Vladislav A Yastrebov
email: vladislav.yastrebov@mines-paristech.fr

A G Shvarts
email: andrei.shvarts@glasgow.ac.uk

G Anciaux

J Vignollet
email: julien.vignollet@safrangroup.com

J F Molinari

Contact of rough surfaces in presence of interfacial fluid flow

Keywords: Roughness, Contact, Fluid Flow, Permeability, Fluid Solid Contact Coupling, Trapped Fluid

Introduction

Contact and friction interactions play an essential role in many quotidian contexts, including those related to industry (e.g., tire-road and wheel-rail contacts, electric switches, bearings, and brake systems), everyday human activity (e.g., walking, handling, touching, and sitting) and natural phenomena (e.g., earthquakes, landslides, and glacier motion). Regardless of such prevalence, contact-related mechanisms (friction, adhesion, and wear) are still not fully understood and thus are among the most cutting edge research topics in the mechanical community. It is especially true when the problem under consideration include not only continuum solid mechanics, but also fluid mechanics, thermal and electric fields, chemistry, etc [START_REF] Vakis | M˙Modeling and simulation in tribology across scales : An overview[END_REF].

Numerous models of contact-related mechanisms exist at structural scale. They serve to model interfacial normal and tangential stiffness, frictional resistance, material removal on rubbing surfaces (wear), heat transfer between contacting solids, contact electric resistance, adhesion, interfacial fluid flow, microstructural changes in near-contact material layers, fretting life-cycle, debris generation, lubrication, especially in mixed regime, and other mechanisms. Admittedly, all the aforementioned phenomena are strongly related to the surface roughness. The associated models can be incorporated in a macroscopic/structural model via constitutive interfacial equations. These equations can be based either on experimental data, and thus remain purely phenomenological, or can take the microscopic roughness as the starting point. The latter class of models shall have a greater predictive power, and potentially can be used for a large spectrum of applications. However, because of the strong non-linearity of the contact/friction mechanisms and extreme complexity of surface roughness, construction of a reliable analytical micromechanical model presents a serious challenge.

In this work, we make an attempt to summarize recent progress we achieved in understanding of interplay between roughness, mechanical contact and interfacial fluid flow in the simplified context of (i) controlled roughness, (ii) small strain elastic behaviour of material, (iii) absence of relative tangential motion between contacting solids, (iv) isoviscous creeping fluid flow, (v) compressible or incompressible fluid model for trapped fluids. The paper is organized as follows. In Section 2, we briefly present the computational models for solids, fluids and contact as well as methods to solve the related equations. In Section 3, we present recent results on the evolution of the true contact area and the effective fluid-conducting areas. In Section 4, the theoretical results are derived for the permeability of the contact interface. The effect of the trapped fluid is discussed in Section 5. In Section 6, the effect of the strong coupling between solid and fluid equation is briefly discussed.

Computational models

Different approaches can be used to solve the problem of permeability of contact interface at microscopic scale. First of all, we would like to mention that too simplified models such as, for example, geometrical overlap of two rough surfaces in which the underlying elastic behaviour of solids is replaced by Winkler's foundation, do not allow to obtain accurate estimation of clearance (or gap) field in the interface, through which the fluid can flow [START_REF] Wolf B Dapp | Self-affine elastic contacts : percolation and leakage[END_REF]. Therefore, here we will not consider models in which mechanical contact is resolved inaccurately. Before presenting the computational models and schemes, let us assume that we will focus on a simple set-up of normal contact between a rigid flat and a portion of nominally flat rough surface (either with symmetric or periodic boundary conditions prescribed on lateral sides, see Fig. 1).

