K Kelfoun

T H Druitt

Numerical modelling of the emplacement of the 7500 BP Socompa rock avalanche, Chile

The 7500 BP Socompa sector collapse emplaced 25 km 3 of fragmented rock as a thin, but widespread (500 km 2 ) avalanche deposit, followed by late-stage sliding of 11 km 3 as Toreva blocks.

Most of the avalanche mass was emplaced dry, although saturation of a basal shear layer cannot be excluded. Modelling was carried out using the depth-averaged granular flow equations in order to provide information on the flow behaviour of this well-preserved, long-runout avalanche. Results

were constrained using structures preserved on the surface of the deposit, as well as by deposit outline and run-up (a proxy for velocity). Models assuming constant dynamic friction fail to produce realistic results because the low basal friction angles (1 to 3.5°) necessary to generate observed runout permit neither adequate deposition on slopes nor preservation of significant morphology on the deposit surface. A reasonable fit is obtained, however, if the avalanche is assumed simply to experience a constant retarding stress of 50-100 kPa during flow. This permits long runout as well as deposition on slopes and preservation of realistic depositional morphology.

In particular the model explains a prominent topographic escarpment on the deposit surface as the frozen front of a huge wave of debris reflected off surrounding hills. The result that Socompa avalanche experienced a small, approximately constant retarding stress during emplacement is consistent with a previously published analysis of avalanche data.

Introduction

Long-runout rock or debris avalanches are one of the most hazardous of geological phenomena [START_REF] Melosh | Giant rock avalanches[END_REF]. During emplacement, the centre of mass follows a low-angle (<< 30°) trajectory, forming a thin, widespread deposit. Avalanches on Earth with volumes greater than 10 6 m 3 are generally of long-runout type. Long-runout avalanches are emplaced in a catastrophic manner, with observed or inferred velocities of 20-100 m s -1 and runouts reaching in some cases many tens of km. They occur both in terrestrial and marine environments by sudden mobilisation of large rock masses, either in volcanic or non-volcanic contexts. The ability of avalanches to travel large distances in a fluid-like manner is not well understood, apparently requiring greatly reduced dynamic friction, and a number of possible friction-reduction mechanisms have been proposed (see recent articles by [START_REF] Davies | Runout of dry granular avalanches[END_REF][START_REF] Legros | The mobility of long-runout landslides[END_REF], and Collins and Melosh, 2003, and references therein).

In this paper we use numerical modelling to place constraints on the flow dynamics of the long-runout avalanche that formed 7500 years ago by sector collapse of Socompa Volcano in northern Chile. The model solves the equations of motion for a granular flow and has the advantage of taking into account basal friction, internal friction and volumetric spreading behaviour in a rigorous manner. The modelling is constrained by deposit outline, run-up (a proxy for velocity), and structures preserved on the surface of the deposit when the avalanche ceased motion. In particular we seek to explain the formation of a high topographic escarpment that is a prominent feature of the avalanche deposit. The study provides some crude, but intriguing, constraints on the rheological behaviour of the avalanche during motion.

Socompa avalanche

Socompa avalanche in northern Chile (Fig. 1) has been described in papers by [START_REF] Francis | Catastrophic debris avalanche deposit of Socompa volcano, northern Chile[END_REF], [START_REF] Wadge | The Socompa collapse and avalanche event[END_REF] and [START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF], on which the following summary is based.

It formed by gravitational collapse of the northwestern flank of the 6000-m-high stratovolcano, leaving an amphitheatre 12 km wide at its mouth and with cliffs 300-400 m high. The avalanche flowed across a broad topographic basin northwest of volcano (Monturaqui Basin) to a maximum distance of 40 km, and covered 500 km 2 . The vertical drop from the volcano summit to the lowest point of the basin was 3000 m; at its northwestern limit the avalanche rode part way up a range of hills before being deflected to the northeast, forming a frontal lobe. The volume of rock transported is estimated to be about 25 km 3 , with another 11 km 3 preserved as intact ('Toreva') blocks up to 400 m high at the foot of the collapse scarp.

The morphology of the avalanche deposit is perfectly preserved in the hyper-arid climate of the Atacama Desert (Fig. 1a). The margins are steep and well defined, with thicknesses ranging from 10 to 60 m [START_REF] Wadge | The Socompa collapse and avalanche event[END_REF]. In some places levees are present (labelled L on Fig. 1a). A zone of convergence and SE-verging thrusting called the 'median escarpment' (ME on Fig. 1a) separates the proximal part of the deposit, characterized by longitudinal surface ridges, from the distal part characterized by convoluted surface texture (Van wyk de [START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF]. A complex assemblage of surface structures, including normal faults, strike-slip faults, thrusts, and longitudinal and transverse ridges records the last increments of movement of the avalanche on a local scale.

The 5-km-wide central zone (CZ on Fig. 1a) immediately north of the median escarpment is particularly rich in structures (Fig. 1a) and lies 30-60 m higher than neighbouring areas.

Ignimbrites, gravels, sands and minor lacustrine evaporites from the subvolcanic Salin Formation dominate the avalanche sheet (Reconstituted Ignimbrite Facies; RIF ~ 80%). Brecciated lavas and volcaniclastic deposits from the edifice itself (Socompa Breccia Facies; SB) constitute ~ 20 %, and are confined mainly to the upper levels of the deposit. The eastern half and outer margins of the deposit consists almost entirely of RIF, with a thin overlying layer of SB no thicker than a couple of metres, whereas the southwestern half is composed of RIF overlain by up to 15 m of SB (see fig. 10e).

Most of the avalanche probably formed by a series of retrogressive failures that merged to form a single moving mass [START_REF] Wadge | The Socompa collapse and avalanche event[END_REF]. Spreading took place as a semi-rigid mass on a basal layer of shearing RIF (Van wyk de [START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF]. The RIF behaved in a ductile fashion and must have been very weak mechanically to accomodate flow on slopes of 5° or less, as confirmed by the modelling presented below. The SB, on the other hand, behaved in a brittle fashion, breaking up passively as it rode on a layer of RIF lubricant. Perfect preservation of the avalanche margins, and the absence of distal mudflows, shows that any interstitial water was present in insufficient quantities to saturate the majority of the flowing debris.

Numerical modelling of the avalanche

Basic equations

The assumption is made in our model that the bulk of the avalanche slid on a thin basal layer, so that the velocity gradient was essentially normal to the topography. This is commonly assumed in modelling granular flows (e.g., [START_REF] Savage | The motion of a finite mass of granular material down a rough incline[END_REF][START_REF] Shaller | Analysis and implications of large Martian and terrestrial landslides[END_REF][START_REF] Iverson | The physics of debris flows[END_REF][START_REF] Iverson | Flow of variably fluidized granular masses across threedimensional terrain 1. Coulomb mixture theory[END_REF][START_REF] Denlinger | Flow of variably fluidized granular masses across threedimensional terrain: 2. Numerical predictions and experimental tests[END_REF][START_REF] Heinrich | Numerical simulation of the December 1997 debris avalanche in Montserrat, Lesser Antilles[END_REF][START_REF] Patra | Parallel adaptative numerical simulation of dry avalanches over natural terrain[END_REF], and is consistent with field evidence at Socompa and other long-runout avalanches [START_REF] Shaller | Analysis and implications of large Martian and terrestrial landslides[END_REF][START_REF] Takarada | Depositional features and transportation mechanism of valley-filling Iwasegawa and Kaida debris avalanches, Japan[END_REF][START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF].

Using a topography-linked co-ordinate system (Fig. 2), with x and y parallel to the local ground surface and h perpendicular to it, the general depth-averaged equations of mass (eq. 1) and momentum (eqs. 2,3) conservation are:

    0 h hu hv dt x y      [1]       22 1 ( ) sin cos 2 x x actpass T hu hu huv gh k gh t x y x                [2]       22 1 ( ) sin cos 2 y y actpass T hv hvu hv gh k gh t x y y                [3]
where h is flow thickness,

 

, uv u= is flow velocity, is ground slope, T is retarding stress,  is the bulk density of the avalanche, kactpass is the earth pressure coefficient (ratio of ground-parallel to ground-normal stress), and the subscripts denote components in the x and y directions.

For a dry frictional material, the retarding stress is of the form:

2 cos tan x bed u T h g r          u u [4]
where bed is the angle of dynamic friction between the avalanche and the ground surface and pore fluid pressure is assumed to be negligible. Use of this law, even in cases of rapid granular flow, is justified by [START_REF] Savage | The motion of a finite mass of granular material down a rough incline[END_REF]. Shear cell tests show that the ratio of shear to normal stresses in a rapidly deforming granular material can be represented by an approximately constant dynamic friction coefficient, even if inter-particle collisions are important. The second term in brackets is the centrifugal stress, where r is the radius of curvature of the ground [START_REF] Savage | The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis[END_REF]. The ycomponent of T is obtained by switching subscripts.

Following [START_REF] Iverson | Flow of variably fluidized granular masses across threedimensional terrain 1. Coulomb mixture theory[END_REF], the expression of kactpass used if the internal behaviour is frictional is :

  1/ 2 22 int 2 int 1 1 cos 1 tan 21 cos bed actpass k         [5]
where int is the internal angle of friction of the avalanche. This expression is valid if bed<int. The sign ± is negative (and kactpass active) where the local flow is divergent and is positive (and kactpass passive) where the local flow is convergent. If, on the other hand, bed≥int, then kactpass is given by:

2 int 2 int 1 sin 1 sin actpass k      [6]
Numerical scheme

The equations were solved using a shock-capturing numerical method based on a double upwind Eulerian scheme (Appendix 1). The scheme can handle shocks, rarefaction waves and granular jumps, and is stable even on complex topography and on both numerically 'wet' and 'dry' surfaces. Some numerical schemes require the ground ahead of the avalanche to be covered with a very thin artificial layer of avalanche material: a so-called numerically 'wet' surface [START_REF] Toro | Shock-capturing methods for free-surface shallow flows[END_REF].

