Patrick Maillé
email: patrick.maille@imt.fr

Bruno Tuffin
email: bruno.tuffin@inria.fr

Neutral and Non-Neutral Countries in a Global Internet: What Does it Imply?

Keywords: Net neutrality, Service differentiation, Game theory, Regulation

Network neutrality is being discussed worldwide, with different countries applying different policies, some imposing it, others acting against regulation or even repealing it as recently in the USA. The goal of this paper is to model and analyze the interactions of users, content providers, and Internet service providers (ISPs) located in countries with different rules.

To do so, we build a simple two-regions game-theoretic model and focus on two scenarios of net neutrality relaxation in one region while it remains enforced in the other one. In a first scenario, from an initial situation where both regions offer the same basic quality, one region allows ISPs to offer fast lanes for a premium while still guaranteeing the basic service; in a second scenario the ISPs in both regions play a game on quality, with only one possible quality in the neutral region, and two in the non-neutral one but with a regulated quality ratio between those. Our numerical experiments lead to very different outcomes, with the first scenario benefiting to all actors (especially the ones in the relaxedneutrality region) and the second one mainly benefiting mostly to ISPs while Content Providers are worse off, suggesting that regulation should be carefully designed.

Introduction

The network neutrality debate has been raging for close to two decades and is still a very sensitive issue worldwide. Basically, network neutrality is "the principle that traffic should be treated equally, without discrimination, restriction or interference, independent of the sender, receiver, type, content, device, service or application". This type of definition was introduced by the Federal Communications Commission, the regulator in the US in 2005, and by the European Union in 2014, among others. It is part of the principles for an open Internet according to which resources available on the Internet should be easily accessible to all entities. The debate has been highlighted in 2005 with Ed Whitacre, CEO of the Internet service provider (ISP) AT&T, complaining that distant content providers (CPs) were using his network without financially participating to its infrastructure maintenance and upgrade, while at the same time the proportion of telecommunications economy coming from advertisement and going to CPs was increasing. The threat to differentiate traffic or even block some services raised a lot of protests. Since, numerous attempts to discriminate traffic have been observed, such as ISP Madison River Communications fined in 2005 for preventing its clients from using VoIP in competition with its own "voice" offer, Comcast blocking in 2007 BitTorrent (P2P) traffic, or the recent exclusion of some traffic from data caps in wireless subscription offers (the so-called zero rating). For more on Net neutrality and its history, the reader is advised to look at [5, 7-9, 11, 13, 14] and references therein.

An important issue barely addressed in the literature is that while neutrality principles are imposed in many countries, it is not the case everywhere. As of March 2019, we can define two, and even three sets of countries regarding net neutrality3 :

-Countries having passed laws to protect neutrality; this includes all European Union, Canada, most of South America, Japan, India, etc. Remark though that rules are more or less strict depending on the country; for example some authorize sponsored data (that is, the possibility for content providers to pay for their traffic and exclude it from the users data cap) while other don't. -Countries against neutrality as recently the USA, or other big countries such as Russia, China, etc. Claimed reasons are not always the same: economic efficiency in the USA, control of content/traffic by deep packet inspection in China, or congestion control in Russia. -Countries still in the process of deciding, such as Australia or Uruguay.

As a consequence, in a global Internet, some ISPs are allowed to differentiate service for their users but also of traffic of CPs originated or going through their country. This difference of rules could end up with differentiated services for users located in a foreign and neutral country, even if neutrality is imposed and applied there. This issue is particularly exacerbated by the recent decision, in 2017, of the authorities in the USA to repeal neutrality. The USA being the origin or intermediate of an important part of worldwide traffic, it seems to us that studying the relations between countries applying different neutrality policies is becoming particularly important.

Our goal is therefore to investigate what it implies on all actors (ISPs, CPs, users) to have both neutral and non-neutral countries. To start, we will limit ourselves in this paper to two interacting countries. The actors we consider in each country are CPs, potentially deciding between classes of service for their traffic, ISPs deciding connection prices for given qualities of service (QoS) offered to CPs, and users with demand level depending on the QoS they experience. The interactions between countries come from users requesting traffic to CPs in their own and also in foreign countries, and from traffic having to go through ISPs in the two countries, potentially applying different neutrality policies. Noncooperative game theory [START_REF] Fudenberg | Game Theory[END_REF][START_REF] Osborne | A Course in Game theory[END_REF] is used to analyse the interactions of selfish actors. The question we would like to answer is: Is there a "winner" with such a heterogeneous situation? We wish to compare the output with the situation of a fully neutral Internet.

The literature on modeling and analysis of network neutrality through game theory has been extensive (see among others [START_REF] Altman | Network non-neutrality debate: An economic analysis[END_REF][START_REF] Coucheney | Impact of Reputation-Sensitive Users and Competition Between ISPs on the Net Neutrality Debate[END_REF][START_REF] Coucheney | Network neutrality debate and ISP interrelations: Traffic exchange, revenue sharing, and disconnection threat[END_REF][START_REF] Ma | On cooperative settlement between content, transit, and eyeball internet service providers[END_REF][START_REF] Maillé | Telecommunication Network Economics: From Theory to Applications[END_REF][START_REF] Njoroge | Investment in two sided markets and the net neutrality debate[END_REF] and references therein), trying to answer various questions, but to our knowledge no work has been dealing with the impact of interactions between countries applying different rules. Again, given the current tendency of countries to evolve in different political directions, this is becoming an issue of primary interest.

The results provided in this paper highlight how the specifics of net neutrality regulation relaxation can affect all actors, including those in the region where neutrality remains enforced. Our numerical results show in particular that if the non-neutral ISP still has to offer the same quality as the neutral ISP (in addition to an improved quality), then all actors are likely to benefit from the relaxation, while only the non-neutral ISP would benefit if it is given more freedom (even its hosted CPs would prefer the all-neutral situation).

The remainder of the paper is organized as follows. Section 2 introduces our two-zones, several-CP model with the available strategies and utility functions for all actors. We then investigate in Section 3 the case when the non-neutral ISP can only offer a high-quality service in addition to the basic one (the one in the neutral zone). In Section 4 we analyze numerically, on the same instance, what happens when the regulator imposes a given ratio between the low-quality and high-quality services offered by the non-neutral ISP, while the neutral ISP fixed its quality to maximize its revenue. We provide conclusions and suggest directions for future work in Section 5.

Model

Topology and actors

The topology we study in this paper is described in Figure 1. We consider two geographic areas, with a single ISP and several CPs in each one; the set of CPs in the neutral (resp., non-neutral) area is denoted by L N (resp., L D ). We assume a peering relationship between the two ISPs. We will consider that net neutrality is enforced in one area, while neutrality constraints will be relaxed in the other one. The neutral area may correspond to the European Union and the non-neutral one to the United States, after net neutrality regulations have been repealed.

Service qualities and prices

Let q N be the performance level offered by the neutral ISP, and assume that the non-neutral ISP can offer two different quality levels, namely q L and q H (with q L > q H ). We assume q N , q L , q H ∈ [0, 1]. Without loss of generality, the higher the value of q, the better the performance. The per-unit-of-volume prices (paid by CPs to their host ISP) are p N (in the neutral area), and p L and p H for performance levels q L and q H , respectively, in the non-neutral area.

Prices will be assumed fixed, imposed by the regulator(s) or decided through competition: we only focus on quality levels as decision variables for ISPs.

CP demands and utilities

CPs also have a per-unit-of-volume gain (from advertisement) a for CP . Each CP has a volume demand coming from its own area, plus another one coming from the other area, both depending on the offered performance q (defined just after). Let D j i (q) be the demand of content of CP j from customers in area i. We will for example later consider the standard linear expressions D j i (q) = β j i + α j i q. Users in area i and looking at CP j located in that same area just need to use the local ISP. Thus q = q i , the performance at ISP i chosen (if a choice is available) by that CP. On the other hand, when accessing the CP j from the other area, traffic goes through both ISPs, and overall performance is assumed to be the product of the two ISP qualities q = q N • q D , so that a null quality at a network leads to a null quality along the path, and a perfect quality at a node (that is q N = 1 or q D = 1) reduces the overall quality to the quality of the other node along the path.