The simplest method (which can be considered rather accurate for many applications) consists in oneway coupling of solid and fluid equations. The contact problem between two solids with rough surfaces can be solved in absence of fluid, and the resulting gap field g(x, y) can be used to solve Reynolds equation for viscous fluid flow in contact interface [START_REF] Vallet | Sampling effect on contact and transport properties between fractal surfaces[END_REF][START_REF] Sahlin | A mixed lubrication model incorporating measured surface topography. part 1 : theory of flow factors[END_REF][START_REF] Sahlin | A mixed lubrication model incorporating measured surface topography. part 2 : roughness treatment, model validation, and simulation[END_REF][START_REF] Durand | Multiscale approach of contact and watertightness problems[END_REF][START_REF] Wolf B Dapp | Self-affine elastic contacts : percolation and leakage[END_REF][START_REF] Pérez-Ràfols | Modelling of leakage on metalto-metal seals[END_REF]. However, if the fluid pressure is high enough, how for example in case of elasto-hydrodynamic lubrication, or for seals used for highly pressurized fluids, a more accurate approach could be needed which takes into account the bilateral coupling of fluid and solid equations [START_REF] Shvarts | Coupling mechanical frictional contact with interfacial fluid flow at small and large scales[END_REF]. Both one-way and two-way coupling approaches could be implemented using boundary and finite element methods. Note that there is not particular difficulties to use compressible fluid models. The main difficulty, which will be discussed later, is the handling of trapped fluid, interfacial volumes filled with a fluid and surrounded by contact areas. Note that even if for a liquid fluid flow, an incompressible model works rather accurately in a very broad interval of possible loads, an accurate compressibility model of the trapped fluid should be chosen. The initial compressibility (of non-pressurized fluid) of most liquids is smaller than the compressibility of most of solids, however the compressibility of the fluid grows rapidly with the fluid pressure. This effect should be taken into account in the trapped fluid model to enable accurate quantitative and even qualitative results. Finally, it is worth noting that many techniques exist to construct realistic roughness with controllable parameters, for example, filtering white noise with a specially designed low and high frequency cut-offs and appropriate spectral decay [START_REF] Hu | Simulation of 3-D random rough surface by 2-D digital filter and fourier analysis[END_REF].

Evolution of the contact area and of the fluid-conducting area

The true contact area growth under increasing squeezing pressure A(p 0 ) controls many aspects of interfacial physics : friction, wear, adhesion and conductivity [START_REF] Pei | Finite element modeling of elasto-plastic contact between rough surfaces[END_REF][START_REF] Carbone | Asperity contact theories : Do they predict linearity between contact area and load ?[END_REF][START_REF] Vladislav | From infinitesimal to full contact between rough surfaces : evolution of the contact area[END_REF]. Measuring the true contact area is not always a trivial task both in experiments and in numerical simulations [START_REF] Martin H Müser | Meeting the contact-mechanics challenge[END_REF]. In the latter, the inevitable discretization error can be quite significant, especially when the contact area fraction remains small, which is often the case in practical applications. Therefore, to accurately estimate the contact area, we suggest to use an error-compensation technique, suggested in [START_REF] Vladislav | On the accurate computation of the true contact-area in mechanical contact of random rough surfaces[END_REF]. Among other things, this technique enabled us to uncover a subtle dependence of the evolution of the true contact area on the Nayak parameter [START_REF] Nayak | Random process model of rough surfaces[END_REF][START_REF] Vladislav | The role of the roughness spectral breadth in elastic contact of rough surfaces[END_REF]. However, if one is interested in permeability problems, the knowledge of the true contact area A is not sufficient to predict the effective permeability because the remaining area A 0 -A can contain both areas through which fluid can flow A f but also, out-of-contact areas A t of trapped fluid, which do not participate in fluid transmissivity. Therefore, the relevant fluid-conducting area is given by A f (p 0 ) = A 0 -A(p 0 ) -A t (p 0 ). We demonstrate that this area grows quite linearly (contrary to the true contact area) with the applied pressure until a certain threshold pressure, at which large areas of fluid becomes trapped which corresponds to pressures near the percolation point.