In order to check the accuracy of our numerical scheme we performed tests to compare the numerical results with analytical solutions and with simulations based on other numerical schemes.

Some of these are presented here. Figures 345show comparisons between numerical and exact solutions of dam-break problems. In the first case (Fig. 3) the slope is horizontal and there is zero friction. This problem simulates the breakage of a dam separating an initial layer 1.5 m thick (left) from a layer 0.5 m thick (right). Our solution reproduces almost exactly the analytical solution, and particularly the frontal shock wave and the thickness of the central plateau.

Figure 4 shows three comparisons with exact solutions obtained by [START_REF] Mangeney | Analytical solution for testing debris avalanche numerical models[END_REF] for a dam-break problem on a slope with non-zero friction, and with zero thickness in front of the initial dam. The shape and velocity of the flow are accurately reproduced, even for the least favourable case of a steep slope and high friction angle. Note that the vertical exaggeration of the yaxis exaggerates the difference between numerical and analytical solutions.

Since our numerical scheme is based on a rectilinear coordinate system, we also performed circular dambreak tests to ensure that the calculations are isotropic. In Fig. 5, a 6-m-diameter cylinder of zero-friction fluid, 1.5 m thick, is released onto a 0.5-m-thick, horizontal layer of the same fluid. The resulting degree of isotropy and shock resolution are both satisfactory, some small numerical oscillations disappearing progressively during the calculation.

We also applied our code to published laboratory experiments of granular flows down chutes. These include the experiments of [START_REF] Savage | The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis[END_REF], [START_REF] Pouliquen | Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane[END_REF],

and [START_REF] Gray | Shock waves, dead zones and particle-free regions in rapid granular free-surface flows[END_REF]. In all cases our code is able to reproduce the experimental results as well as schemes presented by the authors and based on other numerical approaches (the frictional law of our model can be easily changed to take into account the various frictional laws used by the authors to reproduce their experimental results). In one numerically challenging experiment, in which a high-friction flow at high velocity encounters an obstacle [START_REF] Gray | Shock waves, dead zones and particle-free regions in rapid granular free-surface flows[END_REF]Fig. 4), our scheme reproduces the shape and velocity of the flow; however, it is somewhat less stable than the numerical scheme used by the same authors to simulate their experiment (using the same time and space steps). The advantage of our scheme is that the computing time necessary for simulating flow over terrain with a large number of mesh cells is less than for many published methods. In this paper we calculate the emplacement of an avalanche on a 460 x 570 mesh topography in about 1 day with 3GHz computer. The computation time could be reduced, but we have chosen a time step five times lower than necessary to ensure stability.

Geological starting conditions

The pre-avalanche topography north of Socompa Volcano was estimated as follows. The presentday topography of the volcano and avalanche (Fig. 1a) was extracted from Shuttle Radar

Topography Mission (SRTM) data. Field and borehole constraints on deposit thickness [START_REF] Wadge | The Socompa collapse and avalanche event[END_REF] were used to subtract the 25 km 3 of avalanche deposit and to obtain a best estimate of the pre-avalanche landscape (Fig. 1c). The ~11 km 3 accumulation of Toreva blocks at the northern foot of the volcano were removed, and the sectorial scar filled in using Fig. 13 of Van Wyk de Vries et al. ( 2001) to reconstruct the pre-collapse morphology of the volcano (Fig. 1c). We reconstruct the La Flexura anticline north of the volcano (LF, Fig. 1a) from descriptions of Van Wyk de Vries et al.

(2001), as well as the small pre-existing relief north of La Flexura. The combination of these constraints resulted in little freedom in reconstructing the pre-collapse morphology. Since in this paper we only model emplacement of the (fluid) 25 km 3 avalanche, 11 km 3 of the scar fill was left in place during our calculations (to slump subsequently as Torevas).

One significant uncertainty is the exact geometry of the initial collapse volume. In the absence of precise evidence concerning the shape of the avalanche headwall scarp (partly buried by post-avalanche products), we assume two end-member cases: (1) a wedge-shaped volume with hemi-cylindrical headwall scarp 5 km in radius (Figs. The shallow geometry is not really compatible with field evidence, but provides an alternative limiting case.

Numerical results

Different models were run with the aim of satisfying the following field constraints. -c).

In model 2 (Fig. 6 e-h) bed  0° but int = 0°, so that kactpass =1. This is not necessarily unrealistic because recent laboratory experiments that show that the ratio of ground-parallel to ground-normal stress is close to unity in laboratory granular flows [START_REF] Pouliquen | Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane[END_REF].

In the absence of internal friction, a slightly higher basal friction angle (2.5°) is now required for best fit. The evolution is close to the previous case, but here waves can be observed reflecting off the western, northern and northeastern sides of the basin (Fig. 6f).

Model 3 (not shown in Fig. 6), in which the basal and internal angles are assumed to be the same (best fit for ~2.5°), produces a result very similar to the second model. This is because the values of kactpass are very similar: 1 in model 2 and 1.0038 in model 3.

All three of these frictional models reproduce only very crudely the shape of the real avalanche deposit. A major failing is that, owing to the very low basal friction, the model avalanches flow off any gradients greater than 1 to 2.5° (depending on the case). After reaching their maximum limits, the avalanches drain back into the centre of the Monturaqui Basin.

Consequently the model deposits each have negligible thickness along their limits of maximum extent, whereas thicknesses of up to 60 m are observed along the margins of the real avalanche [START_REF] Wadge | The Socompa collapse and avalanche event[END_REF]. The effect of topographic draining is to cause excess concentration of debris on the floor of the Monturaqui Basin. Models 2 and 3 with low internal friction generate essentially flat-topped ponds that are quite different from the real avalanche. The high angle of internal friction in model 1 permits the preservation of surface topography, but comparison with that of the real avalanche is not favourable. None of the models generate a well defined surface feature resembling the 30-60-m-high median escarpment. The frictional models therefore fail in reproducing some first-order morphological characteristics of the real avalanche deposit.

In order to assess the effect of initial slide conditions on our results, we also ran the same models using the 'shallow' collapse geometry (Fig. 7). Using the same values of int as in Fig. 6 (30° and 0°), we find best-fit values of bed (1° and 3.5° respectively), deposit shapes, and surface morphologies that are similar to those for the 'deep' geometry. We conclude that the form of the resulting deposit is only weakly dependent on the geometry of the collapse volume, so that our uncertainty of the latter does not invalidate the apparent failure of the simple frictional models used above.

We also allowed bed to vary with the Froude Number ( u gh ) of the avalanche, as found for laboratory granular flows [START_REF] Pouliquen | Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane[END_REF] and approximated [START_REF] Heinrich | Numerical simulation of the December 1997 debris avalanche in Montserrat, Lesser Antilles[END_REF] by:

  bed 1 2 1 tan tan tan tan exp gh h Du             [7]
where1 and 2 are limiting angles of friction (with 2 > 1) and D is approximately an order of magnitude larger than the mean particle size. Here, kactpass is considered to equal 1. Equation 6in fact gives results comparable to model 2 (bed  0° and int = 0°) described above (Fig. 6 e-h). The effect of velocity is to increase bed over and above the static value (1). For the mean value of bed result in a runout for Socompa that is much smaller than that observed. Using a more complete form of eq. 7 [START_REF] Pouliquen | Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane[END_REF] gives slightly better results because the friction angle increases just as the avalanche comes to rest, allowing structures to be preserved. However, while this law gives very good results for simulated laboratory experiments, we have not found any combination of the six free parameters in this friction law that give a good fit in the case of Socompa.

Finally we note that the well known Voellmy rheological law also fails to satisfy all three constraints at Socompa. The Voellmy law consists of a frictional stress plus a positive stress term proportional to velocity squared (e.g., [START_REF] Evans | Dynamics of the 1984 rock avalanche and associated distal debris flow on Mount Cayley, British Columbia, Canada; implications for landslide hazard assessment on dissected volcanoes[END_REF]. Although entirely empirical, it has been widely used to model snow and rock avalanches in two dimensions. However in the case of Socompa we find that it fails to generate realistic results for a similar reason as equation 7.

In summary, simple frictional models are able to reproduce the approximate runout of Socompa avalanche only if very low values are used for the basal dynamic friction. However, they are unable to generate deposits either with realistic thicknesses on slopes greater than about three degrees, or realistic surface morphology such as the median escarpment. This is because the low basal friction angles necessary for long runout also result in strong topographic drainback.

Constant retarding stress

In view of the apparent inadequacy of the simple frictional models, we also ran models in which the retarding stress T in equations 2-3 was constant (kactpass was taken as unity). This very simple assumption was motivated by the study of [START_REF] Dade | Long-runout rockfalls[END_REF], who found that the field data for a large number of avalanches can be explained by an approximately constant retarding stress.

The models produce surprisingly good fits to the real avalanche, provided that T lies in the range 50-100 kPa, depending on the initial slide geometry chosen. Using the 'deep' collapse geometry the overall distribution is reproduced reasonably well with a value of 52 kPa (Fig. 8), but with slight excess spreading to the west and east. A 75 kPA resistance produces realistic fits to the western and eastern boundaries, but the northwestern limit is not reached. In the case of a (geologically less realistic) 'shallow' collapse, a resistance of 100 kPa is required, but the frontal lobe is less well produced.