The utility of CP in the non-neutral area is the difference between its advertising revenue and payments to its ISP, both of which are proportional to its total demand:

in non-neutral area ⇒ U C = (a -p k ) D D (q k ) + D N (q k q N ) ,
where k ∈ {L, H} is the performance level chosen by the CP.

Similarly, the utility of a CP in the neutral area is given by in neutral area ⇒

U C = (a -p N )D N (q N ) + (a -(p N + p k -p L ))D D (q N q k ),
with decision k ∈ {L, H} representing the quality that the CP has selected for its flows reaching the non-neutral zone. Note that we assume that if the CP selects the high quality, it then has to pay an extra p H -p L per demand unit to the non-neutral ISP.

ISP utilities

The revenues of ISPs are made of the gain from the volume of data flowing through it, minus the cost for maintaining a network with the given performance level. We therefore get, for the ISP in the neutral area,

U I N = p N ∈LN D N (q N ) + D D (q N q k ) -f N ,
and for the ISP in the non-neutral area we obtain

U I U = ∈LN (p k -p L )D D (q N q k ) + ∈LD p k D D (q k ) + D N (q k q N ) -f D ,
where f N and f D are the cost functions. We assume that the cost borne by an ISP is made of the demand level at the quality times the (unit) cost c i (q i ) (i ∈ {N, H, L}) to provide this level:

fN =   ∈L N (D N (qN ) + D D (qN q k )) + ∈L D D N (q k qN )   cN (qN ) fD =   ∈L D :k =L [D D (qL) + D N (qLqN )] + ∈L N :k =L D D (qN qL)   cD(qL) +   ∈L D :k =H [D D (qH ) + D N (qH qN )] + ∈L N :k =L D D (qN qH )   cD(qH ).
Remark that total demand through a network is composed of the total demand of subscribers to this network, but also of the demand of users of the other network to CPs in this local network. The cost functions c N and c D will be assumed increasing convex, with value 0 at 0 and +∞ at 1. The typical example we will use is c N (q) = c D (q) = α q 1-q with some conversion rate α.

Analysis of the interactions

Each actor takes its own decision, but not at the same time scale. We end up with a Stackelberg game, where:

1. ISPs play a game on performance levels, the one in the neutral area choosing q N , the one in the differentiated area choosing q L and q H (prices being fixed, as described previously);

2. The CPs decide the class of service in the differentiated zone; 3. Demand is computed depending on those strategies.

The game is played by backward induction, i.e., each decision maker is assumed to be able to anticipate the outcome of the later stages when selecting an action.

Different ways of relaxing neutrality

We take as a reference basis the situation where both areas are neutral, and investigate what happens when one region allows some non-neutral behavior from its ISP. To avoid extremely unfair behaviors, we assume that there remains some (relaxed) regulation regarding the non-neutral ISP's actions. For example, we may assume that the ISP may only offer an improved service in addition to that of the reference situation (our first scenario), or that the regulator imposes a fixed quality difference between the high-and low-quality services. Of course, other rules can be imagined, but we think those two are sufficiently simple and realistic to be worth considering.

3 A first scenario: opening to non-neutrality in a zone from an all-neutral situation

In this section, we investigate some possible outcomes when, from a situation where both zones are neutral and provide the same quality q N , the possibility of creating fast-lanes is opened in one zone while the minimum quality should remain q N . This could for example correspond to the situation in the United States, where previous neutrality recommendations have been repealed. With our previous notations, this corresponds to q N being fixed, and the new decision variable being q H . The other parameters are also assumed fixed, with values given below.

p L p H p N α 0.5 0.6 0.5 0.02

Those values have been chosen quite arbitrarily, but so that the players' strategies have an impact. We nevertheless think they can be realistic. The sets of CPs are

L N = {1 N , 2 N , 3 N } and L D = {1 D , 2 D , 3 D }.
We consider linear demand functions for CPs, given in Table 1. In particular, we are considering pairs of CPs, i.e., CPs that have the same demand functions in both regions and only differ by being attached to the neutral or the non-neutral ISP. This will help analyze whether a given CP prefers being hosted by a neutral or a non-neutral ISP. We also consider three kinds of CPs, with one kind (CPs 1 N and 1 D ) equally of interest in both areas, and each of the two other types mainly of interest for users in one area: CPs 2 N and 2 D rather target users in the non-neutral area, while CPs 3 N and 3 D produce content that interests mostly users in the neutral area. We display in Figure 2 the utilities of all CPs when q H varies, with q N = q L fixed. We first remark that, as expected, when q H = q N each CP is better off being hosted in the region where most of its demand lies:

being equally attractive in both regions, CPs 1 N and 1 D get the same utility, suggesting that a "virtual CP1" considering where to locate its service would be indifferent; similarly, a "virtual CP2" (resp., CP3) asking the same question would compare the utility of our CPs 2 N and 2 D (resp., CPs 3 N and 3 D ) and prefer to be in the situation of CP 2 D (resp., 3 N ). This was to be expected, since CPs will seek to minimize the multiplicative impact of qualities on the demand from the alien area.

As q H increases, for our parameter values each CP opts for the improved quality after a certain point (indicated in the figure). Note that the values for this point conform to the intuition: a CP will switch sooner to high-quality if the impact on its demand is larger, i.e., if its target market is in the non-neutral zone and if the CP is itself hosted in the non-neutral zone. For the same reason, the improved quality q H favors more the CPs located in the non-neutral area than their neutral-area-located counterparts, due to the multiplicative term in the demand from the area remote to the CP. When q H becomes high, all CPsincluding the one mostly targeting users in the neutral area, our "virtual CP3" -prefer being hosted in the non-neutral area than the neutral one.

The net revenues (utilities) of both ISPs are also plotted in Figure 3, illustrating how the non-neutral ISP could choose its high-quality level q H . We notice some discontinuities, corresponding to CPs switching from low-quality q L to high-quality q H . Those switches first have no noticeable impact on the neutral ISP, but then a positive impact since demand increases with q H ; however we do not consider here what would happen if CPs decide to switch regions (as we pointed out above, the non-neutral ISP becomes more attractive to CPs as q H increases).

Finally, in Figures 4 to 6 we vary the common value of q H and q L , and consider that the non-neutral ISP selects the quality q H maximizing its net revenue: that best-response quality q H is plotted in Figure 4, while Figures 5 and6 show the utilities of the actors. As could be expected, when the "lowquality" levels q N = q L is high enough, a high-quality level does not make a significant enough difference, and is therefore not implemented by the nonneutral ISP. With our parameter values, this happens when q N exceeds 0.71. Note also that before that point, the optimal q L is not monotone in q N : it first slowly decreases for low values of q N , but for q N high enough there seems to be a need to maintain q H a certain level above q N to keep attracting CPs, i.e., justifying the price difference, as illustrated in Figure 3 when q N = 0.65.

The impact on each individual CP is shown in Figure 5: when the neutral (basic) quality is low, all CPs prefer being hosted by the non-neutral ISP since they can benefit from its high-quality level and the corresponding demands. However, when that basic quality increases, the gain from the high-level quality q H is less significant, and after some threshold (around 0.35 for our example) the CP mainly targeting users in the neutral zone prefers to be hosted in that zone. The CP targeting the non-neutral area always prefers being hosted by the non-neutral ISP, while the CP equally demanded in both regions prefers the nonneutral one until the non-neutral ISP non longer offers service differentiation. We also display in Figure 6 the revenues of both ISPs, and the cumulative revenues of the CPs in each zone. This allows to see what an advantage it is for an ISP to be allowed to offer an improved service; we also see the two regimes (when it is beneficial for the non-neutral ISP to offer q H > q N , and when it is not).