Permeability of contact interface : self-consistent model

Knowing the effective fluid-conducting area is still not enough to predict the permeability of the rough contact interface. Using a self-consistent or effective medium homogenization approach [START_REF] Kirkpatrick | Percolation and conduction[END_REF][START_REF] Lorenz | Leak rate of seals : Effective-medium theory and comparison with experiment[END_REF], the effective permeability K can be estimated through the probability density of gap distribution P (g, p 0 ) in the contact interface for a given squeezing pressure p 0 by solving the following equation :

(A 0 -A f ) ∞ 0 g 3 P (g, p 0 ) g 3 + K m 3/2 0 dg = A 0 2 .
The only difference between this equation and the one found in [START_REF] Lorenz | Leak rate of seals : Effective-medium theory and comparison with experiment[END_REF] is that the factor before the integral should contain the total non-conducting area whereas in [START_REF] Lorenz | Leak rate of seals : Effective-medium theory and comparison with experiment[END_REF] the authors used the total non-contact area.

Effect of the trapped fluid

As was already mentioned, the fraction of trapped fluid can be considerable especially near the percolation point. Since the trapped fluid can be pressurized, the external normal load splits between the mechanical contact zones and the areas of trapped fluid, thus reducing the macroscopic frictional resistance of the interface. We recently demonstrated that, apart from this quite evident effect, the trapped fluid can gradually open the trap thus reducing even more the true contact area and the effective frictional resistance [START_REF] Andrei | Trapped fluid in contact interface[END_REF]. The effect of the trapped fluid is even more peculiar when elasto-plastic material behaviour is considered : an interplay between plasticity, non-linear growth of the contact area and non-linear compressibility of the trapped fluid can result in a strongly non-monotonous evolution of the macroscopic friction coefficient with the squeezing pressure. In a more realistic context, the trapped fluid affects the whole pressure-permeability curve [START_REF] Shvarts | Coupling mechanical frictional contact with interfacial fluid flow at small and large scales[END_REF].

Weak and strong coupling

Finally, we demonstrate how the account for the strong coupling between solid, fluid and contact equations in the computational framework is related to the accuracy of predictions of the model. We compare one-way and two-way couplings on contact topographies of increasing complexity : from (1) simple wavy surface with trapped fluid [START_REF] Andrei | Trapped fluid in contact interface[END_REF], to (2) a wavy channel brought in contact [START_REF] Andrei | Fluid flow across a wavy channel brought in contact[END_REF], to (3) a wavy channel with an atoll-type morphology in the trough, and finally to (4) a realistic self-affine roughness [START_REF] Shvarts | Coupling mechanical frictional contact with interfacial fluid flow at small and large scales[END_REF] (see Fig. 2). We show that a simple shift of results obtained within one-way coupling scheme by a mean fluid pressure can provide us with an accurate enough evolution of permeability with squeezing pressure. However, the related contact area evolution, which is critical for many interfacial effects, cannot be easily predicted without strong two-way coupling. Moreover, the strong two-way coupling allows to link the effective permeability with the squeezing pressure, mean fluid pressure and also to reveal a subtle dependence on the fluid pressure gradient [START_REF] Shvarts | Coupling mechanical frictional contact with interfacial fluid flow at small and large scales[END_REF].

Conclusion

We derive a consistent computational framework to handle coupling between solid mechanics and fluid in contact interface, which can either flow in the narrow contact interface and/or be trapped and surrounded by contact zones. Numerous aspects of this problem are discussed and illustrated on model and realistic examples. Among computational aspects, several accurate and approximate analytical solutions are derived and compared with numerical results. A novel phenomenological permeability law for rough contact interfaces is derived.

F 1 -

 1 Set-up : (a) a deformable "rough" solid with periodic or symmetric displacement boundary conditions on lateral sides is brought in contact with a rigid flat (b), and a pressure-driven viscous fluid flows through the contact interface from inlet to outlet with symmetric or periodic fluid-pressure boundary conditions on lateral sides (c).

F 2 -

 2 Example of finite element simulation of a rough contact within a two-way coupling between solid mechanics and fluid flow in the contact interface including the possibility of fluid entrapment. Three instances at different external pressure are shown : on the left the vertical stress component σ zz and current lines (color corresponds to flux) are shown, on the right the corresponding fluid pressure is depicted.