Unlike the frictional rheologies, this law produces a deposit with a well defined edge and leaves a deposit of realistic [START_REF] Wadge | The Socompa collapse and avalanche event[END_REF] thickness on all slopes, irrespective of angle.

Surface structures on the deposit from this simulation are remarkably similar to those of the real avalanche (Fig. 8 d,e). In particular a well defined NE-SW-trending topographic discontinuity (ME, Fig. 8) strongly resembles the median escarpment both in height (20 to 50 m) and location.

Snapshots of the 52 kPa simulation (Fig. 9, coloured for velocity) provide an explanation for the origin of the median escarpment. The avalanche accelerates down the northern flank of the volcano, attaining a maximum speed of ~ 100 m s -1 . As it runs up the western, then northwestern, slope of the basin, it reflects as three waves (one main one and two smaller ones) that then merge and wash back across the basin. The front of this composite wave then freezes to form the median escarpment. The elevated zone located north of the frozen wave front is also observed on the real avalanche deposit, and in the model represents the peak of the reflected wave (CZ, Fig. 8). This area, which in the natural deposit is rich in complex fault structures, experiences a complex history during the simulation, involving (1) initial stretching as the avalanche accelerates away from the volcano (Fig. 9a), (2) compression as the material decelerates and accumulates against the northwest margin (Fig. 9c), and (3) stretching and shearing during reflection off the northwest margin (Fig. 9d,e). Other similarities between the simulated and real deposits include the frontal lobe (FL, fig. 8) and the over-thickened margins along the northwestern limit of the avalanche that in the model form by accumulation, then back-slumping, of material during wave reflection.

Discussion

We have carried out numerical modelling of the emplacement of Socompa avalanche using the depth-averaged equations for granular flow and a numerical scheme capable of resolving shocks to a high degree of accuracy. The models assume transport of the avalanche on a basal slip layer, as suggested by evidence at Socompa and from other avalanche deposits. Starting conditions are consistent with field observations and the avalanche is assumed to have travelled as a single mass, with the exception of the Toreva blocks, which in our models are left to slump after avalanche emplacement.

The high 'mobility' of long-runout avalanches is normally interpreted in terms of reduced dynamic friction. The results of our modelling using frictional laws indeed confirm that very low basal friction (3° or less) is required to explain runout at Socompa, irrespective of the internal value.

This agrees approximately with the value of arctan (H/L) for the avalanche, which is 4.3° if the maximum values of H (height drop) and L (horizontal runout) are used. Simple scaling arguments show that arctan (H/L) ~ , the mean dynamic friction angle during emplacement (e.g., [START_REF] Pariseau | Rockslides and avalanches: basic principles, and perspectives in the realm of civil and mining operations[END_REF]. The long runout can't be explained by gravitational spreading of a very large volume of rock debris with normal friction. Use of values of  in the range 20-30° typical of dry granular materials results in runouts that are grossly inferior to that observed. No variation of the geometry of the initial slide mass within geologically realistic limits changes this conclusion.

Many hypothetical mechanisms of friction reduction have been proposed for rock avalanches; see [START_REF] Davies | Runout of dry granular avalanches[END_REF], [START_REF] Legros | The mobility of long-runout landslides[END_REF] and [START_REF] Collins | Acoustic Fluidization and the Extraordinary Mobility of Sturzstroms[END_REF] for recent summaries. We focus here on just a few that are relatively well constrained physically.

Elevated pore fluid pressure may play an important role in friction reduction in many avalanches by decreasing the effective normal stress at the bed. Fluid pressures close to lithostatic have been measured in debris flows [START_REF] Major | Debris-flow deposition: Effects of pre-fluid pressure and friction concentration at flow margins[END_REF] and are likely in wet rock avalanches such as Mount St. Helens [START_REF] Voight | Nature and mechanics of the Mount St Helens rockslide-avalanche of 18 May 1980[END_REF]. Although there was insufficient water in Socompa avalanche for subsequent decantation and mudflow formation, saturation of a thin basal layer can't be excluded. Water could have been derived from the water table beneath the volcano or from the ground surface over which the avalanche travelled. It is possible that a shallow lake or watersaturated sediments existed in the Monturaqui Basin in late postglacial times (Van wyk de [START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF]. Pressurized hydrothermal fluids derived from the edifice and/or over-ridden atmospheric air could also have played a role. Other mechanisms, such as acoustic fluidization [START_REF] Melosh | Acoustic fluidization[END_REF][START_REF] Collins | Acoustic Fluidization and the Extraordinary Mobility of Sturzstroms[END_REF], mechanical fluidization [START_REF] Davies | Spreading of rock avalanche debris by mechanical fluidization[END_REF], self-lubrication [START_REF] Campbell | Self-lubrication for long-runout landslides[END_REF][START_REF] Campbell | Large-scale landslide simulations; global deformation, velocities, and basal friction[END_REF] or dynamic fragmentation [START_REF] Davies | Runout of dry granular avalanches[END_REF] may generate velocity dependencies of dynamic friction in the absence of pore fluids.

Although frictional models can account crudely for the long runout of Socompa avalanche, the low basal friction allows neither realistic deposition on slopes nor preservation of surface morphology like the median escarpment. A better fit is obtained if we simply assume a constant retarding stress in the range 50-100 kPa. We emphasise that we don't consider this to be necessarily an accurate rheological description of the avalanche; constraints on the starting conditions are too crude to enable any unique rheology to be inferred. Avalanches will probably exhibit very complicated time-dependent and spacially variable mechanical behaviour [START_REF] Iverson | New views of granular mass flows[END_REF]. Most likely, the condition represents some average value of a retarding stress that varied with time during runout. However it's consistent with the finding of [START_REF] Dade | Long-runout rockfalls[END_REF] that an approximately constant stress in the range 10-100 kPa can explain the spreading behaviour of rock avalanches with a wide range of volumes. Indeed it was this observation that led us to try models of this type. Other authors have also concluded that long-runout avalanches exhibit some kind of yield strength by comparing avalanche deposit thicknesses on Earth and Mars [START_REF] Mcewen | Mobility of large rock avalanches; evidence from Valles Marineris, Mars[END_REF][START_REF] Shaller | Analysis and implications of large Martian and terrestrial landslides[END_REF]. That a constant retarding stress can also capture to a first order the emplacement dynamics of Socompa avalanche lends some support to Dade and Huppert's analysis and raises the question of the origin of this behaviour.

We speculate that conditions in the avalanche may have varied with time in such a way that the retarding stress could have remained approximately constant, even though the rheological behaviour was fundamentally frictional (i.e., basal shear stress was a product of an apparent friction coefficient times the lithostatic normal stress, modified by a centrifugal term [eq 4]). Consider a hypothetical avalanche in which high fluid pressure is initially present in the basal shear zone, so that motion commences (when the avalanche is thick) with low basal friction. During runout, pore fluids migrate away from the shear zone, so that friction increases progressively by pressure diffusion at the same time that the avalanche spreads and thins (e.g., [START_REF] Iverson | Flow of variably fluidized granular masses across threedimensional terrain 1. Coulomb mixture theory[END_REF].

The result could be that the basal stress remains approximately constant due to the competing effects of basal friction and flow thickness (i.e., lithostatic normal stress). In the case of a velocitydependent process such as acoustic fluidization or mechanical fluidization, the basal friction might be reduced at initial high velocity (when the flow is thick), but would increase at lower velocities and approach the value of static friction as the avalanche comes to rest (once the flow had thinned).

In both examples, acquisition of high apparent friction as avalanche motion ceased would permit preservation of surface morphology. A third possibility is that basal friction remains negligible throughout runout (for example due to fluid pressure  lithostatic overburden), and that the retarding stress is a cohesive component related to grinding and crushing of particles in the basal layer and/or to rock breakage within the overriding mass as it spreads across the landscape. Stresses of 50-100 kPa indeed lie in the range of cohesive strengths of volcanic materials measured in laboratory experiments ( e.g., [START_REF] Voight | The 26 December (Boxing Day) 1997 sector collapse and debris avalanche at Soufrière Hills Volcano[END_REF].

Irrespective of the exact dynamics, our study provides two general constraints on the flow behaviour of the avalanche. First, all models investigated require peak velocities of ~100 m s -1 to achieve the observed runout. This is due to the large height differential between the volcano summit and the basin floor (3000 m): one of the largest known for a terrestrial avalanche. Second, the results suggest that the median escarpment is the frozen front of a huge composite wave of rock debris reflected off the western northwestern and northern margins of the Monturaqui Basin.

Reflection is observed to different extents in all the models run, but it is only in the constant-stress simulation that the wave front is preserved as a high escarpment.

The reflection hypothesis is further investigated in Figs. 10a-d, in which the 52 kPa constant-stress model is re-run with the avalanche surface coloured according to rock lithology. The initial distribution of lithology colours is arbitrarily adjusted, but is geologically realistic (Van wyk [START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF]oral comm.). White tracer particles track the motion of the avalanche as they are advected along. The distribution of surface lithologies on the resulting numerical deposit closely resembles that evident on the Landsat image of the avalanche (Fig. 10e). Moreover the backreflected trails of the tracer particles mimic the stretching and folding fabrics on the avalanche surface. As the wave is reflected back in the model, material behind the wave drains northwestward to form the frontal lobe. Although certainly not a unique solution, Fig. 10 demonstrates that avalanche reflection, as well as generating the median escarpment, can plausibly account for the surface textures observed on the deposit surface for a geologically realistic pre-collapse distribution of lithologies on and around the volcano.