Finally, in Figures 7 and8 we compare the all-neutral situation (when the same quality q N is offered in both areas) to the partially neutral one studied here, where a high-quality q H can be offered in the non-neutral region. We observe that for our parameters, relaxing the neutrality constraint benefits to all actors, except (for a small range of values of q N ) the neutral ISP. All CPs benefit from that relaxation, in particular those hosted by the non-neutral ISP. Note however, again, that we did not consider CP mobility in our model (CPs that would switch ISPs). 4 A second scenario: quality game between ISPs, with a fixed q H /q L ratio in the non-neutral region

We now consider a different scenario, where both ISPs play a non-cooperative game on their qualities-the neutral ISP chooses q N and the non-neutral ISP chooses q L and q H -but a fixed ratio between q H and q L is imposed to the nonneutral ISP, to avoid excessive differences between basic and improved services.

For the numerical investigations, we consider the same CPs with their specificities (location and demand functions) as in the previous scenario. They are given in Table 1.

When the quality q N is fixed and the non-neutral ISP varies q H (and q L to maintain the quality ratio), the utilities of the CPs are plotted in Figure 9. We observe the same trend as with the previous scenario: the CPs hosted in the non-neutral region prefer the "higher quality" q H over q L sooner (i.e., for smaller values of q H ) than their counterparts hosted in the neutral region. Also, CPs whose main demand lies in the non-neutral region switch sooner to q H . Another thing worth noting is that for all CPs, the switching point is below the quality value q N in the neutral network: here even if q H cannot be said to be high quality, CPs still choose it to avoid the worse quality q L . The net revenues (utilities) of both ISPs are also plotted in Figure 10, illustrating how the non-neutral ISP could choose its high-quality level q H . For our 10. ISP revenues versus qH , for qN = 0.5 and the ratio qH /qL fixed to 2.This is just some fill-in text... This is just some fill-in text... numerical values, the non-neutral ISP should choose a high quality around 0.8, and therefore a basic quality 0.4.

However, in this scenario we do not consider q N fixed but rather determined through a non-cooperative game played between ISPs. To analyze that game, we plot the ISP best-responses (q H versus q N , since q L is directly determined by q H ) in Figure 11, which exhibits continuous best-response that intersect at only one point, a (stable) Nash equilibrium. Note that the best-response q H is above q N , and seems to equal q N when q N is large enough. Here at the equilibrium we have q H > q N .

We then vary in Figure 12 the regulated ratio q H /q L , and plot the equilibrium values of the qualities. The resulting revenues of ISPs and CPs are displayed in Figures 13 and14. The figures highlight two regimes: when the ratio q H /q L is low, the non-neutral ISP cannot a significantly higher quality q H to justify the price difference, and all CPs prefer the basic quality q L . The results therefore do not depend on the specific value of the regulated ratio, provided it is low enough. Note that the equilibrium quality q L , the one all CPs choose, is slightly below the quality of the neutral ISP, even though their price is the same. That regime is actually equivalent to the all-neutral equilibrium (when the ratio is 1, i.e., no differentiation is allowed); we have the same qualities (except q H , that is not chosen by any CP) and the same utilities for stakeholders. Therefore, such a limited relaxation of neutrality constraints has no impact. -When the regulated ratio q H /q L is large enough, the price difference is justified by the quality difference, hence all CPs select that high-quality. Again, as a result the equilibrium qualities do not depend on the regulated ratio in that regime. Note that in this regime, the chosen quality in the non-neutral zone q H is strictly above the one in the neutral zone. It is also worth noting that both ISPs-even the neutral one-prefer this regime over the all-neutral situation, while it is the opposite for CPs: all of them were better off in the all-neutral setting than in this relaxed scenario, the most affected being the CPs hosted in the non-neutral zone.

Between those two regimes, there is a small range of values for the regulated ratio, where some CPs would select q L and others q H . The impacts on the actors in that limited range are less clear.

Conclusions

Changing the net neutrality rules in a part of the Internet may affect actors in other parts; in this paper we have focused on a simple scenario with two domains having different regulations, and have investigated the resulting decisions from ISPs (in terms of offered qualities) and the consequences on content providers. The specifics of the new rules can lead to very different outcomes. With the same parameter values, our numerical analysis has for example shown that, when a non-neutral ISP can offer two qualities q H and q L and a neutral ISP only one quality q N :

if we impose q L = q N , i.e., non-neutrality is only allowed to offer improved service, then all stakeholders-in particular the non-neutral ISP and its hosted CPs, but also the other ones to a lesser extent-would prefer a relaxation of neutrality rules; if a given ratio q H /q L is imposed, then either nothing is changed with respect to the neutral situation, or all CPs are worse off.

Those results suggest that regulatory decisions about relaxing net neutrality rules should be made with great care, taking into account the whole ecosystem that is affected.

The setting described in this paper opens several perspectives for future work. A first direction would be to develop the analytical study of the model proposed here rather than investigate numerical examples. Also, one can imagine other versions of regulation to constrain the non-neutral ISP in other ways, with the objective to favor user welfare, CP innovation, or fairness among users or among CPs.

Fig. 1 .

 1 Fig. 1. Topology

Fig. 2 .Fig. 3 .

 23 Fig.2. CP utilities versus qH , for qL = qN = 0.5. The situation when qH = 0.5 corresponds to the all-neutral case. The marks highlight the values after which a CP selects qH rather than qL.

Fig. 4 .Fig. 5 .

 45 Fig.4. Best-response qH (qN ) when qL = qN (no value is shown when offering a high-quality service is not beneficial, i.e., when the non-neutral ISP prefers offering only qN ).

Fig. 6 .

 6 Fig. 6. ISP and cumulative CP utilities (revenues) versus qN , with best-response qH .

Fig. 7 .Fig. 8 .

 78 Fig. 7. CP utilities (revenues) differences when switching from an allneutral situation to a non-neutral ISP optimizing qH , versus qN = qL.

Fig. 9 .

 9 Fig. 9. CP utilities versus qH , for qN = 0.5 and the ratio qH /qL fixed to 2. The marks show after which value of qH the CPs prefer qH over qL.

Fig.

  Fig. ISP best-responses when the ratio qH /qL is fixed to 2.

Fig. 12 .

 12 Fig. 12. Equilibrium qualities when the ratio qH /qL varies.

Fig. 13 .

 13 Fig.[START_REF] Schulzrinne | Network neutrality is about money, not packets[END_REF]. ISP net revenues at equilibrium when the ratio qH /qL varies.

Fig. 14 .

 14 Fig. 14. CP net revenues at equilibrium when the ratio qH /qL varies.

Table 1 .

 1 CP demand functions and advertisement revenue factors.

	CP	CP location CP adv.	Demand	Demand in non-
	index	rev. a	in	neutral	neutral region
			region
	1N	Neutral ISP 1	0.1+1.0q	0.1+1q
	2N	Neutral ISP 1	0.05+0.5q	0.2+2q
	3N	Neutral ISP 1	0.1+1.0q	0.036+0.36q
	1D	Non-Neutral ISP 1	0.1+1.0q	0.1+1q
	2D	Non-Neutral ISP 1	0.05+0.5q	0.2+2q
	3D	Non-Neutral ISP 1	0.1+1.0q	0.036+0.36q

See https://en.wikipedia.org/wiki/Net_neutrality_by_country for an exhaustive list or https://www.reddit.com/r/MapPorn/comments/7k9wus/status_of_ net_neutrality_around_the_world2060x1400/ for an instructive map


Beatriz Palacios-Munoz

Bruno Peuportier
email: bruno.peuportier@mines-paristech.fr

Luis Gracia-Villa

Belinda López-Mesa
email: belinda@unizar.es

Sustainability assessment of refurbishment vs. new constructions by means of LCA and durability-based estimations of buildings lifespans: a new approach

Keywords: Life Cycle Assessment, lifespan, reinforced concrete, energy consumption, refurbishment, new construction

A common practice in Life Cycle Assessment (LCA) of buildings is to consider a default value for their lifespan. This paper addresses the importance of estimating the lifespan of each evaluated building when refurbishment and new construction are compared, using a case study. The lifespans of the refurbished and the new buildings are estimated by applying degradation models of reinforced concrete structures. A simplified economic analysis is also performed. Two thermal performance levels are evaluated: standard and passive, in both alternatives, the refurbished and the new building. Results show that a new building can have a lifespan more than six times longer than a refurbished one. Passive refurbishment appears to be the best choice from an environmental point of view. Even if a new passive building obtains slightly better results, these can only be ensured if it is in use for a long period, in our case 210 years. This is not easy to guarantee in real practice, according to usual trends. The new passive building results to be the most cost-effective, but the same constraints regarding guaranteeing a long lifespan are applicable. The results reveal a strong dependence of LCA results on the lifespan. Its value can alter the order of preference of the solutions when comparing alternatives. There is a high potential of environmental improvement of buildings behavior by changing current practices and extending buildings' lifespan up to their physical limit.

