metamorphism in the North China Craton[END_REF]. Along the strike-slip shear zone, but out of the high-strain domain, a down-dip to highly plunging lineation, with the southern side moving downward, accounts for an early vertical movement [START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF].

[ Figure 10 ]

Review of P-T paths and radiochronological data

P-T evolution of the HP rocks

The commonest relics of HP rocks encountered in the Chengde Massif, Xuanhua Massif and Datong-Huai'an-Northern Hengshan area (Fig. 1) are retrograded eclogites and highpressure granulites. These rocks crop out as 10 cm-to 10 m scale boudins or flat sheets within amphibolite and granulite facies diatexites (Figs. 2A and 2B;[START_REF] Zhai | Discovery and preliminary study of the Archean high-pressure granulites in the North China[END_REF][START_REF] Zhao | Metamorphism of basement rocks in the Central Zone of the North China Craton: implications for Paleoproterozoic tectonic evolution[END_REF]Zhao et al., , 2001a;;[START_REF] Guo | High-pressure granulites in the Sangan area, North China Craton: metamorphic evolution, P-T paths and geotectonic significance[END_REF][START_REF] O'brien | The petrology of two distinct granulite types in the Hengshan Mts, China, and tectonic implications[END_REF][START_REF] Zhang | High-pressure mafic granulites in the Trans-North China Orogen: Tectonic significance and age[END_REF]. The protoliths of the mafic granulites are magmatic rocks of doleritic and gabbroic composition interpreted as mafic dykes intruding a TTG gneissic sequence also known in the literature as the Grey Gneiss or Huai'an gneiss [START_REF] Zhang | Extensional collapse and uplift in a polymetamorphic granulite terrain in the Archean and Paleoproterozoic of north China[END_REF][START_REF] Guo | Sm-Nd and SHRIMP U-Pb zircon geochronology of high-pressure granulites in the Sanggan area, North China Craton: timing of Paleoproterozoic continental collision[END_REF]Kröner et al., 2005b;[START_REF] O'brien | The petrology of two distinct granulite types in the Hengshan Mts, China, and tectonic implications[END_REF]. The occurrence of felsic granulites and metapelites indicates that the entire continental crust, i.e. the TTG basement gneiss, sedimentary cover and the mafic intrusions experienced the HP eclogitic and granulitic metamorphism during the early stages of the Trans-North China Orogeny.

The HP granulites of the Hengshan, North Datong, Huai'an, and Chengde massifs experienced a rather similar evolution (Fig. 11). The reconstructed P-T paths obtained for the high-pressure mafic granulites of the HPB are characterized by a clockwise evolution with a near-isothermal decompression followed by a final cooling (Fig. 11). Peak assemblages (M 1 ) are defined by a granultie facies garnet + clinopyroxene ± quartz association and sometimes by an eclogite facies mineral assemblage of garnet + quartz + omphacite pseudomorphs (Zhao et al., 2001a;[START_REF] Zhang | High-pressure mafic granulites in the Trans-North China Orogen: Tectonic significance and age[END_REF]. The P-T path is then defined by medium-pressure granulite facies garnet + plagioclase + clinopyroxene + orthopyroxene ± quartz assemblage (M 2 ) and a low-pressure granulite facies orthopyroxene ± clinopyroxene + plagioclase ± quartz assemblage (M 3 ). The end of the P-T path is defined by an amphibolite facies hornblende + plagioclase assemblage (M 4 ). M1 took place at 800-850 °C / 14-16 kbar, M2 and M3 occurred for T/P conditions of 800-825°C/10kbar and 800°C/7-8kbar, respectively. Thermo-barometric conditions of 650°C/5kbar were estimated for M4 (Table 1;Fig 11;[START_REF] Zhai | Discovery and preliminary study of the Archean high-pressure granulites in the North China[END_REF][START_REF] Liu | Two types of Precambrian high-grade metamorphism, Inner Mongolia, China[END_REF][START_REF] Zhang | Extensional collapse and uplift in a polymetamorphic granulite terrain in the Archean and Paleoproterozoic of north China[END_REF][START_REF] Zhao | Metamorphism of basement rocks in the Central Zone of the North China Craton: implications for Paleoproterozoic tectonic evolution[END_REF]Zhao et al., , 2001a;;[START_REF] Guo | High-pressure granulites in the Sangan area, North China Craton: metamorphic evolution, P-T paths and geotectonic significance[END_REF][START_REF] Guo | Sm-Nd and SHRIMP U-Pb zircon geochronology of high-pressure granulites in the Sanggan area, North China Craton: timing of Paleoproterozoic continental collision[END_REF][START_REF] O'brien | The petrology of two distinct granulite types in the Hengshan Mts, China, and tectonic implications[END_REF][START_REF] Zhang | High-pressure mafic granulites in the Trans-North China Orogen: Tectonic significance and age[END_REF] [ Table 1 ] [ Figure 11 ] 2 summarize most of the available high-T radiochronological ages obtained for rocks within the HPB and its close surrounding units. This synthesis shows that the tectonic-metamorphic evolution of the TNCO can be subdivided into five periods, namely (1) 2550-2450 Ma, (2) 2300-1900 Ma, (3) ~1880 Ma, (4) ~1850 Ma (5) 1840-1800 Ma.

Radiochronological dataset

The 2550-2450 Ma period: Archean protoliths

A first pool of about twenty ages that fall into the range 2450-2550Ma is recorded in the HPB rocks (Table 2; Fig. 2). Most of the available ages recorded within the Trans-North China Orogen range between 2550 and 2450 Ma (e.g. [START_REF] Zhao | SHRIMP U-Pb zircon ages of the Fuping Complex: implications for accretion and assembly of the North China Craton[END_REF][START_REF] Zhao | Late Archean to Paleoproterozoic evolution of the North China Craton: key issues revisited[END_REF][START_REF] Zhao | Composite nature of the North China Granulite-Facies Belt: Tectonothermal and geochronological constraints[END_REF][START_REF] Guo | Sm-Nd and SHRIMP U-Pb zircon geochronology of high-pressure granulites in the Sanggan area, North China Craton: timing of Paleoproterozoic continental collision[END_REF]Kröner et al., 2005a-b;[START_REF] Wilde | Archean to Paleoproterozoic evolution of the North China Craton[END_REF]). All the recent geochronological investigations using CL imaging and SHRIMP U-Pb zircon dating revealed that the ~2500 Ma ages represent protoliths ages obtained on inherited grains or core of grains (Kröner et al., 2005a-b;[START_REF] Wilde | Archean to Paleoproterozoic evolution of the North China Craton[END_REF][START_REF] Zhao | Late Archean to Paleoproterozoic evolution of the North China Craton: key issues revisited[END_REF]. Correspondingly, within the HPB, the 2550-2450 Ma ages may represent the timing of formation of the Archean-Paleoproterozoic magmatic protolith.

