Daigo I.(a), Iwata K. (a), Oguchi M.(b) and Goto Y.(a)
a) The University of Tokyo, Tokyo, Japan
b) National Institute of Environmental Studies, Tsukuba, Japan

Keywords: lifetime distribution; observation year; shipment year; actual lifetime; discard year.

Abstract: We summarised different types of the lifetime distributions on the basis of demolition year, in other word, observation year, which was termed D-based distribution in this study. Lifetime distributions denote distributions of years from construction to demolition for groups of buildings. The D-based distributions are expected to show a chronological change of the whole lifetime of buildings in Japan during emerging replacement in the late 1980s. As expected, we could observe a change on the average lifetime from the years from 1987 to 2010. During an extended boom, we could observe that the average lifetime of buildings steadily decreased due to enhancement of replacement. On the other hand, during a depressed period, it steadily increased. We can conclude that D-based distributions are valuable for analysis on changing the average lifetime which is decided by decisions on replacement.

Introduction

Buildings are constructed, used for a certain period, and then demolished. A dynamic model in the field of industrial ecology is an analytical model which simulates a relationship of numbers of buildings between construction, being in use (buildings stock), and demolition (van der Voet et al. 2002). Similar approaches have been performed in a field of demography and in an application for automobiles, which are named as cohort analysis (Evan 1959) and fleet analysis (Gallez 1994; Dargay and Gately 1999), respectively. A dynamic model can estimate future trends of in-use building stocks and building demolition in scenarios on longer lifetime, change of legislations, and so on (Hashimoto and Terashima 2000). Regarding lifetimes of buildings, it is significant data for conducting material flow analysis (MFA) and life cycle assessment (LCA) (Oguchi et al. 2010; Frijia et al. 2012). In a case of LCA studies, regarding energy consumption and greenhouse gases (GHGs) emissions in a life cycle of buildings, though energy consumption in use phase and GHGs emissions associated with that is dominant, the average of the whole lifetime of the product is generally assumed with very limited evidence on actual lifetime on the basis of observation (Frijia et al. 2012). In a dynamic MFA, time-series annual consumption of materials by end use in the past and lifetime of each end use are used for the analysis. Especially, lifetime of buildings is a key parameter in dynamic MFA studies on steel (Daigo et al. 2006) and wood (Hashimoto and Terashima 2000). In this paper, a lifetime distribution denotes a distribution of years from construction to demolition for a group of buildings. In cases of many types of products, actual lifetime distributions have not been observed (Murakami et al. 2010; Oguchi et al. 2010). On the basis of some cases where actual lifetime distributions were observed, it has been recognised that lifetime of products change over time. For instance, the average lifetime of automobiles in Japan has been increased (Adachi et al. 2005; Oguchi et al. 2010). The average lifetime of mobile phones in Japan has also been dramatically increased after the year 2000 (Murakami et al. 2009). With regard to buildings, time-series change of lifetime has not been analysed.

Many former studies have observed lifetime distributions of a group of products manufactured in the same year. Oguchi et al. (2010) categorised two types of lifetime distributions which are drawn on groups of products which were produced in the same year and which were discarded in the same year. The former and latter types of distributions are named as a construction year based (C-based) distribution and a discard year based (D-based) distribution, respectively. We hypothesised that lifetime of buildings in industrialised countries where most of new construction are caused by replacement are decided by situations at the time of demolition. The hypothesis leads to the recognition that actual lifetime distributions of buildings can be observed in the type of a D- based distribution. This study aims to reveal a change of average lifetime of buildings over time on the basis of a D-based distribution.

Types of lifetime distribution

Method

Basic equation

We employed the basic equation which is well- known in the field of industrial ecology. (Hashimoto and Terashima 2000; van der Voet et al. 2002; Adachi et al. 2005; Daigo et al 2007) In this equation, a condition of constructed floor area, demolished floor area and lifetime of building was described as follows:

Equation

where, Di(t) denotes demolished floor area of type i buildings in the year t, C(x) denotes constructed floor area in the year x, and R(y, t) denotes remaining rate of the buildings which past y years after construction at the beginning of the year t. Here, the function R has a possibility of varying with time of observation, and then has a variable parameter of t. In the next section, this point is described in detail. Here, annual data was used for our analysis due to data availability. In addition, the equation 1 which is expressed in the form of cumulative distribution function can be deformed to equation 2 in the form of probability density function as follows:

Equation 2

where w(x,t) denotes the portion of the demolished floor area of buildings which constructed in the year x to the total constructed floor area in the year x. Note that though the variables in the distribution w differ from those used in the distribution R for the sake of convenience, dimensions of the variables are same.