Introduction

One of the European Union's (EU) fundamental objectives is sustainable development [1]. The contribution of buildings in environmental impacts is high. On the one hand, they account for nearly 40% of energy consumption in European Union. This is why buildings are central to the EU's energy efficiency policy [2]. On the other hand, they consume a large number of natural resources (materials, water, etc.) and represent an important source of harmful emissions to the environment. Life Cycle Assessment (LCA) provides the best framework for assessing the potential environmental impacts of products, according to the European Commission [1]. In this document, the need for more consistent data and for consensus on LCA methodologies is highlighted.

One question recently posed in the field of buildings LCA is whether or not it is more sustainable to refurbish than to rebuild [START_REF] Palacios-Munoz | Simplified structural design and LCA of reinforced concrete beams strengthening techniques[END_REF]. Most of the literature on LCA focuses on new construction [START_REF] Zabalza Bribián | Life cycle assessment in buildings: State-ofthe-art and simplified LCA methodology as a complement for building certification[END_REF][START_REF] Zabalza Bribián | Methodological aspects and design implications to achieve life cycle low emission buildings. A case study: LCA of a new university building[END_REF][START_REF] Ortiz-Rodríguez | Life cycle assessment of two dwellings: One in Spain, a developed country, and one in Colombia, a country under development[END_REF][START_REF] Cuéllar-Franca | Environmental impacts of the UK residential sector: Life cycle assessment of houses[END_REF][START_REF] Nemry | Options to reduce the environmental impacts of residential buildings in the European Union-Potential and costs[END_REF], whereas refurbishment is dealt with at a lower extent [START_REF] Vilches | Life cycle assessment (LCA) of building refurbishment: A literature review[END_REF][START_REF] Famuyibo | Achieving a holistic view of the life cycle performance of existing dwellings[END_REF][START_REF] Mohammadpourkarbasi | Eco-Retrofitting Very Old Dwellings : Current and Future Energy and Carbon Performance for Two Uk Cities[END_REF][START_REF] Peuportier | Assessment and design of a renovation project using life cycle analysis and Green Building Tool[END_REF]. The comparison between the refurbishment of an existing building versus its demolition and new construction is a matter more recently studied [START_REF] Assefa | To demolish or not to demolish: Life cycle consideration of repurposing buildings[END_REF][START_REF] Ding | Demolish or refurbish-Environmental benefits of housing conservation[END_REF][START_REF] Alba-Rodríguez | Building rehabilitation versus demolition and new construction: Economic and environmental assessment[END_REF][START_REF] Schwartz | The life cycle carbon footprint of refurbished and new buildings -A systematic review of case studies[END_REF].

The results of such a comparison depend on the building construction stage but also on the level of performance achieved after the refurbishment and the new construction, as well as on the quality and life span of the building elements.

The studies found in the literature often address the influence of the construction stage and the performance of the buildings, but that of the lifespan is seldom studied.

Lifespan is a major factor in the LCA [START_REF] Pan | Rethinking system boundaries of the life cycle carbon emissions of buildings[END_REF] and the results are strongly dependent on it [START_REF] Islam | Life cycle assessment and life cycle cost implication of residential buildings -A review[END_REF]. However, there is no consensus on the lifespan of buildings [START_REF] Cuéllar-Franca | Environmental impacts of the UK residential sector: Life cycle assessment of houses[END_REF] and different values are used by the authors, e.g. 40 years [START_REF] Nemry | Options to reduce the environmental impacts of residential buildings in the European Union-Potential and costs[END_REF], 50 years [START_REF] Adalberth | Life-Cycle Assessment of Four Multi-Family Buildings[END_REF], 60 years [START_REF] Frenette | Using life cycle assessment to derive an environmental index for light-frame wood wall assemblies[END_REF] or 100 years [START_REF] Iyer-Raniga | Evaluation of whole life cycle assessment for heritage buildings in Australia[END_REF]. The most commonly used value is 50 years, e.g. [START_REF] Zabalza Bribián | Life cycle assessment in buildings: State-ofthe-art and simplified LCA methodology as a complement for building certification[END_REF][START_REF] Ortiz | Sustainability based on LCM of residential dwellings: A case study in Catalonia, Spain[END_REF][START_REF] Adalberth | Energy use during the life cycle of single-unit dwellings: Examples[END_REF]. But data on real building stocks show higher values [START_REF] Johnstone | Energy and mass flows of housing: A model and example[END_REF][START_REF] Bergsdal | Dynamic material flow analysis for Norway's dwelling stock[END_REF] with possibly decreasing values [START_REF] Aksözen | Reconstitution of the dynamics of an urban building stock[END_REF]. Increasing the life span of buildings may constitute one way to reduce their environmental impacts.

When comparing refurbishment (R) and demolition plus new building (D&N), the same lifespan is usually considered for both the refurbished and the new building, and a methodology to determine this value is often not considered, but a default value is chosen instead.

To properly determine the lifespan is especially important when comparing R and D&N because the construction stage impacts play a major role. The main advantage of R compared to D&N is that R allows to avoid most construction stage impacts by means of using already existing elements. As a counterpart, the difference in the durability between the new and the refurbished building must be taken into account, to make a fair comparison. This second issue is often unaddressed in the literature. In this paper we claim the importance of this issue in the analysis and the results.

A building is made of different elements such as walls, ceilings, windows, etc. Those elements have different lifespan values. When a LCA of a whole building is done, a lifespan value for the complete building should be introduced. The general accepted criterion is to take the value of the structure lifespan as the one for the complete building [START_REF] Haapio | Service Life of a Building in Environmental Assessment of Buildings[END_REF] as all the other elements depend on its stability.

To evaluate the structure lifespan, and therefore that of the building, the methodology proposed by [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF] for reinforced concrete (RC) structures is applied here. This methodology is based on the degradation models of this type of structures.

A building structure is exposed to multiple external actions often classified as physical, mechanical and chemical ones [START_REF] Carrió | Durability vs Vulnerability[END_REF]. Environmental factors can cause several degradation phenomena in the reinforced concrete (corrosion, alkali-aggregate reaction, erosion, leaching, chemical attack, etc.), and they can occur simultaneously. The degree of knowledge about the different phenomena is diverse. According to Budelmann [START_REF] Budelmann | Durability related life-cycle assessment of concrete structures : Mechanisms , models , implementation[END_REF], the main concrete damage mechanisms in above ground RC structures are: (i) corrosion (induced by chloride or CO 2 ) and (ii) alkali aggregate reaction (AAR). In this paper, just the corrosion induced by CO 2 is considered among the wide amount of degradation phenomena.