The 2300-1900 Ma period: Thermal and magmatic event

The oldest evidence for this event are a fine grained orthogneiss, a granite-gneiss and a trondhjemitic gneiss dated at 2358.7 ± 0.5, 2331 ± 36, 2329.7 ± 0.6 Ma, respectively (Table 2; Fig. 12; Kröner et al., 2005b). Three felsic granitoids, one pegmatite and one anatectic granite have also been reported by Kröner et al. (2005b) at 2248.5 ± 0.5 Ma and 2113 ± 8 Ma, respectively. One gabbroic rock from a metatexite of the OVU, south of the HPB, yielded a SHRIMP U-Pb age at 2193 ± 15 Ma. Within the Huai'an massif, some ages around 2100 Ma are also reported from Al-rich metasediments and some granitoids such as the Dongjiagou gneissic granite dated at 2036 ± 19 Ma (G.C. [START_REF] Zhao | SHRIMP U-Pb zircon geochronology of the Huaian Complex: constraints on Late Archean to Paleoproterozoic crustal accretion and collision of the Trans-North China Orogen[END_REF]. Similar 2.3-2.1 Ga ages were reported in the different TNCO massifs, in particular those obtained from plutonic and volcanic rocks in the Hengshan, Wutaishan and Fuping Massifs that argue for a tectono-thermal event around 2.1 Ga [START_REF] Wilde | SHRIMP U-Pb zircon dating of granites and gneisses in the Taihangshan-Wutaishan area: implications for the timing of crustal growth in the North China craton[END_REF][START_REF] Wilde | Archean to Paleoproterozoic evolution of the North China Craton[END_REF][START_REF] Zhao | SHRIMP U-Pb zircon ages of the Fuping Complex: implications for accretion and assembly of the North China Craton[END_REF][START_REF] Trap | Contrasted tectonic styles for the Paleoproterozoic evolution of the North China Craton. Evidence for a ~2.1 Ga thermal and tectonic event in the Fuping Massif[END_REF]. However, the significance of this event in the tectonic evolution of the NCC still remains difficult to settle. The 2.3-2.1 Ga magmatism and volcanism might correspond to the formation of a marginal back-arc basin coeval with the development of the OVU [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF][START_REF] Wang | Reply to the comment by Zhao et al. on: "Tectonic evolution of the Henghsan-Wutai-Fuping complexes and its implicaion for the Trans-North China Orogen[END_REF].

In the southern part of the HPB, two sets of magmatic zircons from two mafic highpressure granulites yielded mean 207 Pb/ 206 Pb ages of 1915 ± 4 Ma and 1914 ± 2 Ma, respectively, interpreted as reflecting the time of emplacement of the gabbroic dyke precursors [START_REF] Kröner | Zircon geochronology and metamorphic evolution of mafic dykes in the Hengshan Complex of northern China: evidence for late Palaeoproterozoic extension and subsequent high-pressure metamorphism in the North China Craton[END_REF]. Due to the scarcity of such ages within the Trans-North China Belt, they are difficult to interpret in term of a tectono-metamorphic event.

Nevertheless, the ~1915 Ma ages reported in two metapelites of the southwestern located Lüliang Massif represents a thermal or tectonic-metamorphic event older than the main regional metamorphism dated at ~1880 Ma (Trap et al., 2009b). 5.2.3. The 1880 ± 10 Ma period : time of peak metamorphism and crustal thickening SHRIMP U-Pb ages of metamorphic zircons of 1881±8 Ma and a mean evaporation 207Pb/206Pb age of 1881.3±0.4 Ma have been reported in the Hengshan migmatites (Table 1; Kröner et al., 2005a[START_REF] Kröner | Zircon geochronology and metamorphic evolution of mafic dykes in the Hengshan Complex of northern China: evidence for late Palaeoproterozoic extension and subsequent high-pressure metamorphism in the North China Craton[END_REF]. Along the Zujiafang Shear Zone, a chemical U-Th-Pb monazite age from a kyanite-bearing metapelite yield a 1883±11 Ma age [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF]. [START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF] interpreted the concordant U-Th-Pb monazite ages of 1887±4 Ma, 1886±5Ma and 1884±11 Ma from three metapelites located in the southern adjacent OVU unit as the age of the prograde amphibolite facies metamorphism coeval with nappe-stacking. In the Xuanhua Massif, [START_REF] Guo | Sm-Nd and SHRIMP U-Pb zircon geochronology of high-pressure granulites in the Sanggan area, North China Craton: timing of Paleoproterozoic continental collision[END_REF] obtained a zircon SHRIMP U-Pb age at 1872 ± 16 from the highpressure granulites. We interpret the 1870-1890 Ma period as the time of peak metamorphism coeval with nappe-stacking and crustal thickening during D1 event. In addition, the age of 1872 ± 17 recorded in a migmatitic leucosome of granitic composition (Kröner et al., 2005b) argues for the onset of partial-melting in response to crustal thickening, in agreement with [START_REF] Zhang | Extensional collapse and uplift in a polymetamorphic granulite terrain in the Archean and Paleoproterozoic of north China[END_REF] that postulated that melt was present at peak-assemblage conditions during the 1870-90 Ma period.

[ Table 2 ] 5.2.4. The 1850+-10 Ma period: time of widespread crustal melting Zircon conventional U-Pb multigrain and SHRIMP U-Pb datings within the HP granulites yield pooled ages around 1850 Ma (Table 2; Fig. 12; [START_REF] Zhao | SHRIMP U-Pb zircon ages of the Fuping Complex: implications for accretion and assembly of the North China Craton[END_REF][START_REF] Zhao | Late Archean to Paleoproterozoic evolution of the North China Craton: key issues revisited[END_REF][START_REF] Zhao | Composite nature of the North China Granulite-Facies Belt: Tectonothermal and geochronological constraints[END_REF][START_REF] Guo | Sm-Nd and SHRIMP U-Pb zircon geochronology of high-pressure granulites in the Sanggan area, North China Craton: timing of Paleoproterozoic continental collision[END_REF]Kröner et al., 2005a-b;[START_REF] Wilde | Archean to Paleoproterozoic evolution of the North China Craton[END_REF][START_REF] Wan | Further evidence for ~1.85 Ga metamorphism in the Central Zone of the North China Craton: SHRIMP U-Pb dating of zircon from metamorphic rocks in the Lushan area, Henan Province[END_REF][START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF]Wang et al., 2010a). In the Hengshan Massif, Kröner et al. (2005b) obtained metamorphic zircon U -Pb ages of 1848 ± 5 1850 ± 3, 1867 ± 23, 1859.7 ± 0.5 Ma from the high-grade granitoid gneisses and high-pressure mafic granulites. An ICP-MS U-Pb age at 1850 ± 5 Ma from metamorphic zircons rims of an anatectic leucosome has been interpreted to date partial-melting [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF]. In the Datong-Huai'an area, SHRIMP U-Pb dating of magmatic zircon from an anatectic charnockite and a granite (Dapinggou pluton), yield ages of 1849 ± 9.8 Ma and 1850 ± 17 Ma, respectively [START_REF] Zhao | SHRIMP U-Pb zircon geochronology of the Huaian Complex: constraints on Late Archean to Paleoproterozoic crustal accretion and collision of the Trans-North China Orogen[END_REF]. Furthermore, the metamorphic zircons from TTG gneisses, Paleoproterozoic granitoids and khondalitic rocks yield similar concordant 207 Pb/ 206 Pb ages around 1850 Ma, coeval with the emplacement of the Huai'an anatectic charnockite and Dapinggou syn-collisional granite [START_REF] Zhao | SHRIMP U-Pb zircon geochronology of the Huaian Complex: constraints on Late Archean to Paleoproterozoic crustal accretion and collision of the Trans-North China Orogen[END_REF].