The topographic reflection of a huge wave of fragmented rock debris off the side of the Monturaqui Basin is a striking illustration of the high fluidity that characterises long-runout rock avalanches like Socompa. where  is the local slope, z  is the horizontal azimuth of that slope, and  is the retarding stress dependant on the rheological law chosen. The algorithm first calculates a fictive velocity due just to terms aw and ap. The retarding acceleration ar is then computed in the direction opposed to this fictive velocity. This approach increases the stability of the algorithm and ensures isotropy of the solutions. The value of new velocity (called s) due to the action of source terms is then:

  d 1 2, 1 2, d tt i j i j w p r t       s u a a a
The second stage of the algorithm computes the advection terms. The fluxes of mass and momentum are calculated using an upwind scheme.

                  
Note that the exponents used for  do not indicate time, but the quantity advected : mass h and momentum hu and hv. From these fluxes, we calculate the new thickness and the new mean velocity at the centre of each cell:

      d , , 1 2, 1 2, , 1 2 , 1 2 dd , , 1 2, 1 2, , 1 2 , 1 2 , , dd , , 1 2, 1 2, , 1
i j i j i j i j i j t ij t ij h h t S u h t S u h v h t S v h                                                     
where S is the surface of the cell.

Finally, the x and y components of the new velocities at the edges, modified by advection, are calculated using a second upwind scheme. For example, if , The figures to the right show the initial shape at t=0, without vertical exaggeration.

  1c, d), referred to in what follows as the 'deep' collapse geometry, and (2) a slab-like initial slide volume, referred to as the 'shallow' geometry (see the legend of Fig. 1 for details). The deep geometry appears to be most compatible with field evidence (Van wyk de Vries et al., 2001) and has been used for most of the simulations.

  (1) Best fit to the northwestern margin, where the avalanche ran up a distal slope approximately perpendicular to the flow axis. (2) Best fit to the overall outline of the avalanche deposit, including the frontal lobe. (3) Reproduction of major structures observed on the avalanche deposit, in particular the median escarpment. Only models satisfying reasonably all three constraints are taken as acceptable approximations of reality. All the results presented below were obtained by flow across numerically 'dry' topography.Frictional rheologyModels were run assuming a frictional avalanche rheology (eq. 4) considering three combinations of basal and internal angles of dynamic friction: (1) bed << int = 30°, the static angle of friction for dry granular debris; (2) bed  0° but int = 0°; (3) bed = int  0°. In each case the parameters were varied in multiple simulations. The visual best-fit solutions are presented in Fig.6using the 'deep' collapse geometry.In the first best-fit model (Fig6 a-d) int = 30°, and a value of bed = 1° is necessary to reach the northwestern margin of the Monturaqui Basin and produce the observed runup. A high internal friction may be realistic for Socompa avalanche, which exhibits field evidence for the rafting and progressive brittle break-up of SB material on top of a base of shearing, low-friction RIF (Van wyk[START_REF] Van Wyk De Vries | A gravitational spreading origin for the Socompa debris avalanche[END_REF]. Bed friction angles higher than 1° result in reduced runout, and lower ones cause excess spreading. The avalanche first accelerates away from the volcano, attaining a maximum velocity of ~100 ms -1 , before reflecting progressively off the northwestern margins of the basin(Figs. 6a

  necessary to reproduce the observed runout (2.5°), 1 needs to have an even lower value, irrespective of D and 2. Once a given part of the avalanche is slowing down, bed reverts to 1 and, as in the constant-bed case, formation of surface topography is prevented by the high fluidity of the material. It is worth noting that values for 1, 2 and D used by[START_REF] Heinrich | Numerical simulation of the December 1997 debris avalanche in Montserrat, Lesser Antilles[END_REF] to simulate the ~0.005 km 3 26 December 1997 debris avalanche on Montserrat (11°, 25° and 15 m respectively)

Figure 1 :

 1 Figure 1: (a) Shaded topography of Socompa avalanche, showing the median escarpment (ME), the

Figure 2 :

 2 Figure 2: Geometry of the calculation domain. The ground topography is defined using horizontal

Figure 3 :

 3 Figure 3: Comparison between numerical and analytical solutions for a dam-break onto a

Figure 4 :

 4 Figure 4: Comparison between the analytical solution of Mangeney et al., 2000, (dashed gray), and

Figure 5 :

 5 Figure 5 : Circular dambreak tests viewed from above (and in cross section in the lower part of each

Figure 6 :

 6 Figure 6: Snapshots of the emplacement of frictional avalanche models 1 and 2 at t = 200 s and t =

Figure 7 :

 7 Figure7: Best-fit simulations using a 'shallow' slab-like initial slide geometry, to be compared with

Figure 8 :

 8 Figure 8: Avalanche evolution using a constant retarding stress T = 52 kPa. The colour scale

Figure 9 :

 9 Figure9: Snapshots every 100 s of the constant-stress (52 kPa) simulation of Fig.8, coloured according to velocity (m s -1 ). The reflected wave is particularly clear in these figures, as is the late-

Figure 10 :

 10 Figure 10: (a-d) The constant-stress (52 kPa) simulation of Figs. 8 and 9, with surface rocks

Figure A1 .

 A1 Figure A1. Definitions of scalars, vectors and cell notation in the numerical scheme.

  For example, if the x component of 1 2,

														s	ij 	is
	negative, fluxes through the side are computed by:
	h						t		d t
	i	1 2,	j	i s	1 2,	j	i h	,	j	dy
	hu						t	dd t t t
	i	1 2,	j	i s	1 2,	j	i u	,	j	i h	,	j	dy
	hv					t	dd t t t
	i	1 2,	j	i s	1 2,	j	i v	,	j	i h	,	j	dy

Acknowledgements

Ben van Wyk de Vries shared his knowledge of Socompa with us and advised us on reconstructing the pre-avalanche terrain. Thierry Buffard and Stephan Clain helped us test the numerical code. Barry Voight, Geoff Wadge, Herbert Huppert and two anonymous reviewers provided useful feedback. The work was financed by two research programs of the French CNRS: 'Relief de la Terre' and 'Aléas et Changements Globaux'.

We use cell edge (i-1/2, j) to illustrate the main steps of the algorithm (Fig. A1b). For each time increment we first compute the source terms of the conservation equations, then the advection terms. The governing equations contain three source-term accelerations:

 


Sami Basly
email: baslysami@yahoo.fr

INTERNATIONALISATION OF FAMILY FIRMS IN A KNOWLEDGE-BASED VIEW

Introduction

Despite the profusion of research about knowledge-based processes within the firm, rare studies tried to analyze them for the family firm i . The family firm can be defined as a firm controlled by one or more families involved in governance or management or at least holding capital stakes in this organization ii . Due to its specificities, this entity exhibits a specific behavior as for the creation, development, sharing, protection and transmission of knowledge. [START_REF] Habbershon | A Resource-Based Framework for Assessing the Strategic Advantages of Family Firms[END_REF] initiated the research aiming at the identification of the specific resources of the family firm. But, more than specific resources and capacities, the family firm uses a collective tacit knowledge needed to integrate, coordinate and mobilize effectively its resources [START_REF] Cabrera-Suarez | seems to initiate a knowledge-based approach for the family firm. ii The recurring problem of family firm definition will not be addressed[END_REF]. The aim of the present contribution is to analyze the characteristics of the family firm critical to the knowledge-based processes. Due to its founding characteristics, family SME seems to be a closed, hermetic and rigid organization. Although this description can be criticized and challenged, it remains valid for many of these entities. The interaction between the family system and the firm system appears to be the essential element preventing the organization from quickly adapting to the changing conditions [START_REF] Moloktos | Change and Transition and Family Businesses[END_REF]. [START_REF] Moloktos | Change and Transition and Family Businesses[END_REF] explains that when the life cycles of these two systems do not evolve at the same speed, the risks of crisis are significant. Thus, conservatism constitutes a first obstacle to knowledge development. Besides, small and medium family enterprise is strongly oriented towards independence which has advantages but also many drawbacks. The impact of this orientation on the system of resources and in particular on knowledge can be crucial. Conversely, the family firm is characterized by social networking which impact on knowledge development is positive. In this article, we will study the influence of these three variables on the knowledge base of the firm in a context of internationalization.