Reinforcement corrosion is a major cause for degradation of existing RC structures [START_REF] Ta | A new meta-model to calculate carbonation front depth within concrete structures[END_REF]. It leads to several damage types that influence the structure physical lifespan, among others, the reduction of rebar section, the bonding loss between steel and concrete and the cracking of concrete cover due to the increase in volume of the oxides with respect to the original volume of the parent steel [START_REF] Pedrosa | Corrosion induced cracking: Effect of different corrosion rates on crack width evolution[END_REF]. The corrosion phenomena is considered as a two-stage process: (i) corrosion initiation stage; and (ii) corrosion propagation stage [START_REF] Tuutti | Corrosion of steel in concrete[END_REF].

The carbonation of cementitious materials is driven by carbon dioxide (CO 2 ) in the air. The depth of the carbonated cement concrete front increases with time. When it reaches the reinforced layer, corrosion is likely to occur because steel bars are not passivated any more [START_REF] Ta | A new meta-model to calculate carbonation front depth within concrete structures[END_REF]. The time when corrosion is likely to start is called initiation time, t i.. This t i depends on a wide range of parameters (humidity, temperature, concrete cover, porosity, etc.). The combination of concrete quality and concrete cover thickness is apparently the most important parameter that controls the rate of carbonation ingress [START_REF] Tang | Recent durability studies on concrete structure[END_REF].

The objective of this paper is to evaluate the influence of lifespan in the comparative LCAs of a complete building considering R and D&N scenarios. To address this question, both alternatives are compared in a case study considering two performance levels (standard and passive).

Material and methods

In this paper, a comparison between R and D&N is performed in a case study considering its estimated value of lifespan and two performance levels. One is the standard performance corresponding to the coming Spanish regulation [34] and the other corresponds to a very low energy consumption performance. In the case of the standard performance, the project of the future Spanish regulation is taken as a reference as it sets the requirements of a nearly zero energy consumption building. We name this level as standard (S). In the very low energy consumption case, the Passive House standard [START_REF]Passive House Institute, Criteria for the Passive House, EnerPHit and PHI Low Energy Building Standard[END_REF] limit for heating and cooling demand is used, i.e. less than 15 kWh/m². We name this level as passive (P). The lifespans of the refurbished and the new buildings are estimated adapting the methodology proposed by [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF] for reinforced concrete structures. Specifically, the following steps are taken.

(i) First of all, the case study is defined, including the selection of the existing building, the refurbishment operation and the new construction characteristics (section 2.1). The selected refurbishment operations are techniques currently applied in residential buildings in Spain. The difference between the two refurbishment options is just the insulation thickness and the windows to obtain different performance levels. The rest of the needed materials and operations are similar to avoid disturbances in the results comparison.

In the case of the new building, the same volume, living area and architectural configuration as the original ones are considered. Current building solutions and techniques in Spain are considered to define the building characteristics. The difference between the solution with standard behaviour and passive one is the insulation thickness and the windows characteristics.

(ii) Thermal behaviour is analysed to evaluate the use stage impacts of every solution. Thermal dynamic simulations using COMFIE Software [START_REF] Peuportier | Simulation tool with its expert interface for the thermal design of multizone buildings[END_REF] are carried out to obtain the heating and cooling demand of the original building, the two refurbishment alternatives and the two new building alternatives. The operational conditions defined in the Spanish regulation [34] are considered to calculate thermal loads: internal temperature in summer and winter, ventilation, electricity and equipment loads, etc.

To obtain the consumption, systems are included in a simplified way by considering the efficiency of the reference systems provided in the regulation. The same systems are considered for the refurbished and the new building and both in the standard and passive performance. This decision is taken in order not to disturb results because of systems, as every system could be implemented in all the solutions.

(iii) The lifespan of the existing building (and therefore, the refurbished one) and of the new building are estimated (section 2.2).

(iv) LCAs of the different options are done taking into account the predicted lifespan (section 2.3).

(v) Economic estimation are undertaken, and solutions are evaluated in terms of cost-effectiveness (section 2.4).

2.1

Case study

Original building

The case study consists of a residential block built in 1956 in Zaragoza (Spain). The building has eight floors and two dwellings per floor, even in the ground level. The heated and cooled surface is 1257.44 m².

The structure is made of reinforced concrete. The slabs also include ceramic elements to lighten them.

The external walls consist of two layers of brick without air chamber between them and a ceramic tile cladding on one of the façades and mortar plaster on the rest of them, with no insulation layer. The building has a tile roof without thermal insulation and the windows are of wood frame with single glazing.

The yearly heating and cooling demand of the original building are 74 kW•h/m² and 26 kW•h/m², respectively.

The structure consists of three multi-storey frames with a span between them of 4.10 m and a span between beams of 4.00 m. All the beams are considered to be of the same cross section of 400 mm width -600 mm height, with a concrete cover of 40 mm. Tensile and compressive rebars areas are 2591.82 mm² and 157.08 mm², respectively. The beams are considered to be under simple bending with a maximum supported moment of 140 kN•m. The material properties used for the estimations are those of commonly used materials in the 60's in Spain, which were obtained from the codes of that time and are shown in Table 1.

Table 1 Material properties of original and new building structure Material Existing New

f d [MPa] γ E c [MPa] f ctm [MPa] f d [MPa] γ E c [MPa] f ctm [MPa] Concrete 11.77 (2)
1.5 22983 (1) 1.50 (1) 25 1.5 30000 (1) 2.20 (1) Inner rebars 117.68 (2) 1.15 180000 (2) -500 1.15 200000 - (1) Equation in Eurocode 2 [START_REF]1992-1-1: Eurocode 2: Design of concrete structures -Part 1-1 : General rules and rules for buildings, The European Union Per Regulation 305/2011[END_REF] (2) Usual materials in Spain in 1956, according to [START_REF] Torroja | Instrucción H.A. 61 Especial para estructuras de hormigón armado[END_REF]

Refurbishment

The refurbishment operation consists of adding exterior thermal insulation in the façade and in the roof.

The ground floor in contact with the sanitary chamber is also insulated. The windows are replaced for new ones with better thermal characteristics. Some materials must be demolished or replaced to execute the refurbishment operation. The difference between the option that just fulfils the regulation and the option that fulfils the very low consumption standard is the insulation thickness as well as the type of windows.

In the case of the standard energy refurbishment (SR) that fulfils the regulation, the thickness of the glass wool that is added in the façade, roof and ground floor is 10 cm. The windows are of wood frame with double glazing 6/16/6 with argon (U = 1.85 W/m 2 .K). In the case of the passive energy refurbishment (PR), the thickness of the glass wool added in the façade, roof and ground floor is 10 cm, 19 cm and 18 cm, respectively. The windows are of wood frame with triple low emissivity glazing with argon (U = 1.09 W/m 2 .K).

The heating and cooling demand of SR are 30 kWh/m² and 7 kWh/m², respectively. The heating and cooling demand of PR are 15 kWh/m² and 13 kWh/m², respectively. The cooling load would be much lower considering that people open their windows at night in summer more than the operational conditions of the regulation, that are considered here, represent.

The heating system is a natural gas boiler, with an efficiency equal to 0.92, and an electric heat pump for the cooling, with EER (Energy efficiency ratio) equal to 2.00. Hot water is produced by solar thermal energy (60 %) and natural gas boiler (40%). As previously exposed, those are the efficiency values of the reference systems in the Spanish regulation.

The structure of the original building is maintained, and no structural intervention is considered.

New building

For the new building the same volume, living area and distribution is considered in order to be able to compare solutions. As the building is protected by a heritage regulation, the same architectural configuration must be ensured.

The new building structure is also of reinforced concrete. The slabs additionally include polystyrene pieces to lighten them and they are finished with ceramic tiles laid on mortar. The external walls are made of concrete blocks with external insulation of glass wool covered with mortar. The internal layer is finished with gypsum. The building has a traditional tile roof insulated with glass wool.

The internal walls of the building are made of concrete blocks with glass wool and gypsum.