Flora Szkordilisz
email: f.szkordilisz@mut.hu

János Balázs Kocsis

Ryad Bouzouidja

Emőke Kósa

Véronique Beaujouan

Béatrice Béchet

Pierre-Emmanuel Bournet

Adeline Bulot

Patrice Cannavo

Etienne E Chantoiseau

Barnabás Körmöndi

Philippe Bodénan

; Hervé

Thierry Lebeau

Laure Vidal-Beaudet

René Guenon

Marjorie Musy

Germain Adell

How to use nature-based solutions in urban planning systems of Europe?

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

INTRODUCTION

In developed countries, the level of urbanization is still rising and expected to reach 83% in 2030 [United Nations, 2012]. As a result of rapid growth of urban areas and population, the urban planners face several challenges. For example, risks of flooding due to overload of the drainage system, and pollution due to combined sewer overflows and diffuse pollution, consequently increase significantly. Questions about biodiversity promotion and urban heat islands are also emerging as major issues in the construction of sustainable cities [START_REF] Berretta | Moisture content behaviour in extensive green roofs during dry periods: The influence of vegetation and substrate characteristics[END_REF]2014].

European Commission, [2015] highlighted naturebased solutions in order to address the mentioned urban problems related to climatic, demographic and technological changes. The aim is to bring new solutions into urban planning and thus, to address those challenges and to improve the well-being sensation, quality of life of city dwellers.

Nature-based solutions (NBS) are one of the newest concepts for tackling urban challenges. The concept of NBS was meant to reform the methodology of urban planning in EU countries and deliver multiple environmental, social and economic benefits through introducing and implementing a new toolkit based on natural resources. The concept of NBS can be characterized as the use of nature in tackling challenges such as climate change, food security, water resources, or disaster risk management, encompassing a wider definition of how to conserve and use biodiversity in a sustainable manner [START_REF] Balian | Outcomes of the strategic foresight workshop[END_REF]. In urban landscapes, the co-benefits of NBS are being increasingly recognized as a result of increased provisioning and improved availability of urban green spaces. Such benefits include, for example, improved quality of life, mental and physical health, and reinforced cultural identities, supporting a sense of belonging and place [START_REF] Keniger | What are the benefits of interacting with nature?[END_REF][START_REF] Hartig | Nature and health[END_REF]].

NATURE-BASED SOLUTIONS AND URBAN PLANNING

In the Horizon 2020 project, Nature4Cities besides multi-thematic and multi-scalar evaluation of naturebased solutions and their effectiveness in addressing different urban challenges we aim to deliver a platform used by urban planners. As a first step of the research, which is described in this paper, we analyse the possibilities of implementing nature-based solutions in the different planning systems of Europe. First, we give a short overview on similarities and differences between planning systems, and the different kind of plans (master plans, action plans, authorization plans, etc.) Secondly, we describe Nature4Cities concept on NBS-typology, and thirdly we analyse the possibilities of inserting the particular nature-based solutions into the different kind of plans in different scales. ICUC10 -10 th International Conference on Urban Climate, 6-10 August 2018, New York, NY, USA

DEFINITION OF NATURE-BASED SOLUTIONS

In Nature4Cities we took European Commissions definition as a basis, however, some modifications were made to adapt this definition to the urban context and render it more operational. Thus, the definition which we use in the project is the following: "Nature-based solutions are positive responses to social challenges, and can have the potential to simultaneously meet environmental, social and economic objectives. They recognize the importance to develop a systemic approach and at the same time to adapt interventions to the local context. They also integrate the temporal factor to meet the challenge of durability.