Therefore we interpret the numerous 1850-1860 Ma ages as the date of the period corresponding to the peak of crustal melting and related anatectic plutonism. This is in agreement with Wang et al. (2010a) that compiled metamorphic zircon ages for high-grade metamorphic rocks from the whole TNCO and revealed three age peaks at 1876 ± 6 Ma, 1849 ± 2 Ma and 1814 ± 4 Ma. These authors poposed that 1845 ± 7 Ma is the best estimate for the timing of the HP metamorphism in the Huai'an Massif. In the light of the compilation we rather suggest that the 1845 Ma age corresponds to the age of peak partial-melting and magmatism that post-date the peak pressure clearly settled at ca 1880 Ma.

The <1850 Ma ages

A set of magmatic ages around 1820 ± 20 Ma is recorded in a charnockite pluton and some granulites blocks (Table 2; Fig. 12). Rimmed zircons within a migmatitic leucosome recorded a magmatic core at 1846 ± 21 Ma and a metamorphic rim at 1819 ± 13 Ma (Wang et al., 2010a). The 1820 ± 20 Ma ages might reflect a thermal metamorphism due to a latemagmatic pulse within the partially molten HPB. Finally, the latest ages of 1806 ± 15 and 1803 ± 9 Ma [START_REF] Guo | Sm-Nd and SHRIMP U-Pb zircon geochronology of high-pressure granulites in the Sanggan area, North China Craton: timing of Paleoproterozoic continental collision[END_REF]Wang et al., 2010a) are similar to magmatic ages of unstrained post-tectonic granites that intrude the whole TNCO (e.g. [START_REF] Geng | Chronological framework of the early Precambrian important events in the Lüliang area, Shanxi Province[END_REF]. Therefore in the TNCO, the crust may have been partially molten during over >50 Ma as bracketed by the 1872 ± 17 and 1819 ± 13 U-Pb ages recorded for two migmatitic leucosomes (Table 2; Kröner et al., 2005;Wang et al., 2010a).

[ Figure 12 ] 6. Discussion

Flow and exhumation of the TNCO thickened crust

Four main tectono-metamorphic events are recorded in the HPB and PMZ that successively accounted for thickening, ductile flow and exhumation of the deeply buried orogenic crust. Within the HPB and surrounding units, the early D 1 event is defined by a locally preserved NW-SE trending lineation with a top-to-the SE sense of shear. This structural pattern is recognized all over the TNCO and is related to the nappe-stacking and crustal thickening during building of the orogenic wedge [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF][START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF][START_REF] Trap | Contrasted tectonic styles for the Paleoproterozoic evolution of the North China Craton. Evidence for a ~2.1 Ga thermal and tectonic event in the Fuping Massif[END_REF]Trap et al., , 2009)). This conclusion is in agreement with [START_REF] Dirks | Exhumation of high-pressure granulites and the role of lower crustal advection in the North China Craton near Datong[END_REF] that suggested that a NW-SE trending mineral lineation marked by sillimanite inclusions within garnet could represent the early prograde event responsible for the interleaving of metasedimentary rocks and TTG gneiss of the HPB during burial and crustal thickening. The achievement of crustal thickening might have occurred around 1880 ± 10 Ma that dates the peak M 1 .

During the D2 event, the SW-NE to E-W trending coaxial flow and doming that developed in the core of the HPB is interpreted to result from interplay between diapirism and SE-NW to N-S shortening, during the eastward extrusion of the deep crust. Diapirism is related to uprising of low density partially-molten and magmatic rocks (diatexites) and is responsible for transposition of the vertical foliation toward a horizontal one in the upper part of the HPB. The N-S shortening is also documented by north-verging folding in the southern and upper part of the partially molten zone, in the Hengshan massif. This north-verging folding occurred in the inner part of the orogenic wedge during ongoing compression whereas the foreland domain suffered south-verging folding [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF][START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF]. As a consequence, the Hengshan-Wutai domain is structured as a fan-type wedge (Fig. 8; Trap et al., 2009b;[START_REF] Zhang | Deformation history of the Hengshan Complex: implications for the tectonic evolution of the Trans-North China Orogen[END_REF][START_REF] Zhang | Polyphase deformation of the Fuping Complex, Trans-North China Orogen: Structures, SHRIMP U-Pb zircon ages and tectonic implications[END_REF]. In the deeper part of the orogenic wedge, and together with the general E-W trending lateral flow, the top-to-the W-and top-to-the SW shearing observed in the western edge of the HPB suggests an eastward extrusion of the deep crust.

The dominant sinistral strike-slip shearing observed along the northwestern and northern limit of the PMZ is also interpreted as the expression of this general eastward lateral flow of the PMZ. The flow direction turns from NNE-SSW in the southwestern part of the HPB to E-W in the middle and eastern parts, i.e. it parallels the Trans-North-China Suture.

The D2 event occurs under syn-anatectic conditions, during the retrograde metamorphic evolution that postdates M 1 , i.e. the part of the P-T path between M 1 and M 3 that follow the melt-enhanced geotherm (Fig. 11). This portion of the retrogressive P-T path argues for decompression from ~14 kbar to ~8 kbar, which corresponds to nearly 20 km of unroofing (Fig. 11). As shown above in section 4, the D 2 flow is mainly horizontal. Nevertheless, even a weak plunge of the L 2 lineation will be sufficient to accommodate the amount of exhumation inferred from thermobarometry. For instance, a 100 km E-W striking flow along a 10° (respectively 15°) westward plunging flow line will produce a vertical displacement of 17 km (respectively 26 km).

The D3 event developed under subsolidus conditions after the M 3 metamorphism.