As in the case of the refurbishment, the difference between the demolition plus standard new building (SD&N) and the demolition plus passive new building (PD&N), are the insulation layer thickness and the windows. In the case of SD&N, the thicknesses of the glass wool in the façade, roof and ground floor are 17 cm, 20 cm and 10 cm, respectively. The windows are of wood frame with double glazing 6/16/6 with argon (U = 1.85 W/m 2 .K). In the case of the PD&N, the thicknesses of the glass wool in the façade, roof and ground floor is 11 cm, 23 cm and 22 cm, respectively. The windows are of wood frame with triple low emissivity glazing with argon (U = 1.09 W/m 2 .K).

The heating and cooling demand of the new building according to the regulation are 27 kWh/m² and 6 kWh/m², respectively. In the passive building the heating and cooling demand are 15 kWh/m² and 12 kWh/m², respectively.

The considered heating and cooling systems are similar to those of the refurbished building (natural gas boiler with 0.92 efficiency, and heat pump with EER of 2.00). Hot water is produced by solar thermal energy (60 %) and natural gas boiler (40%).

The considered structure is similar to that of the original building. To simplify, all the beams in the new building are considered to be of the same cross section of 300 mm width -350 mm height, with a concrete cover of 30 mm. Tensile and compressive rebar areas are 1256.64 mm² and 157.08 mm², respectively. It is supposed that all the beams need to support the same load (maximum bending moment of 140 kN•m).

Material properties fulfil structural regulation requirements [START_REF]Ministry of Development (Spain), Instrucción de Hormigón Estructural (EHE-08)[END_REF] and are showed in Table 1.

Determining the lifespan

As already exposed, the considered building lifespan is that of its structure. In this paper, we consider the degradation phenomenon of corrosion due to carbonation since it is the most frequent one.

The methodology followed is the one defined in [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF], for this type of degradation.

The applied method is based on iterative structural calculations, in which the mechanical characteristics are updated in every step according to the degradation model. In this case, the iteratively updated parameter is the rebar section that decreases as the corrosion increases. It must be noted that corrosion can also lead to other mechanical effects that influence the lifespan, such as the bonding loss between steel and concrete, and the cracking of concrete cover due to the increase in volume of the oxides with respect to the original volume of the parent steel [START_REF] Pedrosa | Corrosion induced cracking: Effect of different corrosion rates on crack width evolution[END_REF]. However, these effects are not considered here due to the scope of this paper which is just to provide a rough value that can be used in LCA.

Corrosion is a localized phenomenon and occurs in specific structural elements (i.e. a beam or a column).

To extend the method to a whole building some simplifications have been made in order to narrow the problem. On the one hand, the different structural elements of the building are exposed to environments with different levels of aggressiveness (interior, exterior, etc.) and corrosion damage might not be the same for all of them. This study focuses just on beams because they are more sensitive to rebar section losses than columns. Beams are classified, depending on their exposure conditions, into: indoor, outdoor, below the roof or in contact with sanitary floor slab. Therefore, the degradation model is applied to four types of beams.

The shortest value that is obtained is considered as the building lifespan. This can lead to a lower value than the potential one, but it remains on the security side. This same hypothesis is used for both R and D&N.

Two improvements are made to the methodology proposed by [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF]. The first of them is explained next.

To model the initiation time of corrosion, the model proposed in the fib Model Code (MC2010) [START_REF]The International Federation for Structural Concrete (fib), Model Code 2010[END_REF] is applied, instead of the model proposed by V.-L. Ta et al. [START_REF] Ta | A new meta-model to calculate carbonation front depth within concrete structures[END_REF] that was used in [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF]. This is because the model proposed in MC2010 provides statistical data of the distributions and deviations of the input parameters. This allows to calculate the deviation of the final result as well as the probability associated to a certain data of lifespan which is important due to the considerable uncertainty in the determination of this parameter.

To estimate the lifespan of a structural element like a beam or a column, affected by corrosion, different steps must be taken.

(i) First, the time when corrosion is likely to start (initiation time, t i ) must be obtained. To do this the model in the MC2010 is applied.

(ii) Secondly, the propagation of corrosion with time, this is, the loss of reinforcement bars section with time, must be calculated. This phenomenon depends on the corrosion rate, v corr . This value must be measured and is not constant with time. However, when no data are available, it can be approximated by the values from Table 2 adapted from [START_REF] Andrade | Modelos de propagación del deterioro del hormigón[END_REF] depending on the Eurocode 2 [START_REF]1992-1-1: Eurocode 2: Design of concrete structures -Part 1-1 : General rules and rules for buildings, The European Union Per Regulation 305/2011[END_REF] exposure classes. The standard deviation of this parameter is taken from [START_REF] Šomodíková | Modeling of degradation processes in concrete: Probabilistic lifetime and load-bearing capacity assessment of existing reinforced concrete bridges[END_REF] to make an estimation. (iii) Thirdly, an admissible limit in the structural performance must be defined. This is the second improvement we have made to the method proposed by [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF]. [START_REF] Palacios-Munoz | Influence of refurbishment and service life of reinforced concrete buildings structures on the estimation of environmental impact_In press[END_REF] leave the selection of the admissible limit entirely to the technician, whereas we propose the use of the partial factor method and its adaptation to existing structures [43]. Next, we explain this method.

Usually, the design value of the beam's capacity is bigger than the required capacity. This is because reinforcing bars diameters are standardised and a combination of them must be chosen to, at least, overcome the required capacity. In the corrosion process the diameter of the reinforcing bars decreases with time. The admissible limit is set at the moment when the design value of the resistance of the beam is strictly equal to the supported bending moment.

The design of structures according to Eurocodes is based on the concept of limit states and their verification by the partial factor method [43]. In the structural assessment process there are uncertainties related to the determination of the loads, material properties, geometry, etc. To obtain the design value, different partial safety factors are introduced that need to be applied to materials properties and loads to ensure a certain reliability level. These factors are defined in the regulation in the case of new structures.

For concrete and steel, they are 1.5 and 1.15, respectively.

When existing structures are assessed, the uncertainty regarding the available information is different.

Therefore, to ensure the same reliability level than in new structures, the value of the partial factors are different. The same target reliability index (β = 3.8) has been assumed for both existing and new buildings. Assuming that the tests of material properties yield to coefficients of variation V c =0.15 and V s =0.05 [43] and the variability of geometrical uncertainties is insignificant, material factors for concrete and steel are 1.353 and 1.097, respectively.

(iv) Finally, iterative calculation must be done considering in every step the appropriate diameter of the rebar, according to degradation models. To do this, as already explained, t i and v corr are needed. Those are not deterministic values but can be described by means of a normal distribution defined by a mean value and a standard deviation. To assess the mean and standard deviation of the final result from the structural calculation, the structural model is approximated to a quadratic Taylor series.

The time when the admissible limit is reached is taken as the lifespan value of the analyzed building. The lifespan of R is the difference between the lifespan of the existing building and the time when the refurbishment is done. This is because the refurbishment that is considered in this paper does not improve the structure but just the building's thermal performance.

LCA

LCA methodology is applied to evaluate four solutions: SR, PR, SD&N, and PD&N. The alternatives are evaluated according to the Global Warming Potential (GWP) indicator, based on 2007 IPCC v1.02 methodology, and using the Ecoinvent (v2.2) database [START_REF] Frischknecht | Overview and Methodology[END_REF] adapted to the Spanish electric mix of 2017, with the software tool EQUER [START_REF] Polster | Evaluation of the environmental quality of buildings -a step towards a more environmentally conscious design[END_REF]. This indicator is chosen because it is among the most widely used [START_REF] Vilches | Life cycle assessment (LCA) of building refurbishment: A literature review[END_REF], as in [START_REF] Famuyibo | Achieving a holistic view of the life cycle performance of existing dwellings[END_REF][START_REF] Mohammadpourkarbasi | Eco-Retrofitting Very Old Dwellings : Current and Future Energy and Carbon Performance for Two Uk Cities[END_REF].

The functional unit of these LCAs is housing 80 adults in a collective apartment building of 1257.44 m² living area, maintaining the architectural configuration of a 60 years old existing building, ensuring at least the fulfilment of the current energy demand regulation, during the lifespan of the building. The reference flow corresponds to 1 m² and 1 year.