They are actions inspired by, supported by or copied from nature. Such solutions bring more, and more diverse, nature and natural features and processes into cities. They are living solutions, and as much as possible they take part in complex and functional ecosystems (Note that GMO, and other solutions that artificially alter nature are excluded.) Nature-based solutions use the features and complex system processes of nature. By using the natural flows of matters and energy, these are low-input solutions. If these solutions are conceived and implemented in a proper way, low-maintenance, cost savings, energy and resource efficiency are expected. NBS also benefit from the malleability of nature (capacity to evolve and to adapt) and are thus more resilient to changes.

They both use and enhance existing solutions to challenges, as well as explore more novel solutions." [START_REF] Cerema | Towards an EU research and innovation policy agenda for naturebased solutions & re-naturing cities[END_REF]

CATEGORIZATION AND SCALES OF NATURE-BASED SOLUTIONS

In Nature4Cities 75 types of NBS were listed, which are classified according to a systemic approach. In this paper, we concentrate only on those NBSs which can demonstrate their role in urban planning projects. These NBSs are the following:

• ensuring continuity of ecological networks The listed NBSs are categorized according to their impact on social urban challenges. These are rather important from urban planning point of view, as some of the NBSs might act similarly in plans or might have similar social effects. Therefor it makes easier to understand their impact mechanism and role in urban planning if we can handle them in categories. Categorization enables us to show the different scenarios of implementation based on scale and urban planning tool.

The concept of nature-based solutions is a rather new concept, and we can state, that the implementation of EU policies depends greatly on the planning system of the particular country. That is, the type of plans, which are usually strictly regulated, and thus, the tools, which can be used in the plans too. Introducing shortly the four existing planning approaches in Europe. This categorization is shown in Table I. City scale should consider the agglomeration of the city, but most of the cases urban planning tools can deal with the territory within the administrative boundaries of the city. [Halbert, 2006, Williams et al, 2016] which usually leads to inconsistency between planning scales and urban challenges.

Neighbourhood scale is defined as a section of a city defined by the distinguishing character of urban fabric or a certain administrative division. Neighbourhood scale seems to have the biggest potential in NBS implementation, however numerous aspects need to be investigated and complex expertise is needed for decision making.

Object scale refers the scale of a building plot: that is a building or an open space with dimensions of some hundred meters with local characteristics. [Barbano et al.,2015].

URBAN PLANNING SYSTEMS OF EUROPE

In Europe during a long history of urban planning and according to the different history, culture and economic and social development of the countries, we can distinguish four different planning traditions according to literature [Thornley and Newmann, 2002; Williams, 2018; CEC 2 , 1997]. Figure 1 shows the connections between them, and the countries, for which they are most characteristic.

Figure 1. The four planning traditions of Europe. [START_REF] Salamin | hatása az európai országok térbeli tervezési rendszereinek transzformációjára (Europeanization of Shaping Geographic Space: The influence of the European Union's spatial planning, strategies, and Cohesion Policy on the transformation of the spatial planning systems of European countries)[END_REF] 2 Commission of the European Communities

The four planning traditions have originated from certain countries, however, during a European integration of planning systems, they might have spread wide and a country's planning system is surely influenced by more than one approach.

• Regional economic planning focuses on the management of economic and social inequalities with development and infrastructure programs. This planning tradition has originated from France, however it influenced numerous countries' urban planning system, such as: Portugal, Ireland, UK, Latvia and Lithuania.

• Land use management "tradition" puts emphasis on the regulation of land-use change with strategic and local plans. This approach focuses on the management of physical space by applying the urban planning tools as regulations. Most characteristic to the planning of the British Isles (UK, Ireland), it has affected Cyprus and Malta (former British protectorates) and other countries too.

• The comprehensive integrated planning approach, which is mainly related to the Dutch tradition, involves the various tools of space-shaping, the coordination of the various actors in the development of spaces. Focusing on the spatial effects of policies and the coordination of actors and sectors, vertical and horizontal coordination is highly important.