From M 3 to M 4 , the P-T path does no more follow the melt-enhanced geotherm and enters the stability field of amphibole (Figs. 10G and11). The D 3 event is also characterized by an E-W trending flow and the motion along the DCSZ. All along the DCSZ, a top-to-the NW normal shearing with a sinistral strike slip component has been documented (cf. section 4). The sense of shear on the channel detachment is top-to-the-WNW on its western part and top-to-the NNW along its northern part. The activity of this strike-slip shear zone may account for the late stage of the exhumation and eastward tectonic escape of the HPB. The diatexite/metatexite transition probably played the role of a rheological boundary along which the D 3 deformation concentrated.

Critical parameters for the HPB exhumation: orocline geometry and partial melting

Ductile flow and exhumation of the deep parts of the thickened crust are mainly controlled by the interplay between boundary forces and gravity related forces (i.e. buoyancy forces). Along an orogenic belt, boundary forces mostly change as a function of the belt geometry due to the shape of crustal blocks involved in the collision. Gravity related forces driven by buoyancy change in response to lateral variations of crustal thickness [START_REF] Royden | Coupling and decoupling of the crust and mantle in convergent orogens: implications for strain partitioning in the crust[END_REF][START_REF] Rey | Gravitational collapse of the continental crust: definition, regimes and modes[END_REF]. Modifications of rock density due to metamorphic reactions, partialmelting and magma displacement are the main parameters that control the buoyancy force [START_REF] Vanderhaeghe | Migmatites, granites and orogeny: flow modes of partially-molten rocks and magmas associated with melt/solid segregation in orogenic belts[END_REF]. Hereafter, we discuss the concurrent effect of oroclinal bending and partial-melting to produce the finite architecture of the High Pressure Belt.

TNCO geometry and boundary forces balance

The PMZ lies in a specific location along the Trans-North China Suture from the core of the orocline and to the eastern part of the belt. Along the N-S trending branch of the Trans-North China Orogen, where the crustal nappes are rooted in the TNCS [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF]Trap et al., 2009b), the tectonic regime is compressional, whereas along the E-W part of the belt, a strike-slip regime is predominant. One might consider that boundary forces are greater in the compressional domain than in the strike-slip dominant one. Therefore, the ongoing compression of the thickening orogenic root is responsible for forceful lateral eastward extrusion-exhumation of the deep rocks softened by partial-melting. The transpressional regime progressively turns into a transtensional one concentrated along the DCSZ.

Partial melting

Onset of partial-melting and formation of metatexites at peak metamorphism is responsible for a first strength drop of the buried continental crust. This rheological softening may have enhanced the lateral flow of the thickened crust which is also controlled by the bulk architecture of the orogen. The radiometric ages recorded in the HPB show that the deep crust was partially molten over a 50 Ma lasting period.

During this time-scale, the partially molten crust evolved. Firstly the melt fraction increased due to decompression related reactions. Secondly, the melt migrated and was collected in the diatexite level, such as describe by Vanderhahge (2009) in several orogenic belts. This led to the subdivision of the PMZ with a core made of diatexites mantled by metatexites, the former forming a high volume, low density body complete around 1850 Ma.

Within this partially molten crust, the HPB was delimited by two main discontinuities, the DCSZ and the ZSZ that both developed along the diatexite-metatexite boundary. This subdivision is responsible for a second strength drop with deformation accommodated along the diatexite/metatexite transition. The transtensional regime observed along the DCSZ has been triggered by the gravitational-thermal instability created by the migration and accumulation of melt within the crust. Similarly, the ZSZ is located along the metatexitediatexite boundary along which strain localized during deformation coeval with crustal melting and continues at sub-solidus state. The ZSZ certainly participated to the unroofing of the HPB. Indeed, a vertical offset of about 15 km between both sides of the shear zone has been documented [START_REF] O'brien | The petrology of two distinct granulite types in the Hengshan Mts, China, and tectonic implications[END_REF]. However, the D4 sinistral strike slip shearing completely erased any previous D 2 fabric evidence along this shear zone.

In several HP rocks occurrences worldwide, the decompressional steep part of the P-T-t paths commonly argues for rapid upward movement of the HP units that prevents thermal reequilibrium (e.g. [START_REF] Platt | Exhumation of high pressure rocks: a review of concepts and processes[END_REF][START_REF] Selverstone | Intracontinental subduction and hinged unroofing along the Salmon River suture zone, west central Idaho[END_REF][START_REF] Štípská | Inverted metamorphic zonation in a basement-derived nappe sequence, eastern margin of the Bohemian Massif[END_REF].

Following this assumption, [START_REF] Guo | High-pressure granulites in the Sangan area, North China Craton: metamorphic evolution, P-T paths and geotectonic significance[END_REF] considered that the geometry of the ITD part of the P-T-path recorded in the HPB suggests that the rate of exhumation was clearly high at the beginning of unroofing. However, the main part of the adiabatic decompression for the HPB rocks occured for high-temperature suprasolidus conditions, and follows the melt-enhanced geotherm (Fig. 11; [START_REF] Depine | Near-isothermal conditions in the middle and lower crust induced by melt migration[END_REF]. The evolution followed by the high-pressure rocks then remained isothermal during unroofing because of thermal buffering by melting reactions [START_REF] Depine | Near-isothermal conditions in the middle and lower crust induced by melt migration[END_REF]. Thus, an appraisal of the exhumation rates can hardly be derived from the shape of the P-T path even in the case of the steep decompressional path recorded in the HPB. Further studies focused on the construction of precise P-T-t-deformation paths are needed to estimate the exhumation rate of the HPB.

Conclusion

The HP rocks of the TNCO are exhumed through lateral flow of a partially molten channel and subsequent detachment shearing. This exhumation history was controlled by the bulk architecture of the TNCO orocline and by intense partial-melting of the thickened crust. Partial-melting is critical since it triggers strength drop and lateral flow and buffers temperature allowing the preservation of a high thermal regime and weakness of the crust for a long time period (~50 Ma). These rheological conditions may have accommodated ductile, along-strike flow over more than 100 km that corresponds to ca. 20 km in vertical component of unroofing. Therefore the onset of partial-melting in the deep crust is the critical threshold in the collision orogeny, from which compressional forces are balanced by orogen-parallel lateral escape. During the ongoing flow of the partially molten crust, melt migration yield to the development of diatexite unit and two rheological discontinuities at the metatexite/diatexite boundaries. These two limits are the preferred site along which subsolidus ductile deformation concentrate as shown by the Chengde-Datong Shear Zone that is responsible for the late stage of exhumation of the HP rocks. Orogen, with the three-fold subdivision of the NCC and two suture zones as described in [START_REF] Faure | Polyorogenic evolution of the Paleoproterozoic Trans-North China Belt, new insights from the Lüliangshan-Hengshan-Wutaishan and Fuping massifs[END_REF] and [START_REF] Trap | Late Paleoproterozoic (1900-1800 Ma) nappestacking and polyphase deformation in the Hengshan-Wutaishan area: implications for the understanding of the Trans-North-China Belt, North China Craton[END_REF][START_REF] Trap | Contrasted tectonic styles for the Paleoproterozoic evolution of the North China Craton. Evidence for a ~2.1 Ga thermal and tectonic event in the Fuping Massif[END_REF]Trap et al. ( , 2009a-b)-b). First interpreted boundaries of the TNCO, from [START_REF] Zhao | Metamorphism of basement rocks in the Central Zone of the North China Craton: implications for Paleoproterozoic tectonic evolution[END_REF] are also represented in dashed line.