The reference study period corresponds to the period from the renovation or construction work until the end of life of the structure. In every alternative (SR, PR, SD&N, PD&N) the estimated lifespan is considered.

The common hypotheses in the LCA include:

(i) No transport of occupants and no household waste is included in the studied system.

(ii) Water consumption (per person and day): Hot water 40l, Cold water 100 l.

(iii) Constant electric mix (22% nuclear, 33% renewable, 17% carbon and 28% gas); grid losses 9%.

(iv) Surplus of materials during construction: 5%.

(v) Mains water efficiency: 80%.

(vi) Transport distance for materials: Production site to construction site, 100 km; site to recycling, 100 km; site to inert landfill and to incineration, 20 km.

Building materials quantities are derived from the geometry and composition of walls, floors and roof.

Equipment is also considered (boiler, cooling system and solar thermal panels). Besides, the following building services materials are added, including plumbing (sanitary equipment, drinking water and wastewater system), electrical and telecommunication services. We proceeded by considering fixed ratios of these elements per m² of floor (Table 3). [START_REF] Bizcocho Tocón | Aplicación del análisis de ciclo de vida a la gestión de los residuos de construcción[END_REF], we make the assumption that in the future, when the demolition stage takes place, this will have changed according to this regulation.

Wood and plastics are considered to be incinerated, and the rest of materials landfilled.

Economical aspects

To achieve efficient buildings that are also affordable from an economical point of view, is an important issue. This is especially relevant in the case of building refurbishment if the purpose is to increase the refurbishment rate of the building stock in Europe. In this paper this is analysed in a simplified way.

To calculate the initial construction costs, the CYPE database [START_REF] Cype Ingenieros | Generador de precios de la construcción[END_REF] for construction prices in Spain is used. This database makes a distinction in the prices depending on the type of work (refurbishment or new building) and the location in Spain.

To calculate the operational costs, the gas natural and electricity prices are taken as an average of the prices offered today by the main energy distributors in Spain. The prices considered are the ones depending on consumption, but not the fixed ones of the energy price corresponding to power, taxes, etc.

This results in 0.13 €/kWh for electricity and 0.05 €/kWh for natural gas.

Results and discussion

Dependence of the kg CO2-eq./m² year indicator on lifespan

Prior to estimating the lifespan, we have made a theoretical study of the impacts of five solutions along a time period of 150 years considering an existing building of 50 years old. In Fig. 1 the kg CO 2 -eq./m² of the different solutions are plotted.

Fig. 1 kg CO 2 -eq./m² of the original building and different intervention alternatives at t=50 years: SR, PR, SD&N and PD&N

As can be seen in Fig. 1 depending on the year of analysis, the best solution would be different. For example, after a time lapse of 50 years since the intervention both types of R obtain better results than D&N. In contrast, if a time lapse of 150 years is considered, SR has equivalent impact to PD&N. This type of analysis has the implicit assumption that R and D&N have the same lifespan. This is usual practice in comparative LCA of R and D&N. However, this is not likely to happen.

The total amount of kg CO 2 -eq./m² depends on the number of years considered. For this reason, the results are usually annualised and transformed into kg CO 2 -eq./m²•year. This allows to compare different stages and different buildings. However, this does not correct the problem of different lifespans. Even if the results are annualised, the value of this indicator is still strongly dependent on time, as can be seen in In addition, when comparing R and D&N, the lifespan of the refurbished and the new building will not probably be the same. It is reasonable to think that a new building will have a longer lifespan than a similar one built 60 years ago. This is because the new building will comply with current regulation, and therefore will consider phenomena that were not even known before (as AAR) and will include strong control procedures. Additionally, if the same lifespan is considered for both R and D&N, it is as if the opposite assumption was done (the existing buildings lasts longer), because in R 50 years have already elapsed.

For this reason, we consider that estimating lifespans is necessary to obtain more robust results in LCAs of buildings.

Lifespan results

According to the methodology exposed in 2.2, the structural capacity decreases with time. In Fig. 3, the case of the existing building is presented. The structural element, in this case, a beam of the original building, has an initial bending resistance of 144.45 kN•m, in design value. A final resistance of 140 kN•m is considered to be the admissible limit in this case study. The admissible limit is reached no before than 80.5 years with a 25 % of probability, no before than 94.45 years with a 50 % of probability (mean value) or no before 108.4 with a 75% of probability. As exposed in 2.2, the smaller value (the most adverse) is chosen as the structure lifespan. In Table 5 the values actually used for the lifespan of the whole building for the different alternatives are presented. In real practice, physical degradation is not the only cause of building demolition. In fact, it is not even the most common, being the main cause the subjective perception (44%), followed by change in use (26%), according to [START_REF] Marteinsson | Service Life Estimation in the Design of Buildings[END_REF]. Deterioration was the cause of only 17% of the projects [START_REF] Marteinsson | Service Life Estimation in the Design of Buildings[END_REF].

In the case of Spain, statistical lifespan data, depending on their construction period, can be found in Rincón et al. [START_REF] Rincón | Service life of the dwelling stock in Spain[END_REF]. This value is also included in As can be seen in Table 5, the new building has a lifespan 2.2 times greater than the original one, for the same structural reliability level. If we also take into account that a part of the lifespan of the existing building has already elapsed at the time of refurbishment, the lifespan of the new building is about 6 times longer than the refurbished, in this case study.

Results obtained taking into account the calculated value of lifespan

In Fig. 4 the value of kg CO 2 /m².year is shown taking into account a lifespan of: (a) 100 years for all the solutions (similar to usual practice), (b) the specific estimated lifespan for each of the solutions, and (c) the statistical data of lifespan according to [START_REF] Rincón | Service life of the dwelling stock in Spain[END_REF], which is also different for each solution. In According to these results, when the same lifespan is considered (Fig. 4a), PR is, by large, the best alternative, but this is not a reliable result as discussed before. PR also results to be the best option when the statistical values of lifespan are considered (Fig. 4c), although the difference with the other alternatives is significantly reduced. According to Fig. 4b PR is the second best option. Therefore, we can conclude that PR is one of the best alternatives from the point of view of CO 2 emissions.

PD&N obtains the best results when the estimated lifespans are considered (Fig. 4b). However, it requires to ensure a very long lifespan (around 210 years) which is very difficult to guarantee in practice.

SR is the worst solution when lifespans are estimated (Fig. 4b). This reveals that SR requires a CO 2 -eq. investment which does not provide an optimal performance of the building and its useful life is short.

Refurbishment should aim to reach passive standards to optimise the CO 2 -eq. investments.

The estimated value of lifespan has an uncertainty that derives from the degradation model. This uncertainty has different effects in the results of the kg CO 2 -eq./m²•year indicator. In the case R solutions, the influence of this uncertainty in the results is higher because the lifespan is shorter. This is aligned with the findings in Fig. 2. For short lifespans, the value of the indicator significantly varies with little time increments. This is because the contribution of the construction and demolition stages to the global impact is high. On the contrary, in the case of new buildings, as their lifespan is long, the value of the indicator is almost established, and it is not so sensitive to changes. In the case of the new buildings, the uncertainty is produced mostly because of the huge difference between the estimated physical lifespan and the statistical data rather than because of the durability model. This statistical data takes into account that buildings are often demolished for reasons other than degradation.

Economic consideration

Table 6 shows the costs at different stages for the different alternatives. The construction costs include materials, machinery and manpower. Taxes, other expenses like technicians' fees, waste management, etc. are not taken into account. As can be seen in Table 6, the cost of D&N is considerably higher than R for this case study. As a counterpart, in both PR and PD&N, the use stage costs of heating are the lowest. In the case of cooling, the cost is higher for PR and PD&N, because the building is more insulated and just the night ventilation proposed in the regulation is considered.