• Urbanism is rooted in the action of urban construction, and primarily targets the control of construction itself. The tradition of urbanism conditions urban design, cityscape and construction with zones and regulations. [START_REF] Salamin | hatása az európai országok térbeli tervezési rendszereinek transzformációjára (Europeanization of Shaping Geographic Space: The influence of the European Union's spatial planning, strategies, and Cohesion Policy on the transformation of the spatial planning systems of European countries)[END_REF] After listing the differences between planning systems, here we list some important common features of urban planning and the relevance in implementing NBS.

City or metropolitan scale:

Master planning is a tool widely used around Europe, and is a highly relevant tool for NBS planning too. A good example to demonstrate the importance of master planning in city or metropolitan scale NBSs, is the socalled Finger plan of Copenhagen. [START_REF] Vejre | The Copenhagen finger plan: keeping a green space structure by a simple planning metaphor[END_REF]. The Finger plan was established in 1947 [Cervero, 1998], and aimed mainly to manage a mass of commuters in the area and providing suitable places for industrial and commercial activities. The master plan affects today above 30 municipalities of the metropolitan area of Copenhagen. The importance of the Finger plan in green space network development is, that the plan as designated the areas between the "fingers" as green spaces, preserving them from urban sprawl, and creating well-defined green corridors around the city. The finger plan concept was adapted by Helsinki and Stockholm too. A similar approach is represented in Abercrombie's Greater London Plan (1944) establishing ICUC10 -10 th International Conference on Urban Climate, 6-10 August 2018, New York, NY, USA a green belt around the city for controlling urban expansion. [START_REF] Roosmalen | London 1944: Greater London Plan[END_REF].

Neighbourhood scale:

Neighbourhood planning is an important element of British and Irish planning system, however, it is often used in urban rehabilitation all around Europe too. [START_REF] Bukowski | Problems and barriers in urban rehabilitation policy co-ordination across cities and regions of Europe[END_REF]. Neighbourhood scale interventions are also beneficial for being an appropriate scale for participatory planning. Public engagement can be conducted on several levels, and NBS is usually a highly popular topic [Frantzeskaki and [START_REF] Kabisch | Nature-based solutions to climate change mitigation and adaptation in urban areas: perspectives[END_REF] A good example is two rehabilitation projects in Budapest's 8 th District, Józsefváros, where local residents have been involved in planning and planting greenery in open spaces (Mátyás tér, Magdolna Negyed, Teleki tér). According to literature [START_REF] György | Városi zöld könyv, Kulcs a fenntartható városhoz ; Budapest: ÉTK[END_REF] public security has increased in the area, and economic uptake has been detected after the implementation of the projects.

Object scale:

The implementation of NBS on object scale can be discussed either investigating natural interventions on buildings or on open space projects. Investigating the urban fabric, green open spaces have certainly a potential in mitigating urban heat island effects on microscale [Szkordilisz, 2014]. However, due to the multiple criteria that arise during the planning, it might be difficult to implement NBS making full advantage of its benefits. Visible transparency, public safety and easy management are usually the key considerations when refurbishing an open space. Most important is the implementation of NBSs such as keeping old trees (not only while planning but throughout the construction period too), using soft and natural solutions to keep management needs low: for example: phytoremediation, mulching, and preferring unsealed surfaces to sealed ones. On the other hand, the use of nature-based solutions near buildings also depend on the function, the orientation, solar exposure, and envelope. Implementation of NBS might be of significance on public buildings. However, due to economic factors, investors are highly motivated to implement naturebased solutions in buildings, if economic benefits are foreseen. Numerous studies have shown [Luay et al, 2016], that office buildings with green labelling (EnergyStar, LEED) realize a higher prize (selling or renting) on the real estate market. Therefor, investors are directly interested in investing in the implementation of nature-based solutions, that will enhance the wellbeing of those using the building.

After introducing the scales, we list the most commonly used planning tools to be used in urban planning throughout Europe. Usually, spatial scale and the timeframe of the plan are connected, larger scale plans tend to influence long-term (country or county land use plans), and smaller scale plans (rehabilitation plan, action plan etc.) refer to neighbourhood scale and for short-term interventions. Not only plans, but long-and mid-term development strategies might also influence the implementation of NBS. Also, there are some countries (Ireland, United Kingdom, and Hungary) using so-called design manuals, that also make suggestions on the planting of vegetation around the building itself. [Shay Scanlon, 2009]. Table 2. summarizes the different type planning tools in a non-exhaustive list.