Figure

  Figure12and Table2summarize most of the available high-T radiochronological

Figure captions Figure 1

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Photographs of some morphological types of migmatitic rocks within the Partially-

Figure 3 .

 3 Figure 3. Structural map and synoptic representation of D 1 , D 2 , D 3 and D 4 structural elements

Figure 4 .

 4 Figure 4. Photographs of some D 2 structural elements within the partially-molten HPB rocks.

Figure 5 .

 5 Figure5. Geological and structural map of the Datong-Huai'an area (see location in figure3).

Figure 6 .

 6 Figure6. Geological and structural map of the Xuanhua massif (see location in figure3).

Figure 7 .

 7 Figure 7. Geological and structural map of the Chengde massif (see location in figure 3).

Figure 8 .

 8 Figure 8. Cross-sections throughout the HPB in the Datong-Huai'an area (A), the Xuanhua

Figure 9 .

 9 Figure 9. Photographs of D 2 and D 3 deformation features. A: Syn-anatectic north verging

Figure 10 .

 10 Figure 10. Photographs of D3 fabric along the Datong-Chengde Shear Zone. A: S 3 mylonitic

Figure 11 .

 11 Figure 11. Combined thermobarometric data and P-T paths for mafic HP granulites within the

Table 1 .

 1 Compilation of thermobarometric data recorded for the high-pressure mafic rocks within the HPB.

	Massif	Prograde assemblage	Peak assemblage	Retrograde assemblages		References	Label (Fig. 11)
		(Inclusion)				Early		Late			(P-T path)
		P, sP	T, sT	P, sP	T, sT	P, sP	T, sT	P, sP	T, sT
		(kbar)	(°C)	(kbar)	(°C)	(kbar)	(°C)	(kbar)	(°C)
	North Hengshan Massif			(18-20)	(> 750)					Zhao et al. (2001a)
				13.4-15.5, 1.5	770-840, 50	6.5-8, 1	750-830, 40	4.5-6, 1.2	680-790, 60	In Zhang et al. (2006)	1
				(14-15)	(> 800)					O'Brien et al. (2005)
				> 11	> 800	7-8	750-800	5-6	650-700	-	2
						7-8, 0.5-1.5	730-20-60 850,			Zhao et al. (2000)
				9-11, 0.5-1.5	820-870, 20-60	6.5-7.5, 0.5-1	740-840, 20-50	4-6, 0.5-1	680-20-40 750,	Zhao et al. (2000)	3
	Xuanhua Massif			12-15	840-890	9-11	780-850	7.5-8.0	500-570	Guo et al. (2002)	4
				11-13	810-860	8-10	780-850			-	5
	East Datong-Huai'an Massif	9-12	680-750	11-14	780-830	9-10.5	790-820	6.5-7.5	570-630	Guo et al. (2002)	6
		8, 1	650, 50	10, 1	825, 50	6, 1	725, 50			Liu (1995)
	West Datong-Huai'an Massif	12-14	800-900	10-14	800-900	7-9	750-800	5-6	650-700	Zhang et al. (1994)	7
				9-12	880-940	9.5, 1	845, 20			Liu (1989) and Liu et al. (1993)
										Zhai et al. (1992)
				14-15	800, 20	7-9	820, 20			and Guo et al.
										(1993)
	Chengde Massif	13-15	760-800	8-10	780-820	5-7	760-800	4-6.5	620-680	Li et al. (1998)

Table 2 .

 2 Geochronological data set of in-situ SHRIMP zircon U-Pb ages (a), U-Th-Pb EPMA monazite ages (b), ICP-MS U-Pb zircon dates (c), (d), and single grain evaporation 207 Pb/ 206 Pb ages (e), published for the High-Pressure Belt and adjacent surrounding units. The set is arranged in decreasing order.

	No. Ages (Ma)	Sample	Sample description	Unit	Reference
		Rim or unzoned grain	Core
	1	2712 ± 2	(a) 990843	Trondhjemitic migmatite	HPB	Kröner et al. (2005b)
	2	2701 ± 5.5	(a) 990838	Gray biotite gneiss	HPB	Kröner et al. (2005b)
	3	2697.1 ± 0.3	(e) 980811	Granodioritic gneiss	HPB	Kröner et al. (2005b)
	4	2670.6 ± 0.4	(e) 980824	Fine-grained biotite gneiss	HPB	Kröner et al. (2005b)
	5	2526 ± 4.7	(a) 990821	Fine-grained biotite gneiss	HPB	Kröner et al. (2005b)
	6	2524 ± 8	(a) 990847	Trondhjemitic migmatite	HPB	Kröner et al. (2005b)
	7	2506 ± 5	(a) 990859	Dioritic gneiss	HPB	Kröner et al. (2005b)
	8	2504.6 ± 0.3	(e) 990854	Trondhjemitic gneiss	HPB	Kröner et al. (2005b)
	9	2504.4 ± 0.4	(e) 990845	Tonalitic gneiss	HPB	Kröner et al. (2005b)
	10	2503.0 ± 0.3	(e) 980838	Trondhjemitic gneiss	HPB	Kröner et al. (2005b)
	11	2502.3 ± 0.6	(e) 980803	Homogenousfelsic gneiss	HPB	Kröner et al. (2005b)
	12	2502.3 ± 0.3	(e) 990871	Tonalitic gneiss	HPB	Kröner et al. (2005b)
	13	2501 ± 3	(a) 989809	Coarse grained pegmatitic gneiss	HPB	Kröner et al. (2005b)
	14	2500.5 ± 0.3	(e) 980802	Homogenous tonalitic gneiss (diatexite)	HPB	Kröner et al. (2005b)
	15	2499 ± 6	(a) 990873	Migmatite	HPB	Kröner et al. (2005b)
	16	2498.8 ± 0.3	(e) 980845	Trondhjemitic gneiss	HPB	Kröner et al. (2005b)
	17	2496.3 ± 0.3	(e) 980825	Fine-grained granite-gneiss	HPB	Kröner et al. (2005b)
	18	2494.4 ± 0.3	(e) 980833	Granitic gneiss	HPB	Kröner et al. (2005b)
	19	2479 ± 3	(a) 980814	Dioritic gneiss	HPB	Kröner et al. (2005b)
	20	2455 ± 2	(a) 990803	Dioritic gneiss	HPB	Kröner et al. (2005b)
	21	2358.7 ± 0.5	(e) 980806	Fine-grained orthogneiss	HPB	Kröner et al. (2005b)
	22	2331 ± 36	(a) HG4	Pegmatitic granite-gneiss	HPB	Kröner et al. (2005a)
	23	2329.7 ± 0.6	(e) 19990850	Layered trondhjemitic gneiss	HPB	Kröner et al. (2005a)
	24	2248.5 ± 0.5	(e) 990881	Pegmatite	HPB	Kröner et al. (2005b)
	25	2201 ± 68	(a) M17	HP granulite	HPB	Zhao et al. (2008a)
	26	2193 ± 15	(a) WS85	Gabbro	OVU Z.H. Wang et al. (2010)
	27	2113 ± 8	(a) 990844	Anatectic granite	HPB	Kröner et al. (2005b)
	28	2040 ± 39	(a) M17	HP granulite	HPB	Zhao et al. (2008a)
	29	1915 ± 13	(a)	Core of a HP-granulite boudin	HPB	Kröner et al. (2006)
	30	1914 ± 26	(a)	Gabbroic dyke	HPB	Kröner et al. (2006)