Research which explicitly conceived the internationalization of the firm as a process of organizational learning is infrequent. At most, this phenomenon is deemed as underlying the process of resource commitment abroad. Here, we analyze internationalization in the light of the theoretical developments about learning and knowledge development within the organization. Internationalization can be conceived as a process of learning and accumulation of knowledge [START_REF] Eriksson | Effect of Variation in Knowledge Accumulation in the Internationalisation Process[END_REF]. [START_REF] Johanson | The Internationalization Process of the Firm -A Model of Knowledge Development and Increasing Foreign Market Commitments[END_REF] took the first steps in considering knowledge within the context of internationalization. The stream of the literature initiated by these authors analyzes the process of international development as a sequence of steps permitting to the firm to gain knowledge of international environment. The move from one stage of commitment to another as well as the move from a given market to another are done incrementally. This incremental dynamics is precisely justified by an underlying process of foreign market knowledge development. Built on the analysis of [START_REF] Carlson | International Business Research[END_REF], this reasoning suggests more precisely that the firm managers fight against uncertainty through two strategies implying the development of two distinct forms of knowledge. The first mode to reduce uncertainty is based on a process of acquisition of objective information, on a cognitive learning. For instance, [START_REF] Knight | Information Internalisation in Internationalising the Firm[END_REF] emphasize that the process of internalization of information and its translation into relevant knowledge is a fundamental step in order to accomplish an internationalization project whatever its form or its localization. The second way of reducing uncertainty is the engagement of the firm in an action-based international expansion permitting to develop an international competence incrementally and cumulatively. [START_REF] Johanson | The Internationalization Process of the Firm -A Model of Knowledge Development and Increasing Foreign Market Commitments[END_REF] distinguish between objective knowledge and experiential knowledge [START_REF] Penrose | The Theory of the Growth of the Firm[END_REF]. The first is a public good and therefore transferable at a weak or null cost. The latter is unique to the firm since it is acquired only through market experience. Recently, [START_REF] Eriksson | Experiential Knowledge and Cost in the Internationalization Process[END_REF][START_REF] Eriksson | Effect of Variation in Knowledge Accumulation in the Internationalisation Process[END_REF] analyzed more thoroughly the different dimensions of knowledge relevant to international operations. In addition to operational and institutional knowledge, internationalization knowledge is of a crucial importance. In sum, two dimensions of knowledge, a resource and a competence, are together necessary and underlie the progression of the firm through the dimensions of internationalization (modes of entry, markets, products, etc). The first is the market knowledge which is constituted of a set of information in relation to a specific market or a number of markets. [START_REF] Johanson | The Internationalization Process of the Firm -A Model of Knowledge Development and Increasing Foreign Market Commitments[END_REF] deal with this type of knowledge which requires obviously the activity on the market but could especially be acquired in an explicit form through cognitive learning. The second type of knowledge is synonymous of international competence. Behavioral learning largely contributes to the development of this knowledge whose form is primarily tacit. This article is structured as follow: after analyzing the main idiosyncratic variables influencing the development of internationalization knowledge, we discuss some theoretical implications. Indeed, the study of these variables raises questions about the efficacy of the organizational memory within the family firm. This organization runs particular risks because of the peculiarity of its knowledge management mechanisms. Intergenerational transmission and transfer of knowledge could be the solution to protect and perpetuate valuable knowledge.

Idiosyncratic characteristics of small and medium family enterprise and development of internationalization knowledge

Three variables are distinctive as for the processes of knowledge development within family SME. These are characteristics frequently emphasized by the literature as being specific to this organization. We will study the effects of conservatism (1.1), independence orientation (1.2) and social networking (1.3) on the development of the knowledge base of small and medium family enterprise.

Conservatism

The conservatism limits the variation and accordingly the extent of knowledge developed by the firm. Indeed, the literature stresses that this variation, i.e. the diversity of environments to which the firm is exposed, is strongly correlated with the amount of knowledge accumulated and developed. Organizations exposed to a variety of business and institutional actors are likely to develop knowledge of an important set of events and thus learn more than poorly exposed ones. They are more able to define problems, errors and opportunities than firms whose horizon of action is more reduced [START_REF] Eriksson | Effect of Variation in Knowledge Accumulation in the Internationalisation Process[END_REF]. The weak variation indeed implies a limited number of customers, competitors and other institutional actors. Accordingly, conservative organizations carry out only a simple loop learning which does not reform their theories-in-uses since they accumulate little knowledge.

Conservatism is the attachment to the choices of the past [START_REF] Timur | The Tenacious Past: Theories of Personal and Collective Conservatism[END_REF]. The literature about cultural specificities emphasizes the maintenance of the status quo and harmonious relations not only within the group but also within the entire society. The pursuit of security, conformism and tradition are characteristic of conservative organizations. Particularly with the family firm, [START_REF] Miller | Lost in Time: Intergenerational Succession, Change, and Failure in Family Business[END_REF] explain that the conservative posture of this entity is reflected on its governance, strategy and organization (mainly culture). We will discuss these three components in order to be able to understand their impact on the family SME knowledge base.

Conservatism and firm governance

The first sphere concerned with conservatism is the governance of the firm iii . Conservative organizations and particularly family firms are characterized by the persistence and substantial power of old generations who exert a strong supervision on the ownermanager. Otherwise, conservatism can be due to the owner-manager himself. He plays a significant role in the processes of organizational learning and influences the strategic posture that his firm adopts. A patriarchal family controlling a paternalist organization is the ultimate case of figure (Jenseter and Malone, 1991): being dependent to a high degree on its founder, the organization would be unable to promote change as it is not instigated by the founder. However, the founder or owner-manager may be unwilling to promote change. [START_REF] Hambrick | Executive Commitment to the Status Quo: Some Tests of its Determinants[END_REF] call this tendency to slow down the change "commitment to the status quo" (CSQ). The management believes in the permanent accuracy of current strategies or organizational behaviors [START_REF] Hambrick | Executive Commitment to the Status Quo: Some Tests of its Determinants[END_REF]. Therefore, personal paradigms which by the past proved their efficacy constitute inhibitors to change. Thus, in spite of the evolution of the environment and performance requirements, the owner-manager could become inflexible and rigid by promoting practices and strategies resulting from past successes and avoiding decisions which can threaten his image or his economic wealth [START_REF] Ward | Growing the Family Business : Special Challenges and Best Practices[END_REF]. Consequently, he perceives a weak need for adjustment even in case of critical changes in the external environment. In sum, the conservatism of the owner-manager constitutes a significant barrier to organizational learning and knowledge development within family SME.

The efficacy of the board of directors iv is an indicator of the struggle against conservatism and strategic inertia. According to theoretical descriptions, this corporate body constitutes a source of strategic initiative and relevant information and also a source of expertise, counsel and control since it must also correct the trajectory in case of unsatisfactory management. However, its role within family SME needs to be moderated. [START_REF] Mustakallio | Optimal Governance in Family Firms[END_REF] argue that the role of the board of directors, measured by its composition and by the intensity of control it exerts, would be more significant as the implication of the family members in the management decreases -suggesting at the opposite that the more the family is involved, the less decisive the role of the board would be. In general, the traditional family firm is known to have a board of directors whose members, selected according to their status and influence within the family and not according to their knowledge of the activity or industry, occupy their positions for long periods and have insufficient or inadequate professional competences. According to this description, they constitute a barrier to any attempt of change potentially threatening the stability of the firm. [START_REF] Ranft | Board Composition and High-flying Founders: Hints of Trouble to Come?[END_REF], notice that the founders of high-performing firms are even tempted to weaken deliberately the board of directors of their firms in order to maintain the status quo. The inward orientation is more corroborated in some family firms who simply do not implement such a body [START_REF] Melin | Corporate Governance in Family Firms : The Role of Influential Actors and the strategic Arena[END_REF].

However, the role of the board of directors can be crucial since it should increase the amount of information available to the operational management when planning or implementing strategies. This role is accomplished by insiders as well as external administrators v . The insiders contribute through their thorough comprehension of the firm.

The outsiders would prevent from the dominance of a single line of thought by challenging the assumptions underlying the firm's strategies and injecting external knowledge. The results obtained by [START_REF] Schwartz | Outside Boards and Family Businesses : Another Look[END_REF], based on a sample of 262 family firms, prove the relevance of the incorporation of external administrators. The authors find that they provide unbiased points of view and constitute a precious means for the establishment of networks. As far as the internationalization of the firm is concerned, [START_REF] Sanders | Internationalization and Firm Governance : The Roles of CEO Compensation, Top Team Composition and Board Structure[END_REF] prove the existence of a significant relation between internationalization and the composition of the board. First, it is suggested that the size of the board of directors increases according to the intensity of international activities. Moreover, the authors find that the proportion of outsiders in the board of directors increases with internationalization. In brief, the role of counsel accomplished by the board would have a significant influence on the strategic orientation of the firm by improving the variety and quality of information available for the strategic processes and, consequently, the variation, selection and retention of alternative paths of development [START_REF] Mustakallio | Governance, Entrepreneurial Orientation and Growth in Family Firms[END_REF]. This function of counsel should thus improve the capacity of the firm to innovate and establish new strategic directions such as internationalization.

The study of the conservatism of the family firm governance is necessary because this phenomenon has consequences on firm's strategy selection and implementation. An analysis of the strategic manifestations of this posture will, consequently, be outlined.

Strategic conservatism

Second, the conservatism of the firm is expressed strategically. Generally, the family firm has a tendency to be strongly devoted to a strategy which becomes a source of rigidity. Thus, strategy and pursued business goals constitute factors inhibiting the trigger of internationalization [START_REF] Gallo | Internationalizing the Family Business : Facilitating and Restraining Factors[END_REF]. The literature suggests that the family system attempts to create and maintain a cohesiveness that supports the family "paradigm" which is described as the core assumptions, beliefs, and convictions that the family holds in relation to its environment [START_REF] Gudmundson | Strategic Orientation : Differences between Family and Nonfamily Firms[END_REF]. Information that is not consistent with this paradigm is resisted or ignored [START_REF] Davis | Realizing the potential of the family business[END_REF]. The more the family is conservative the less it works for change. Strategic conservatism implies stagnation and risk of insularity [START_REF] Miller | Lost in Time: Intergenerational Succession, Change, and Failure in Family Business[END_REF]. The firm carries out few changes in its objectives, business and lines of product or markets [START_REF] Miller | Lost in Time: Intergenerational Succession, Change, and Failure in Family Business[END_REF]. Generally, family SME is known to maintain its differentiation through the same activities and policies [START_REF] Gallo | Internationalizing the Family Business : Facilitating and Restraining Factors[END_REF] and to privilege a defensive position with protection of its niche. Accordingly, its market shares are likely to be narrowing and its market potential exhausting. However, internationalizing implies the beginning of a new activity (new markets, new customers, new competitors, etc.) weakly connected to the original activity [START_REF] Gallo | Internationalizing the Family Business : Facilitating and Restraining Factors[END_REF]. So that internationalization starts, a motivation for change, for strategic revival and adaptation to the new requirements of the environment are necessary. For instance, [START_REF] Ward | The Special Role of Planning for Family Businesses[END_REF] stresses that the succeeding family firm renews its business strategy several times as the market and competitive pressures evolve.