NBS and GOVERNANCE

Governance and implementation of NBS, and similar innovative actions, requires both support of the local public that is expressed through the activities of the attitudes and concepts of the policy-makers, especially of the mayor, and the incentives from higher level of the state administration. Besides the standpoint shared about the positive effects of certain policies and programmes, long-term support and longevity of the initiative require also the positive financial outcome, at least in the mid-term, preferably without subsidies vulnerable to political and personal changes.

Holistic, multidimensional approach is a must in creating and implementing effective strategies and plans successful in the long run. Such methods are mostly in essence incompatible with the workings and logic of local administration, despite the countless opposite personal efforts on all levels of the system. The configuration of the local administrations favours onedimensional approaches strictly limited to one professional field as their structure is based on bodies and agencies separated functionally along the abovementioned lines. Such split is further reinforced by mutually illegible professional jargons underpinning clandestinely the exclusive and indisputable importance of the given discipline and organisational body representing it.

Integrated efforts and strategies thus call for sustained and explicit endorsement of local stakeholders, support of the local political élite, especially the mayor, and supporting stance of upper administrative and political bodies.

Involvement of the locals may offer a firm foundation for such actions, although the practice of public participation may seem laborious, lengthy, hazardous and purportedly unprofessional, particularly to the above mentioned municipal and other expert branches.

Researches show that primarily financial aid programmes and subsidy schemes have often detrimental effects on the long-term commitment of local agents and bodies. As a matter of fact, they seem to foster short-term spending depletion of available resources and lead negligence and resistance in the long run. This is especially the case when either local commitment is lacking, or financial sustainability and maintenance is highly dubious.

SUMMARY

Summing up the research done so far, it seems, that the implementation of NBS is not different of other, upcoming and innovative ideas in urban planning. As showed, both on the side of urban planning and governance the process of implementing NBS needs a complex and multi-scale approach, which is not easy to achieve. However, the concept of NBS can be made attractive to the decision-makers, if economic benefits and wide social acceptance is obviously presented. For this purpose, the Nature4Cities platform will be implemented, to spread the concept among wide public, decision-makers and experts.

Table . 1

 . Classes of NBS based on their impact on urban planning issues th International Conference on Urban Climate, 6-10 August 2018, New York, NY, USAThe scale of the nature-based interventions can be multiple. We identified three scales of NBS interventions taking into consideration the practice of urban planning: city, neighbourhood and object.

	ICUC10 -10
	NBS type	NBS class
	ensuring continuity of
	ecological networks
	limit or prevent
	access to area or
	specific uses planning tools to	Strategic elements
	control territorial
	expansion
	green waterfront
	phytoremediation
	keeping old trees	restoration of green areas /
		urban rehabilitation / and
	erosion control	management techniques
	de-sealed areas
	large green spaces
	greening open
	spaces	"patchwork"-like
	community gardens	interventions, green space
		with intensive use
	botanical gardens
	cemeteries
	street tree lines
	green tram tracks	linear interventions
	swales
	green façade and
	wall	point-like interventions
	green roof

Table 2 .

 2 Common planning tools and their scale of intervention.

	planning tool	scale of intervention
	county / regional land-use-plan
	county / regional development plan
	integrated urban development strategy	regional / city
	urban land-use-plan, local building
	code
	urban rehabilitation plan	city /
	action plan	neighbourhood / object
	feasibility study
	green infrastructure development
	concept	neighbourhood
	planning guides and design manuals
	(UK, IE, HU)
	urban rehabilitation plan; landscape architecture plans	neighbourhood
	national urban planning and building
	requirements;
	local building code;	object
	architectural plans

ACKNOLEDGEMENTS

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 730468.