Acknowledgement

The field work for this research was financially supported by a National Science Foundation of China grant no. 40472116. We thank M. Santosh, J. Zhang and an anonymous reviewer that helped us to clarify some key points and improve the manuscript.


Dorian Chauvet
email: dorianchauvet@yahoo.fr

MD Alexandre Carpentier

MD Jean-Marc Allain

MD-PhD Marc Polivka

Jérôme Crépin

PhD Bernard George

PhD Jérôme Crepin

Histological and biomechanical study of dura mater applied to the technique of dura splitting decompression in Chiari

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

INTRODUCTION

Chiari malformation type I (CM-I) is a cerebellar tonsillar herniation through the foramen magnum, leading to a cerebro-spinal fluid (CSF) obstruction at the craniocervical junction. To restore the CSF flow, most of the surgeons enlarge this anatomical area (cisterna magna) by a suboccipital craniectomy associated with a dural graft [START_REF] Batzdorf | Chiari I malformation with syringomyelia. Evaluation of surgical therapy by magnetic resonance imaging[END_REF][START_REF] Milhorat | Chiari I malformation redefined: clinical and radiographic findings for 364 symptomatic patients[END_REF][START_REF] Tubbs | Posterior atlantooccipital membrane for duraplasty. Technical note[END_REF] . We prefer an extradural approach, described by Isu et al. [START_REF] Isu | Foramen magnum decompression with removal of the outer layer of the dura as treatment for syringomelia occurring with Chiari I malformation[END_REF] in 1993, reducing the risks of CSF leak, in which the outer layer of the dura is separated from the inner layer and removed. Thus, a new cisterna magna is created, considering the dural inner part capability of expansion. From our clinical experience, we try to argue in this study the effectiveness of this technique using histological and biomechanical considerations. This work is divided in two parts : in the first one, we examine the posterior fossa dura mater (DM) composition and the orientation of its fibers; in the second one, we emphasize the difference of biomechanical behaviour between entire dura and split dura.

MATERIAL AND METHODS

1) Histological study

We removed 3 specimens (A, B, C) of craniocervical junction DM on fresh human cadavers (2 females, one male; all over 70 years old). For each specimen, 15 samples at precise zones (figure 1) and numbered from 1 to 15 were observed on transversal sections. We added 6 sagittal sections (from B and C specimens). All the samples were fixed in formalin and embedded in paraffin. Microtome sections were stained with hematoxylin-eosin, Masson trichrome for collagen and orcein for elastin. Four sections were not interpretable because of a wrong section plan, so that we examined 47 sections.

The characterisation of DM consists in examination of four criterions under optical microscopy: thickness, presence of two distinct layers with a define boundary, density and orientation of collagen and elastin fibers.

2) Biomechanical study

We removed 22 posterior fossa dural samples from 10 donors (6 females and 4 males; all over 70 years old). We took off 15 intact dural samples and 7 split dural samples (all the split samples had their intact equivalent from the same donor). For the latter, we removed the outer layer of the dura in condition of real surgery using a blade number 15 and a blunt dissector.

No special direction was chosen. All samples were placed in physiological saline solution and kept refrigerated.

Each specimen of DM was cut into strips using a metallic pattern (figure 2) of 30 mm length by 20 mm width. To estimate the cross-section of the sample, thickness was measured by a digital micrometer gauge, at least five times. A pseudo-regular ink marking was made to assess the intrinsic deformation of the sample, by a Digital Imaging Correlation technique (DIC). Each mechanical test was performed at room temperature (20°C) on a uniaxial RAITH ® testing device at monotonic displacement rate that is imposed constant. The tissue was held between small screw-tightened grips and displacement data were measured by CCD camera (2048 x 2048 pixels) (figure 3). From the images, DIC allowed the determination of the displacement between the ink marks deposited on the specimen surface or between the two grips of the testing device [START_REF] Allais | Experimental characterization of the local strain field in a heterogeneous elastoplastic material[END_REF][START_REF] Hild | Multiscale displacement field measurements of compressed mineral-wool samples by digital image correlation[END_REF] . Force was measured with a loading cell of 100 N with an accuracy of 0.1% and the stress in the tissue was defined as the force (F) on the tissue divided by the cross-sectional area of the tissue under that force. Data (in plane strain tensor and load) were collected by a PC and analysed using the softwares CORRELMANUV ® and AGNES ® from LMS, Ecole Polytechnique 1 . When it was possible, we preconditioned the tissue samples to facilitate reproducibility of results by cycling between 0 and approximately 5% strain until a stable stress versus strain curve resulted on successive cycles. Five cycles had always been enough to reach the stabilised cycle.

We carried out two specific tests series. The first one focused on the dural macroscopic mechanical behaviour, at the scale of the whole sample. This allowed us to compare entire and split samples. The second test series consisted in the observation of the structural modifications of the tissue under strain thanks to strain field analysis, in order to understand the local deformation mechanisms during the test.

RESULTS

1) Histological study

The thickness of the samples was measured between 0.625 and 1.475 mm (mean thickness 1.106 mm, standard deviation 0.244 mm). The midline sections were thicker than the lateral ones (table 1). Sections number 5 and 8 had the largest average thickness; this can be explained by the remains of the posterior atlanto-occipital membrane, even if it was macroscopically removed during the dissection.