In sum, the usual conservative attitude of the family business can inhibit internationalization. In fact, the organizational learning remains weak since the direction focuses primarily on problem solving rather than on the search and pursuit of new opportunities. Indeed, it deals exclusively with internal issues relative to the efficiency of operations or the quality of products and neglects issues pertaining to the evolution of market requirements or consumers needs.

The third dimension where conservatism can appear is the culture of the firm. Instead of nurturing the will of change and development, cultural conservatism implies characteristics of preservation and rigidity.

Cultural conservatism

The pursuit of the goal of culture and identity protection constitutes the last element exerting a negative influence on learning orientation within family SME. Many authors emphasize the central role of culture and values in shaping the competitive posture of this organization [START_REF] Dyer | Cultural change in family firms: anticipating and managing business and family transitions[END_REF]. For instance, analyzing values in the family firm, [START_REF] Salvato | Values and Competitive Advantage: The Cultural Determinants of Dynamic capabilities in Family Firms[END_REF] show that they influence activities and routines of the organization aiming to create a competitive advantage. The family firms show an inclination to be independent from their environment and the external culture (Donckels and Fröhlich, 1991). In addition, they insist on artifacts which generally originate from the firm's local environment and are the result of the influence of certain members of the family, in particular that of the founder [START_REF] Gallo | Internationalizing the Family Business : Facilitating and Restraining Factors[END_REF]. Consequently, cultural conservatism inhibits any will of change and learning.

Independence orientation

The second variable influencing the processes of knowledge development within family SME is independence orientation. The independence orientation is a consequence of the family long-term commitment to the business. Paradoxically, this commitment has two contradictory effects on growth. First, it implies the pursuit of future development and continuity of the firm to make sure that the family heritage is passed on to the following generations. On the other hand, commitment implies a strategy of conservation of the heritage which passes by a strong seek for the independence. Aiming to guarantee its continuity, family SME establishes an independence orientation on three levels (see Figure 1). First, from the financial point of view, it avoids as much as possible turning to outside partners [START_REF] Hirigoyen | Les implications de la spécificité des comportements financiers des moyennes entreprises industrielles (M.E.I) familiales[END_REF]. Then, on the human plan, it would be favorable to the appointment of family members or individuals belonging to the close relational circle to the posts of direction and would be reluctant to the recruitment of professional directors [START_REF] Astrachan | A Neglected Factor Explaining Family Business Success: Human Resource Practice[END_REF][START_REF] Johanson | Issues in Growing a Family Business: A Strategic Human Resource Model[END_REF]. Finally, to maintain the decision-making in hands of the family, the family firm tends to avoid the inter-organizational relations, cooperative investments, and tries to limit the sharing of control of its investments (Donckels and Fröhlich, 1991). The contribution of the outsiders (financiers, directors or partner organizations) can, however, be precious to the company. And the introversion would be a major obstacle to the perpetuity of the firm because it inhibits growth. Independence orientation limits the accumulation of internationalization knowledge because, on one hand, the horizons of the company will be limited and little varied, and on the other hand, the potential valuable knowledge contribution of the outsiders is excluded. As a consequence, the more the direction of the firm wishes the independence the more the internationalization will be slowed down.

The financial dimension of independence orientation

Devoted to its goal of continuity, family SME tries to evolve in a more or less hermetic universe. Accordingly, external financial intervention is avoided because it could deteriorate the independence of the firm. The resource dependence theory provides an explanation to this attitude [START_REF] Davis | Governance and Goal Formation Among Family Businesses : A Resource Dependency Perspective[END_REF]: the higher the dependence to the (resource) capital, the more the potential financier would have greater power and influence in the decision-making within the firm [START_REF] Davis | Governance and Goal Formation Among Family Businesses : A Resource Dependency Perspective[END_REF]. Consequently, family SME seems reluctant to adopt modes of financing other than internal ones. Schematically, it appears strongly predisposed to implement or at least to adhere to the recommendations of the pecking order theory [START_REF] Myers | Corporate Financing and Investment Decisions when Firms Have Information that Investors Do Not Have[END_REF]. It favors generally internal financing by the retention of earnings and the constitution of reserves. Moreover, it avoids opening financially to external sources. First, it tends to avoid debt and relies enormously on costly internal capital. Financing through equity has other specificities that fear family SME. Quotation, for instance, could indeed involve a major change in the ownership structure and governance of the firm due to the entry of external shareholders [START_REF] Schulze | Exploring the Agency Consequences of Ownership Dispersion Among the Directors of Private Family Firms[END_REF].

Financial independence has significant consequences on the knowledge base of the firm. Initially, in a managerial vision of the firm, internal financing helps to avoid the diffusion of the cognitive map of management and endangering growth opportunities not perceived by competitors [START_REF] Charreaux | Variations sur le thème : A la recherche de nouvelles fondations pour la finance et la gouvernance d'entreprise[END_REF]. However, this advantage is compensated by the fact that, at the same time, internal financing implies an inward orientation and a weak development of the knowledge base as it prevents from the penetration of a potentially relevant external cognitive contribution. In addition, debt avoidance, even if it permits to limit the risk of diffusion of information and management cognitive schemas towards bankers implies a lot of disadvantages relatively to the firm's knowledge base. Indeed, the contribution of the bank could be valuable since it can take part in the development of the knowledge base through adhering or enriching the management vision and cognitive map [START_REF] Charreaux | Variations sur le thème : A la recherche de nouvelles fondations pour la finance et la gouvernance d'entreprise[END_REF]. Lastly, external shareholders can play a valuable role as for the firm's knowledge base. First, they could exert their influence on the development of the vision of the firm. Then, they can play a significant role in providing proposals for investment opportunities. External ownership thus makes it possible to extend the knowledge base.

Family SME don't recognize these valuable contributions and follow a conservative financial behavior [START_REF] Hirigoyen | Les implications de la spécificité des comportements financiers des moyennes entreprises industrielles (M.E.I) familiales[END_REF]. As a result, financial independence is likely to limit the amount of internationalization knowledge and hence internationalization of small and medium family firms.

The human dimension of independence orientation

The pursuit of independence inhibits internationalization from the human point of view. The family firm adhering completely to the principle of managerial independence is limited quantitatively and qualitatively by the lack of human resources. Indeed, trying to avoid loss of control, family management tends to limit external managerial implication even it would be valuable to undertake international activities. To justify the customary recruitment of family directors and managers, the literature speaks about paternalist management and nepotism characteristics of the traditional family firm. [START_REF] Welsch | The Impact of Family Ownership and Involvement on the Process of Management Succession[END_REF] observes that when the family firm makes a decision relating to its human resources, it is more influenced by family and personality issues more than by a standardized set of performance and competence indicators. The altruism characterizing the owner-manager, generally the father or head of the family, implies a feeling of natural right among members of family. The owner-manager is thus incited to make use of firm resources to provide employment and other privileges to the family members [START_REF] Schulze | Agency Relationships in Family Firms: Theory and Evidence[END_REF]. [START_REF] Dunn | Success themes in Scottish family businesses: Philosophies and practices through the generations[END_REF] indicates a critical consequence of this behavior. Indeed, the pursuit of the objective of preferential employment of family members may often signify the hiring of sub-optimal employees. Besides, the analysis of [START_REF] Harris | Is Strategy Different for the Family-Owned Business ?[END_REF] shows that the rigidities of the family firm when it is about change of paradigm are primarily due to the sclerosis to the human element:

-Family firm privileges internal succession, which is one of its main goals, and devotes the principle of loyalty, whereas new paradigms are likely to come from outside employees or management, -Internally trained successors have weak external experience whereas new paradigms are likely to emerge from the variety of personal experiences, -Heir of the entrepreneur can suffer from a lack of self-confidence whereas the possibility of emergence of new paradigms generally requires a great confidence in its personal judgment.

Another characteristic of family firms is to be emphasized. Indeed, this type of organization is known to be loyal i.e. seeking to keep the same employees for long periods. According to [START_REF] Miller | Lost in Time: Intergenerational Succession, Change, and Failure in Family Business[END_REF], the same policies of recruitment and promotion, for example, are implemented at the profit of the same people. The absence of recruitment implies, however, an ageing of human resources and management in particular (Jenseter and Malone, 1991).

Overall, the prerequisite in external competences is explained by the contribution in knowledge resources that outsiders can offer. Particularly with internationalization, they constitute a privileged source of market-specific knowledge. Despite the availability of increasingly powerful means of communication, moreover, delegation of responsibilities remains necessary because of the geographical distance.