Fig. 5 and Fig. 6 show the relation between cost and CO 2 emissions when a same lifespan of 100 years is considered for all the solutions and when the estimated lifespans are used instead, respectively.

According to Fig. 5, when the same lifespan is considered, there is a big difference between R and D&N.

New construction results to be not only the worst option from a CO 2 emissions point of view, but also it results to be the most expensive alternative. PR results to be, by large, the most cost-effective solution. However, if the emissions and the costs of every solution are evaluated considering their estimated lifespans (Fig. 6) the results considerably differ. In this case, both SD&N and PD&N result to be cheaper per year, as the construction cost is annualised in many years. In fact, if the estimated lifespan value is used, the most cost-effective solution results to be PD&N. However, in this case the long lifespan of 210 years must also be ensured as mentioned before, and the initial cost of construction is, in most cases, a decisive parameter and refurbishment options require fewer initial investments.

Limits of the study

Some limits must be noted in this study.

The estimated lifespans can be considered optimistic, since degradation is not the main cause of building demolition, as already exposed. In addition, not all the degradation models have been included but just corrosion, which is the most common one. However, the results illustrate the durability of reinforced concrete structures considering its physical potential. This gives us an idea of the environmental benefit margin compared to usual demolition trends.

It must also be noted that results are case dependent as each building has its own durability depending on the concrete, the exposure conditions, etc. The available options both for refurbishment and new building are multiple. Anyhow, the methodology proposed can be extended to other cases.

Static life cycle inventory data were used, but there is uncertainty regarding their long-term values (e.g. electricity mix, production processes, etc.). This long-term uncertainty does exit also regarding energy demand, as climate change can lower the heating loads and increase the cooling ones. In addition, building thermal loads could be different by incorporating solar blinds or increasing night ventilation. In this study we considered the operational conditions of current regulations in Spain.

Conclusions

In this paper refurbishment (R) versus demolition and new building (D&N) have been evaluated from an environmental point of view, proposing a new approach that allows to estimate and use the different lifespans of the buildings in a comparative LCA. Two energy performance levels have been analysed, standard (S) and passive (P), resulting in four alternatives: SR, PR, SD&N, PD&N. Economic assessment has also been addressed in a simplified way.

Lifespan is a fundamental aspect in the LCA of buildings, that greatly influences the results. It becomes still more important when comparing refurbishment (above all, of old buildings) and new buildings because their durability may be very different. By not considering the lifespan in an appropriate way the most durable buildings are penalized. We have shown the different results obtained by considering a similar lifespan for refurbished and new buildings, which is the common practice, and by estimating the lifespans of each solution. The different in lifespans is up to 176 years in our case study. The results show that these different lifespans can alter the order of preference of the solutions from an environmental point of view. Therefore, estimating a value for this parameter as reliable as possible is a fundamental task in the LCA of buildings. A broadly accepted methodology that allows to estimate the buildings lifespan does not exist yet. In this paper an approximation to this problem has been defined but more research is required in this direction.

In our case study, in terms of CO 2 equivalent emissions, the alternative PD&N obtains the best result, slightly better than PR, but it requires to ensure a very long lifespan which is highly unlikely to happen according to current practices. Because of this, PR appears as the best choice from the environmental point of view. SR does not yield optimal results and, therefore, refurbishment should aim to reach passive standards.

The economic analysis shows that D&N alternatives are more cost-efficient when considering the annualized costs, due to their longer durability, but not from the initial investments point of view.

This paper reveals the importance of the lifespan to get economic and environmental benefits and render cost-effectiveness in the long term to the building sector. In the case of the existing buildings an important objective should be to extend their lifespan by means of improving their structure, as suggested in [START_REF] Palacios-Munoz | Simplified structural design and LCA of reinforced concrete beams strengthening techniques[END_REF]. In the case of new buildings, the objective should be to ensure their potential durability by changing current human tendencies of early substitution.

Fig. 2 .Fig. 2

 22 Fig. 2. When the considered lifespans are up to 200 years the value of the indicator is sensitive to time. A nearly constant tendency is only reached after long periods of time that do not correspond to the commonly used lifespans in the LCA of buildings.

Fig. 3

 3 Fig. 3 Decrease of the bending resistance of the original building beam with timeIn Table4the values of lifespan for the different structural elements of both the original and the new building are shown.

Fig. 4 bFig. 4

 44 Fig.4kg CO2-eq./m² year taking into account: (a) 100 years for all the alternatives; (b) their specific lifespan according to Table5; and (c) their statistical lifespan according to[START_REF] Rincón | Service life of the dwelling stock in Spain[END_REF]

Fig. 5 Fig. 6

 56 Fig.[START_REF] Zabalza Bribián | Methodological aspects and design implications to achieve life cycle low emission buildings. A case study: LCA of a new university building[END_REF] Relation between cost and CO 2 emissions when a same lifespan of 100 years is considered for all the solutions Fig.6Relation between cost and CO 2 emissions when the estimated lifespans are considered

Table 2

 2 Representative values for Vcorr for the Eurocode 2 exposure classes[START_REF] Andrade | Modelos de propagación del deterioro del hormigón[END_REF]

	Exposure class V corr [μm/year]
	XC1	0
	XC2	4
	XC3	2

Table 3

 3 Materials ratios considered plumbing and electricity

	Element	Unit	Ratio per m²
	Copper	kg	4,36E-01
	Steel	kg	1,31E+00
	PVC	kg	2,72E-01
	Ceramic	kg	2,50E+00
	Polyethylene	kg	6,50E-01
	3-conductor cable	m	6,25E+00
	In relation to the end of life stage reinforced concrete and metals are considered to be recyclable in order
	to follow the European Waste Directive 2008/98/CE [46] that imposes to recycle 70% of building related
	waste. Although they are not being totally recycled in Spain nowadays

Table 4

 4 Calculated lifespan data depending on the element

		t i [years]			v corr [mm/año]		Serivce life [years]
		mean	σ	Dist.	mean σ	Dist.	mean	σ
	Original building 1956
	Exterior beam	28.54	12.09	Normal 0.005 0.00125 Normal	94.45	20.77
	Sanitary slab beam	33.32	13.65	Normal 0.004 0.00100 Normal	125.60	28.76
	Interior beam	22.04	9.03	Normal 0	0	Normal	-	-
	Roof beam	33.32	13.65	Normal 0.002 0.00050 Normal	204.25	44.34
	New building 2018
	Exterior beam	40.80	17.54	Normal 0.005 0.00125 Normal	210.03	47.93
	Sanitary slab beam	47.48	19.70	Normal 0.004 0.00100 Normal	249.5	53.78
	Interior beam	31.40	13.03	Normal 0	0	Normal	-	-
	Roof beam	47.48	19.70	Normal 0.002 0.00050 Normal	456.5	104.18

Table 5 .

 5

		Pr 10%	Pr 25%	Pr 75%
	147	Pr 90%	Pr 50%	admissible
	145
	143
	M d
	141
	139
	137
	0	50	100	150
			time [years]

Table 5

 5 Lifespan results

		Estimated lifespan	Statistical lifespan
				[50]
		mean	deviation	Deterministic
	Original building	94.45	20.77	90
	SR at t=60	34.45	20.77	30
	PR at t=60	34.45	20.77	30
	SD&N	210.03 47.93	80
	PD&N	210.03 47.93	80

Table 6

 6 Cost of the diferent intervention alternatives

		Construction stage	Use stage heating	Use stage cooling	Total use stage
		[€/m²]	[€/m²•year]	[€/m²•year]	[€/m²•year]
	SR	391.00	1.68	0.48	2.16
	PR	439.43	0.84	0.88	1.72
	SD&N	690.39	1.52	0.41	1.93
	PD&N	735.98	0.84	0.82	1.66
	Demolition 57.27	-	-	-

Acknowledgements

This work was supported by the Spanish Ministry of Education, Culture and Sports, through a FPU research grant [grant FPU15/01069] and the Research Group GIA [T37_17R] of the University of Zaragoza (Spain).