Two different layers occurred objectively on only 10 sections (specimen A n°5,11,12,13 / specimen B n°1,6,12 / specimen C n°6,12 + one sagittal section). Among these, a well define boundary between the two layers was observed in 6 samples. It seemed to be more a capillary network than a real interface (figure 4a). In the others samples, we could not distinguish the two layers structure. Moreover, we did not found some particular relation between the localization of the sections of the posterior fossa and the presence of two layers. Thus, we think that the classical description of two distinct layers constituting the DM 36 could be inconstant in the posterior fossa.

Concerning the DM composition, collagen was largely dominant with few elastin fibers (figure 4b). The collagen fibers were dense and strongly organized, distributed inside the tissue. However, we observed some degree of reciprocal density gradient between collagen and elastin, from one face of the dura to the other. There was a tendency of a decrease of collagen density, and conversely an increase of elastin fibers, from the inner to the outer layer (visible on 10 and 9 sections respectively). So the ratio collagen/elastin appeared higher in the inner dural part and lower in the outer one, but these considerations were inconstant.

To define the orientation of the fibers, we compared the transversal sections with the 6 sagittal sections. The collagen fibers appeared in a main cranio-caudal direction with probably some little degree of obliquity. On the 10 sections where 2 layers were identified, we did not observe a clear difference in collagen orientation between the inner part and the outer part.

From a scanning electron microscopic study, DM seemed to be composed of a multilayer structure, with piled up leaves. Each leaf was composed of lined up "big cables" (about 1 micrometer diameter) corresponding to collagen fibers and of a thinner spiderweb network with no preferential orientation corresponding to elastin fibers (figure 5). The observations of samples fracture surfaces obtained from liquid nitrogen fracture confirm that each leaf was separable from adjacent leaves. Therefore, we conclude that the dural splitting dissection does not occur between two macroscopic leaflets: it splits the DM between two layers of a microscopically divided multilayered structure.

2) Biomechanical study a) Macroscopic tensile test

The first campaign consisted with twelve tensile tests. Figure 6 shows a typical mechanical response for tensile tests performed on entire and split DM (from the same donor) at room temperature and under a constant strain rate around 1.5 10 -3 s -1 . As in previous studies 45, [START_REF] Van Noort | The mechanical properties of human dura mater and the effects of storage media[END_REF] , it appears that entire DM presents a large elastic domain (until some 10%) followed by occurrence of damage mechanisms what conducts to failure of the sample. For split DM, the mechanical behaviour is quite different than for intact one, with a smaller elastic domain followed by a larger irreversible strain domain. Partial unloadings were performed during the test to check the evolution of the Young modulus in the irreversible strain region. Decrease of the Young modulus could be considered as a signature of the damage occurrence inside the specimen: the more damaged is the specimen the weaker is the Young Modulus. So for the split dura the Young modulus evolves from 25 MPa to 19 MPa (corresponding to 0.78% of the initial value) even if the irreversible strain is quite large before failure: that means that damage occurs gradually inside the specimen during the test. On the contrary, from entire dura mater the evolution of young modulus seems to be quite different with an increase of the Young modulus in the first part of the test from 44 MPa to 91 Mpa -that could correspond to a rearrangement of the fibers along the stress axis -then a quite constant value is reached until final rupture occurs as observed in figure 6.

b) Displacement and Strain field analysis

From a more local point of view corresponding here to the effect of the fibers distribution, second tensile tests campaign is performed to follow, thanks to optical microscope and DIC, the evolution of the displacement field inside the sample during the test. This campaign has consisted with ten tensile tests performed under optical microscope with a spatial resolution equals to 0.9 µm at room temperature for the same strain rate that the macroscopic ones. It appears from figure 7, obtained from intact DM for two samples coming from two different areas presenting different microstructure's configurations, that the displacement field seems to be homogeneous along the sample and quite independent on the fiber's axis versus the tensile axis. That means that, at this mesoscopic scale (corresponding to a few hundred of microns), the mechanical behaviour of DM could be considered as being homogeneous, with no effect of the orientation of the fibers on the mechanical behaviour. So it seems that the mechanical behaviour of the DM could be considered at first approximation as being isotropic.

c) Modeling of the DM expansion

We estimate the volume benefit from the DM splitting through estimation of the order of magnitude of its deformation. The geometry of the split dural zone is complex. As a first approximation, we assume that this region is a spherical cap with a diameter around 40 millimeters (figure 8).

Prior to deformation (just after bone removal), the curvature radius R c of the DM cap is about the one of the head, which can estimated at 5 cm. Thus, the geometrical characteristics of the spherical cap are: volume of 2.6 cm 3 , surface of 13 cm 2 and maximum height z max (measured between the support line and the top of the cap) around 4 mm.

In order to estimate the deformation in the DM, we need to know the stress in the tissue. The highest component σ θθ of the stress tensor in the DM can be estimated from the mechanical equilibrium of the structure: if an inner pressure P ic (intra-cranial pressure) is applied on the DM cap, the stress on the border (the supporting line) of the membrane has to equilibrate this pressure. Therefore, the stress is related to the applied pressure by:

ic c P h R 2 = θθ σ
with h the thickness of the DM.

We assume that the DM splitting removes half of the thickness (h = 0.5 mm) and that the P ic is about 10 mmHg in CM-I. In that case, the σ θθ stress is around 70 kPa. The deformation associated with this stress in our uniaxial traction experiments is between 2 to 5%, remaining small. Such deformations are not big enough to bring us in the domain of irreversible strains, which implies that there is no risk of leaking of the DM due to the tissue stretching.

The DM membrane is under a biaxial solicitation, while we performed an uniaxial test.

Relating both approaches is not straightforward in the general case, but we can consider, in first approximation, that the relative surface deformation is of the same order of magnitude of the relative length deformation. Therefore, the surface after deformation S def is related to the initial surface S init by S def = S init (1+ε ), where ε is the estimate of the deformation.

From this result, simple geometric considerations lead to the volume and to the maximum height after deformation.

A deformation of ε =2% (lowest estimate) leads to a volume of 3.3 cm 3 , an increase of 22% of the initial one, and the maximum height is about 6 mm, increasing by 45% the original one.

The highest estimate of the deformation of ε =5% leads to a volume of 4 cm 3 (increase of 50%), and a maximum height of 9 mm, twice the initial one. This second estimate is more likely to be closer to the real case than the first one, considering the deformation data from our tensile experiments. This is also in agreement with the observation of the posterior fossa enlargement after dural splitting during surgery [START_REF] Isu | Foramen magnum decompression with removal of the outer layer of the dura as treatment for syringomelia occurring with Chiari I malformation[END_REF] .