In sum, human independence, implying exclusively internal recruitment and responsibility transfer, has a notable negative impact on the knowledge base of internationalizing small and medium family firm. 1.2.3. The relational dimension of independence orientation: co-operation and economic networks [START_REF] Gray | Managing Entrepreneurial Growth : A Question of Control ?[END_REF] observes that owner-managers of small firms adhere to an organizational culture impregnated by individualism and anti-participation. The potential attenuation of independence constitutes a short or long term threat explaining probably the weak cooperative orientation of family SME. Indeed, the co-operation contains a dynamics which can make evolve the co-operation to a relation of global dependence. In fact, the attenuation of the independence, initially limited to the only field of agreement, would be extended to the entire firm (Adam-Ledunois and Le Vigoureux, 1998). Another explanation of the weak organizational networking of family SME can be induced from the explanations of the network approach. Belonging to a network implies, indeed, acceptance of the external influence. The position of a firm within its network can influence and is also influenced by expectations of other actors as for the way it should behave and interact with other organizations (Johanson and Mattson, 1988). Consequently, the position occupied by a firm, even if it permits access to new and valuable resources, relations and markets, is constraining because it shapes its role and relations with the other firms.

According to some authors, when they cooperate, family firms would choose their similar i.e. other family firms. Indeed, pursuing the same principles, in particular independence, and having a comparable size, they would not constitute a threat to independence vi . In summary, family SME exhibits a weak co-operative orientation and a disinclination to integrate economic networks (Donckels and Fröhlich, 1991). Consequently, it is likely to develop a poor knowledge base since the role of the network can be crucial at least on three levels. First, through its implication in a network, a firm can develop a high awareness of opportunities and threats pertaining to its activities since it is strongly exposed to environment. Second, its decisions and actions (concerning strategies to be adopted, for example) can be founded on an imitation of other more experienced actors of the network. Finally, the network allows a direct transfer of knowledge between participants.

In sum, we can argue that the influence of relational independence on the development of internationalization knowledge is negative.

Social networking

The network orientation of the owner-manager and his family is the last variable influencing the process of development of internationalization knowledge. This orientation is to be distinguished from organizational networking analyzed in the preceding section. The family firm shows a weak cooperative orientation in the sense of the pursuit of common objectives with an economic partner but a strong orientation toward social networking. It favors social relationships to economic ones that risk alienating its decision-making independence. The role of social networking in development of knowledge is crucial. Overall, networking was defined as an organizational means aiming to strengthen entrepreneurial processes. Yli-Renko, Autio and Tontti (2002) observe, in addition, that internal and external social capital influence acquisition and creation of knowledge guiding the international development of technological-intensive new ventures. The network approach of internationalization (Johanson and Mattson, 1988), even if it concerns organizational networks, stresses the seminal role of network orientation as for the development of knowledge during internationalization. Transposing this reasoning within the framework of social networks, social networking appears to be much important for the initiation and consolidation of international activities of family SME. In total, social networking influences positively the amount of internationalization knowledge of family SME.

Even if a lot of research analyzes the role of personal networks as a support in period of crises, the way in which social network functions and especially with respect to internationalization is still unexplained. We argue that the role of networking is to be stressed at least on two levels. Initially, this orientation plays a valuable role for the trigger of international activities. Then, the network of personal and family relations contributes to the choices taken as regards markets to penetrate and entry modes to adopt.

Role of the social networking for the initiation of internationalization

The social network constitutes a competitive advantage for SME during its internationalization. [START_REF] Watkins | Internationalisation of Indian small scale industry (SSI)[END_REF] find, for example, that Indian firms (up to 99 % under family control) are favored compared to firms belonging to countries where community and family relations values are not significant. The author explains that social network i.e. personal contacts established through family, friends and close relations and also the rooting of the firm in a community, is the main factor pushing the majority of studied firms to internationalize. Likewise, [START_REF] Dibben | Social Relationships as a Precursor to International Business Exchange[END_REF] argue that social ties are the key trigger of international operations as the management would generally seek to establish durable relations and assigns a minor importance to short-term transactions. [START_REF] Yeung | Limits to the Growth of Family-Owned Business ? The Case of Chinese Transnational Corporations from Hong Kong[END_REF] illustrates the economic potential allowed through personal and familial relations. He describes the case of a Chinese family firm whose international growth was done in particular through these relations. Social networking was not only the fact of the owner-manager but also of the entire family interacting with another family firm established in another country of the region. These two families, having lived experiences together and having a shared past, decided to initiate a business trans-border relation and found the essential complementarities to live this relation and to make it durable. The trust which exists through purely human relations (at the beginning) is thus used to propel a business relation.

The family firm relies enormously on its family relations in the broad sense of the term during its internationalization. The members of the family either assigned abroad or already present on the foreign markets form "an internationally extended family" [START_REF] Fan | Families in the 21st Century: The Economic Perspective[END_REF] able to mobilize resources and especially knowledge of markets to conquer. This knowledge permits to reduce uncertainty [START_REF] Johanson | The Internationalization Process of the Firm -A Model of Knowledge Development and Increasing Foreign Market Commitments[END_REF] because the social ties established abroad are more capable to evaluate opportunities and risks, and manage and govern effectively the activities. Overall, belonging to an ethnic community constitutes an advantage for internationalizing firms and in particular for family SME. [START_REF] Solberg | Market Information and the Role of Networks in International Markets[END_REF] evokes Jewish tradesmen established during centuries in various areas of the world as well as Indian or Chinese and Pakistani migrations during the second half of the last century as many factors having allowed the opening of many international trade routes [START_REF] Solberg | Market Information and the Role of Networks in International Markets[END_REF]. In fact, the cultural proximity, natural honesty and the confidence shared between people of the same ethnic group reduce uncertainty inherent to commercial transactions.

Social networking and international strategic choices

Personal networks (strong and weak ties vii ) are strategically important to the internationalizing firm. Their number and quality determine the choice capacity of the firm. The importance of these relations must be emphasized at least for two aspects of international strategy: the choice of target country and the choice of entry mode.

Choice of target country

Social networks play a significant role in the choice of the country where efforts of internationalization will be directed. This choice can be made according to the relations established in this country. Initially, the family firm can target a particular country at the instigation of members of its network present on this market. Sometimes, between two alternative markets, the firm will choose that where it holds a personal network because of the best knowledge of country these ties permit. In addition, family firm may want to assign its relations established in this country to the management and governance of local operations. Gallo and Sveen (1996) indicate that the existence of individuals belonging to the family, in the broad sense of the term, in foreign countries would facilitate the establishment of business relations with these countries as responsibilities could be assigned to them. A last factor pushing the family firm to choose a specific country reveals the subjective nature of this decision since the owner-family may want simply to invest in his country of origin or "do something for the country". [START_REF] Okoroafo | Internationalization of Family Businesses : Evidence from Northwest Ohio, USA[END_REF] notes indeed that ethnic and racial relations appear to affect choices of country of location of internationalizing family firms.

Another significant aspect has to be emphasized. The literature pertaining to "the immigrant effect" suggests that immigrants originating from a particular host market constitute a "bridge" between the foreign firm and this market. Immigrants often have a significant knowledge of their country of origin and understand profoundly the market culture. The results of certain studies imply that the immigrant effect could be regarded as a localization endowment for an internationalizing firm.

Choice of entry modes

The social ties can also influence the choice of entry modes on a specific market. Initially, through the counsel of its relations established on a market and holding an intimate knowledge of its functioning, the firm can choose a specific mode of penetration. On certain markets, these social ties are crucial because they permit to introduce the firm into the local business networks. Without the adequate contacts, this introduction would be difficult and even impossible in some markets [START_REF] Ellis | Social Ties and Foreign Market Entry[END_REF]. Particularly to the family firm, a supplementary factor needs to be underlined. This organization would be inclined to privilege high control entry modes via direct investment in order to guarantee the implication of its relations in the business (family, friends of childhood). In fact, weak control entry modes require less control, administration and management and therefore do not allow a strong implication of the social ties. Consequently, the role of social ties proves to be more significant in the case of a penetration through direct investment than in case of export operations, since this last procedure implies a less commitment of resources and requires in particular less activity of information search and internalization. Finally, when the family wishes to involve or "do something" with its local partner, it would choose the co-operative modes such as alliances with this partner.

Implications: specificities of learning and knowledge development within family SME

The characteristics of conservatism, independence orientation and networking strongly influence the processes of organizational learning and knowledge development within family SME. The justification of this specificity is due to the fact that this entity shows:

-First, the overlapping of "family" and "company" spheres: the family sphere realizes a unique contribution because it constitutes a supplementary source of knowledge inbound to the company compared with a firm without family involvement, -Then, the frequency of the exchanges within the organization: the processes of exchange of piece of information and knowledge take place not only in the organizational context but also and especially in the family context. The family meetings constitute, for example, supplementary occasions of exchange and sharing of knowledge.

Two consequences are to be analyzed. In this entity, the activities of learning and development of strategic knowledge are centered on the family encouraging causal ambiguity. The second phenomenon is that within the family, knowledge is preserved and perpetuated through a process of intergenerational transfer.

The family in the heart of the processes of knowledge development

The analysis of the conservatism and independence orientation raises questions about the efficacy of the organizational memory within the family firm. What are the mechanisms of preservation of knowledge within the family firm? This organization runs specific risks because of the singularity of the mechanisms of knowledge management.

The typical paternalistic management of the family firm which implies a centralization of power and decision allows obviously the flexibility of the organization. But, at the same time, it influences the processes of learning and development of knowledge which are henceforth centered on the family sphere. The family holds the monopoly of the acquisition, sharing and transfer of knowledge within the organization. Taking advantage of its rights of decision and control, the family dominates the management of knowledge. Overall, internalization of strategic knowledge would be primarily the fact of the owner-manager and his family. Then, the family firm shows a weak socialization of strategic knowledge out of the family circle. In spite of the contribution they provide to the development of the knowledge base, outsiders are likely to be excluded. The essence of knowledge, i.e. its tacit component, being mainly acquired by the family members, there is a tendency to limit its diffusion. There would be, consequently, a conscious will of the management of not engaging a process of externalization. Firms whose "familiness" [START_REF] Habbershon | A Resource-Based Framework for Assessing the Strategic Advantages of Family Firms[END_REF] is weak would behave differently and tolerate sharing activities of strategic knowledge management with outsiders. This sharing should have a beneficial effect on the construction and development of the organization's knowledge base because of the variety and richness of externals' contributions.