Variables x and t in the distribution w(x,t) denote the year constructed and the year observed, respectively. The construction year, x, is taken in the x-axis, the observation year, t, is taken in the y-axis, the demolished floor area, w(x,t), is taken in the z-axis, and then the distribution shown in Figure 1 could be obtained. As described in Figure 1, two types of lifetime distributions on the planes normal to the x- and y-axes can be defined. One of the lifetime distributions on the planes normal to the x-axis is drawn on the basis of construction year (C- based distribution.) The other one of the lifetime distributions on the planes normal to the y-axis is drawn on the basis of demolition year (D- based distribution.) In addition, the vertical axis can be defined not only as the total floor area but also as percentages to the total demolished one or to the constructed one in corresponding construction year. Those different definitions of lifetime distribution were summarised by Oguchi et al. (2010) as shown in Table 1.

Variables in C-based distribution are valid for a cohort of buildings constructed in each specific year, which vary with changes of factors determined at the time of construction; such as improving design for longer service life, changing regulations, improving strength of materials, and so on. Variables in D-based distribution are valid for buildings demolished in each specific year, which vary with change of factors determined at the time of demolishment; such as revenue from recovered materials, economic conditions, regulations for recycling, and so on. Here after, we analysed time-series change of D-based distribution due to focusing on phenomena caused at the time of demolition.

Illustration of lifetime distribution for different base years

Time-series change of the mean lifetime in buildings

In this study, estimated annual demolished floor area was confirmed with statistical demolished floor area by setting appropriate numerical parameters of the remaining rate R for each period. In practical, when R(t-x, t) is given, numerical parameters of R(t-x+1, t+1) was fitted to meet the condition expressed in equation 3, which is deformed from the equation 1 as follows:

Equation3

Here, the parametric functions for R were determined by the former research for each construction type and usage (Komatsu 1992) as shown in Table 2. When a numerical parameter is altered, scale parameter or mean value was changed and other parameters were fixed, which could determine the specified parametric function. A schematic diagram for the analytical method was shown in Figure 2.

Classification of buildings in this study on the basis of structure and usage

The remaining rate curve at the beginning of the year t shown at right hand side was given, and then the curve for the year t + 1 shown at left hand side was changed for fitting the shaded area enclosed by two curves with the statistical value.

The former research surveyed the remaining rate at the beginning of the year 1987 which were fitted by parametric cumulative distribution functions (Komatsu 1992). The parametric remaining rate functions were employed for the year 1987, and then the remaining rates for the year 1988 and on were determined year by year.

Schematic illustration on a relation between remaining rates and demolished floor area in the year

Results

The time-series change of mean lifetimes for the three types of D-based distributions, such as φ, d and w, were calculated. The mean lifetimes for φ and d are exactly same on the basis of those definitions explained in table 1. The mean lifetime of steel structured residence in the forms of φ and d was changed from 14 years in 1987 to 28 years in 2010. Regarding the lifetime in those forms, a part of distribution curve corresponding to the years when constructed floor area are larger than other periods in the past become relatively higher.

Then, the mean lifetime of the distribution was put weight on the years. Our results were weighted on buildings constructed after 1970’s because constructed floor area has been remarkably increased in 1960’s and 1970’s in Japan. Therefore, the estimated mean lifetime was monotonously increased during the estimation period. The estimated mean lifetime at the year 2010 was about 30 years, which indicates that the buildings constructed in the year 1980 which is 30 years ago from 2010 was dominant in buildings demolished in 2010.

In the lifetime distribution in the form of w, the mean lifetime of steel structured residence was changed from 24 years in 1987 to 37 years in 2010. In this form, the time-series change of constructed floor area does not distort the distribution because the demolished floor area was divided by constructed floor area in the corresponding year. Meanwhile, although the total of a probability distribution must be one in general, the total of the demolition rates in the distribution of w not necessarily correspond to one because denominators of each rate are different. Consequently, the mean lifetime was estimated to be relatively short in the observation year when the total of demolition rates was less than one. The estimated mean lifetime in the form of w was sensitive to the total of demolition rates.

The new definition of D-based distribution could be defined as the fourth possible form, which was obtained by differentiating R with respect to the age of buildings. The distribution was defined as r–type distribution. The r–type distribution expresses the expected lifetime of a building demolished at the beginning of year t. The mean lifetime on the basis of r might be the appropriate index for assessing the mean lifetime at the time point of observation, that is, among four types of D-based distribution. The mean lifetime is influenced neither by past annual change of constructed floor area nor by demolition rates. Time-series changes of mean lifetimes estimated on the basis of r-type distribution are shown in figure 3 by construction types. The mean lifetimes of each type of buildings decreased until early 1990’s, and from then on increased. It is considered that a booming economy let the lifetimes become shorter due to active renewals during the late 1980’s to 1992 in Japan.

Time-series changes of mean lifetimes of buildings on the basis of r-type distribution by construction types

Conclusions

We summarised four different types of the lifetime distributions on the basis of demolition (observation) year, which was termed D-based distribution in this study. The fourth one was newly added by this study to the former study (Oguchi et al. 2010). We found that the lifetime distribution in the form of the fourth type, r, is the most suitable for observing time-series change of mean lifetime in D-based distributions.

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