DISCUSSION

The dura mater is a connective tissue surrounding the nervous central system. It is known to be a membrane composed of collagen and elastin fibers with two different layers [START_REF] Robertson | Developmental defects of the cisterna magna and dura mater[END_REF] . Actually, its structure remains controversial, especially concerning the orientation of its fibers. On the contrary of the lumbar DM [START_REF] Patin | Anatomic and biomechanical properties of human lumbar dura mater[END_REF][START_REF] Reina | New perspectives in the microscopic structure of human dura mater in the dorsolumbar region[END_REF] , the posterior fossa dura mater has not been studied yet. From our observations, we think that the presence of two distinct layers on the posterior fossa dura mater is inconstant. The limit between the inner and the outer dural part sometimes appears as a vascular plan (capillary network), but is more often virtual. Previous studies on dura mater in the spinal region [START_REF] Runza | Lumbar dura mater biomechanics: experimental characterization and scanning electron microscopy observations[END_REF][START_REF] Zarzur | Mechanical properties of the human lumbar dura mater[END_REF] have shown a well defined structure in two leaflets. We think that the difference may be due to the location, as the posterior fossa is making the transition between cerebral compartment, with a spherical shape, and the spinal one, with a cylindrical shape.

Based on our observations, we conclude that the structure is closer from a multilayer material, stacking many sheets of fibers. However, the understanding of the fibers orientations of the dura remains difficult. Histological studies indicate more or less a cranio-caudal orientation of the fibers, but we use also other imagery methods, such as scanning electron microscopy and second harmonic generation microscopy (SHG) [START_REF] Débarre | Second-and third-harmonic generation microscopies for the structural imaging of intact tissues[END_REF][START_REF] Werkmeister | Interest of second harmonic generation imaging for diagnosis in thick and opaque tissue[END_REF] , which indicate that the different layers of fibers may have different orientations. SHG studies confirm histological studies about the fact that composition of the dura mater is inhomogeneous in the thickness, with more collagen close from the inner face (figure 4b). Note that SEM and SHG were used in complement of the histological studies, and not in a systematic approach, due to the time they request. The difficulty of finding quantitative results based on histological approach indicates that more specific methods should be used in the future to improve the understanding of the dural structure.

Human DM has its own biomechanical properties, which have been studied in the past [START_REF] Runza | Lumbar dura mater biomechanics: experimental characterization and scanning electron microscopy observations[END_REF][START_REF] Sacks | Local mechanical anisotropy in human cranial dura mater allografts[END_REF][START_REF] Van Noort | A study of the uniaxial mechanical properties of human dura mater preserved in glycerol[END_REF] .

Most of these works concern the lumbar DM and are applied to the comprehension of the post dural puncture headache [START_REF] Fink | Orientation of fibers in human dorsal lumbar dura mater in relation to lumbar puncture[END_REF][START_REF] Patin | Anatomic and biomechanical properties of human lumbar dura mater[END_REF] . Dura has also been tested as a potential component of heart valves [START_REF] Mcgarvey | Mechanical suitability of glycerol-preserved human dura mater for construction of prosthetic cardiac valves[END_REF] . But, posterior fossa DM has not been examined until now.

In this work, we tried to highlight the difference of behaviour between the entire dura and the split dura, correlated to the surgical technique described by Isu et al. [START_REF] Isu | Foramen magnum decompression with removal of the outer layer of the dura as treatment for syringomelia occurring with Chiari I malformation[END_REF] . This biomechanical work is the first to evaluate the posterior fossa dura mater mechanical properties. Also, it is the first investigation of the biomechanical behaviour of split dura mater in association to the specific surgical technique of splitting decompression in CM-I. Our tests compared one entire sample and one split sample from each donor when it was possible. For the intact DM, we found an elastic behaviour, with a small domain where deformation is reversible with stress followed after the yield point by a fragile behavior, as indicated by others authors on lumbar dura [START_REF] Van Noort | The mechanical properties of human dura mater and the effects of storage media[END_REF] . On split DM, we observe the same type of behaviour at small strain, with a slightly smaller stress level for the same strain. The main significant difference between entire dura and split dura is after the yield point: split DM presents a large domain where the mechanical behaviour is elasto-plastic, with permanent strain and a lower stress level, instead of a fragile behavior for the intact DM.

We must nuance in our observations since the tests were performed on samples from elderly fresh human cadavers (over 70 years old). So it is reasonable to think that tests on specimens from younger donors would have shown different results, although no study has been made to compare dural biomechanical behaviour between children and adults for example. Also, we worked on donors from the Ecole de Chirurgie Assistance Publique -Hopitaux de Paris whom we considered to be free of CM-I. We know from Nakamura et al. [START_REF] Nakamura | Dural band pathology in syringomyelia with Chiari type I malformation[END_REF] that DM in CM-I can be thicker than a normal dura. This implies of course that the neurosurgeon must remove a significant thickness of dura to obtain a visual deformation of the split area and then a satisfying decompression. Also, it may modify the mechanical behaviour, as the tissue is inhomogeneous in its thickness.

These experiments concern the instantaneous behaviour of the dura mater. To confirm that they are in agreement with the decompression in CM-I, we build a model of DM expansion. It shows that reasonable stresses due to the malformation on the dura mater lead to a large structural deformation: the volume increases about 50%. But, this model simplifies the real situation: in particular, we did not introduce the head muscles that could prevent the dural extension. However, it shows that the immediate deformation frees enough space to relax the neuraxis constrain and to restore the CSF flow.

A clear extension of our approach should be to study the time-dependent extension by studying the mechanical answer to a creep test. Radiological findings, where an increase of cisterna magna size is observed [START_REF] Isu | Foramen magnum decompression with removal of the outer layer of the dura as treatment for syringomelia occurring with Chiari I malformation[END_REF][START_REF] Limonadi | Dura-splitting decompression of the craniocervical junction: reduced operative time, hospital stay, and cost with equivalent early outcome[END_REF] , seems to support the hypothesis that the split dura could enlarge with time.

Moreover, a more complex model, including creep tests, would be useful to the neurosurgeon to plan the dural splitting decompression and to anticipate the results of the surgery.

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CONCLUSION

This original study demonstrates the capability of the split dura mater to enlarge for suitable stress conditions and quantifies it by biomechanical tests. We have built an experimental model that shows a significant volume benefit at the cranio-cervical junction after splitting. Thus, dural splitting decompression has a real biomechanical substrate to envision the effectiveness of this Chiari type I malformation surgical technique.

Acknowledgment

I thank all the team of Pr Frileux at the Ecole de Chirurgie Assistance Publique -Hopitaux de Paris, especially René Gicquelet and Djamel Taleb.

This is original work that has not been previously published or submitted elsewhere for review. All authors are fully involved in the study and the preparation of the manuscript. There is no financial disclosure. There is no conflict of interest.