Therefore, because of its founding natural characteristics, the family firm nurture mechanisms which reinforce the causal ambiguity (Neslon and Winter, 1982) by strengthening the voluntary effort to avoid either a too fast imitation or the loss of knowledgebased resources if the individual or the group holding it leave the organization (Arrégle, 1995). The family firm is quite inclined to privilege mechanisms of protection of knowledge such as:

-Strengthening the tacit aspect and avoiding formalizing, -Voluntarily maintaining the complexity.

In short, family firms show an inclination to concentrate the processes of knowledge management around its tacit dimension by encouraging its formation contrarily to the explicit element.

However the weak externalization of knowledge coupled with the avoidance of sharing outside the family causes serious risks. First, an obvious risk of deterioration is present because of the weak importance of the organizational protection mechanisms and the strong reliance on individual memory. Particularly to Chinese family firms, [START_REF] Tsang | Internationalizing the Family Firm: A Case Study of a Chinese family Business[END_REF] observes that they can be classified as "the one-man institution" within [START_REF] Shrivastava | A typology of organizational learning systems[END_REF] typology. The owner is the man "who is knowledgeable about all aspects of the business, (and) is the key broker of organizational knowledge. He acts as a filter and controls the flow of information to and from every important manager" (Shrivastava, 1983, p. 20). In sum, even if the family firm exhibits a weak erosion of knowledge because of the weak rotation of directors, an important risk is inherent to the eventuality of a sudden loss of a key member of the family and the company. The organizational memory of the family firm is fragile. Thus, even if operational knowledge gained from the daily activities and profiting to the operational management team is better protected from extinction, the strategic knowledge held primarily by the owner-manager and the members of his family is endangered. Moreover, we suggest a risk of erosion of knowledge due to the fragmentation caused by successions that do not preserve the unity of the firm. There is indeed a risk of "fragmentation" of the strategic knowledge if the company is shared between the potential successors. This risk would be less pronounced if a prior sharing of knowledge with outside directors had been engaged.

In summary, in order to protect experience and knowledge acquired from its activities, which could be lost with the departure of the person or the team holding it, the organization have to set up mechanisms of sharing and diffusion. The solving of the problems of diffusion and transfer of knowledge can, in the case of the family firm, be founded on a specific process: the intergenerational transfer of knowledge.

Intergenerational transfer of knowledge: means of knowledge preservation

Mechanisms inciting to intergenerational transfer of knowledge must be set up because of the negative impact of conservatism and independence orientation on knowledge and due to the fragility of family firm organizational memory. The process of transfer of knowledge through generations is thus crucial to be able to maintain the competitive advantage of the firm. It is important to operate a distinction between the strategic knowledge on one hand and the operational knowledge, on the other hand. Strategic knowledge is the competence generally held by the management implied in decision-making. Operational knowledge is that used or acquired by employees confronted to daily operational management. In fact, the modes of appropriation of these types of knowledge are different. [START_REF] Ward | How a Family Shapes Business Strategy[END_REF] make a similar distinction between the acquisition of business knowledge and the acquisition of leadership capacities. Initially, the successor has to be able to acquire and use the operational knowledge which encompasses the founding know-how of the company. But the learning of the successor is more importantly about strategic knowledge stemming from the experience of direction acquired by the predecessors. It is a question of passing on not only the content of knowledge founding the advantage of the firm but the way of operating and of running business. Indeed, the transfer concerns a managerial competence of direction, in our case relative in particular to the international operations of the firm.

Competence being a competence in action (Le [START_REF] Boterf | De la Compétence. Essai sur un attracteur étrange[END_REF], the successor has to show competence i.e. that he can act with competence. Not subject to be formalized, the most suitable strategy of transfer of strategic knowledge would be observation that young managers make supplemented by a process of action learning. The predecessor has to delegate to the potential successor increasingly significant missions. Thus, the successor has to learn from his actions, discoveries and interactions and also from his experiences and the observation of his peers [START_REF] Hugron | La PME familiale mondiale : conséquence sur la relève[END_REF]. The learning of the successor is grounded mainly on an intense process of socialization. Indeed, strategic knowledge is shared within the family management and communicated to potential successors. In sum, transmission is less about content of knowledge than a methodology of problem solving.

Intergenerational transfer of knowledge within family firms is nevertheless problematic. [START_REF] Cabrera-Suarez | The Succession Process from a Resourceand Knowledge-Based View of the Family Firm[END_REF] identify four obstacles against knowledge transfer:

-Characteristics of transferred knowledge, its causal ambiguity, -Characteristics of the source (the predecessor) and especially its lack of motivation, -Characteristics of the target (the successor): its absence of motivation, limited absorptive and retention capacity, -Context of the transfer: sterile organizational context or difficult relations between the predecessor and the successor.

Conclusion

Even if conservative behavior can be justified in case of extreme uncertainties or abnormal risks weighing on the economic environment, it is, nevertheless, criticisable. Conservatism establishes an attitude and a thinking hostile to renewal. Yet, the theories of organizational learning stress that the commitment of management team is an essential condition to the trigger and success of internationalization. A strong and committed management is necessary in order to motivate the organization and to help it overcome the difficulties. Since human capital of the family firms shows positive characteristics of strong commitment, cordial, friendly and close ties, and the potential allowing for a deep specific tacit knowledge, we can suppose that this organization can be favored (compared to its counterparts) during organizational learning. A condition is that family SME could draw from its human resources, the necessary commitment to struggle against the forces of conservatism. In order to obtain human resources commitment, it is necessary to involve all levels of direction and management during the reflection and planning of international activities and to sensitize them to the importance of their implication for the success of this orientation. The presence of a strong personality (generally the founder or the owner-manager) who motivates the employees and bring them together to achieve the organizational goals is essential. In particular, the owner-manager should realize the benefits of internationalization, supports and encourages the process. He also could transmit the knowledge accumulated through his personal commitment to other family members [START_REF] Tsang | Internationalizing the Family Firm: A Case Study of a Chinese family Business[END_REF]. Thus, in spite of a rigid organizational structure, the owner-manager can lead his organization towards flexibility and change. More generally, the organization must change posture and adopt a positive attitude and open-mindedness.

In addition, family SME needs to tolerate an attenuation of its independence on the financial and human plans. The policy of conservation of financial independence can constitute a significant barrier to future growth and internationalization because the internal financing can be insufficient. Indeed, financial needs appear during the phases of commercial prospecting, establishment and become more important with the increase in working capital requirement [START_REF] Hirigoyen | Le financement des PME exportatrices en Europe[END_REF]. Internationalization of the family firm thus depends on its tolerance to external financial intervention as that of local investors or specialized venture capitalists [START_REF] Gallo | Internationalization via Strategic Alliances in Family Businesses[END_REF]. The recourse to venture capital financing would avoid, indeed, the increase in risk normally due to increase in debt level. Either, the firm should not avoid turning to banking debt but should benefit from the various formulas of loans designed for exporting firms. Studying family firms committed in international strategic alliances, [START_REF] Gallo | Internationalization via Strategic Alliances in Family Businesses[END_REF] indicate that they become less reticent to the opening of capital as the need for investing resources in order to accelerate internationalization becomes urgent and the experience of management as for the sharing and conservation of power in alliances accumulate. Opening up, the family firm can facilitate its access to capital by the institutionalization of appropriate governance mechanisms. In order to ensure that aspirations of capital suppliers, on the one hand, and those of the family, on the other hand, are taken into account simultaneously for decision-making and pursuit of organizational goals, [START_REF] Davis | Governance and Goal Formation Among Family Businesses : A Resource Dependency Perspective[END_REF] recommend a dual structuring of organizational governance processes. Family SME must, in addition, overcome its human independence and seek outside for these valuable resources. This can be done through a process of "familisation" i.e. incorporation to the dominant family of certain external elements through alliances and marriages. Justified by the quality of the relations established with those people and by their honesty and value in the eyes of the family, these processes are very interesting. Indeed, they indicate a relative broadmindedness and an attenuation of the independence attitude. Also, family SME can open up through its natural tendency to networking which could allow for an intense exposure to international economic environment. Schematically, not only small and medium family firms internalize and develop weak knowledge but they also externalize and share a little knowledge. The risks associated with this knowledge strategy are the possible extinction of valuable knowledge. Therefore, the process of knowledge transfer through generations would be crucial to the family SME in order to be able to maintain its competitive advantage. In addition, if know-how is the core resource underlying this competitive advantage then its "transferability" will determine the period during which its holder will obtain returns [START_REF] Spender | Making Knowledge the Basis of a Dynamic Theory of the Firm[END_REF]. In sum, small and medium family firms have to implement a deliberate strategy of knowledge preservation through, for instance, externalization of articulable tacit knowledge and socialization of non articulable knowledge with external managers [START_REF] Nonaka | A Theory of the Firm's Knowledge-Creation Dynamics[END_REF]. This strategy is not optional but could be vital to ensure the survival of these firms.

Figure 1 :

 1 Figure 1 : Dimensions of the independence orientation