MEDIC A METHOD FOR PREDICTING RESIDUAL SERVICE LIFE AND REFURBISHMENT INVESTMENT BUDGETS Methods for predicting service life

Transcription

1 MEDIC A METHOD FOR PREDICTING RESIDUAL SERVICE LIFE AND REFURBISHMENT INVESTMENT BUDGETS Methods for predicting service life F. FLOURENTZOU École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland E. BRANDT Danish Building Research Institute, Hoersholm, Denmark C. WETZEL Fraunhofer Institut für Bauphysik, Holzkirchen, Germany Durability of Building Materials and Components 8. (999) Edited by M.A. Lacasse and D.J. Vanier. Institute for Research in Construction, Ottawa ON, KA R6, Canada, pp National Research Council Canada 999 Abstract The service life of buildings is an important factor e.g. in life cycle assessment and the assessment of global costs. Based on experience much information is available regarding the service life of building elements. However, for existing buildings such information is of little use as the key question is the probable date of repair/replacement. MEDIC is developed on the theories of conditional probabilities to help assess the residual service life and thereby the necessary investments in refurbishment. When passing from working on general products, like the life span of wooden windows, to specific objects, for example 29-year old wooden windows, the current condition of the object must be taken into account. An evaluation of residual service life must for that reason be closely connected to a good diagnosis method. In the European project EPIQR on deterioration of building materials and components is described by the use of a classification system with four classes for the qualitative condition (e.g. of a facade or window). MEDIC calculates the probability to change from one class to another during time. The prediction is based on the combination of the a priori probability based on experience from a large number of previous investigations/refurbishments and the current state of the object under study. Keywords: Budgets, building assessment, refurbishment investment, residual service life, service life prediction, probabilistic methods. Introduction When elaborating a refurbishment scenario, architects and engineers are interested in the residual service life of the building materials and components. When energy saving is one of the goals of the refurbishment operation, this information

2 becomes of primary importance. A life cycle energy balance or a life cycle assessment of an existing element cannot be performed without an estimation of the remaining service life. Most data found in literature concerns new items which is of little use for existent and deteriorated building elements. Knowledge of the probable residual life span of a building element will often be decisive for whether it will be replaced or not. For example, it is questionnable whether windows in a relatively acceptable deterioration state should be replaced only because they are energy inefficient. Knowing that scaffolding will anyway be installed for facade renovation, a replacement of the windows becomes more plausible to consider. To judge whether a replacement of the windows is energy and cost efficient can only be verified by a cost benefit analysis where the energy savings and the probable residual service life are taken into account. Obviously the analysis is highly dependent on whether the residual service life is assessed to 5-8 years or 25-3 years. Consequently it is of importance to develop a model which can simulate the probable deterioration of all building elements thereby making it possible to determine their probable date of replacement. Knowledge of this deterioration for all building elements makes it possible to assess the global development in maintenance and refurbishment costs for the entire building. It also allows planning of future refurbishment actions by listing the probable elements to be replaced in 5, or 5 years from the time of the assessment. 2 Existing methods Quite a few methods are already in use (e.g. Genre J-L (995) and Mayer P. et al., (995)). Of special interest has been the work done for the "Swiss Federal Office for Economic Policy" in the framework of the PI BAT program: MEBI (Genre, 995). MEBI bases its predictions on a large-scale survey of 3 building experts. It is capable of calculating the residual service life of 5 different building elements and assessing the development of the refurbishment investment budget under condition that no refurbishment work is undertaken in the meantime. (Mayer et al, 995) present the deterioration curves of envelope elements studied on 2 buildings. This method distinguishes between three deterioration curves: L max for elements in favourable conditions (good element quality, protected position, good maintenance, etc.), L Ø for normal conditions and L min for unfavourable conditions (inferior quality, exposed to harsh weather, bad maintenance, etc.). For the element "cladding" for example, see figure, L max corresponds to traditional cladding, in a non polluted environment and protected by an overhang. L min corresponds to exposed synthetic cladding while L Ø corresponds to modern mineral claddings. The MEBI curve approximately corresponds to L Ø on the graph in fig:.

3 a b Element relative value Cladding deterioration c d L min L ø L max Fig:. Deterioration curves according to (Mayer P. et al.) 3 The MEDIC method MÉDIC stands for Méthode d Évaluation de scénarios de Dégradation probables dínvestissements Correspondants and is a proposal for a new method to be used together with a surveying tool which uses a classification of the degradation states of the elements, such as. EPIQR (Brandt et al. 998). MÉDIC is intended for use with EPIQR and is based on sub-dividing the building into 5 elements. Four codes {a, b, c, d}, identical to those of EPIQR, are used to describe the deterioration state of the elements. Code a represents an element in good condition, code b an element with minor deterioration, code c an element with more serious deterioration and code d an element that needs replacement. The knowledge base of the method is summarised in 4 probability curves for each building element. For a certain element these curves show at any time in the elements life time the probability for the deterioration code to be a, b, c or d respectively.

4 P(a) P(b ) P(c) P(d) Age in years Fig: 2: Illustrative probability curves for deterioration codes of the element "cladding". The probabilities of figure 2 can also be plotted on a cumulative curve, see figure 3. The sum of the probabilities shall of course at every instant be. Q P(a) P(b) P(c) P(d) Age in Years Fig: 3: Cumulative probabilities of deterioration codes 3. Examples According to figure 3, a -year old cladding is certain to correspond to code a, while a 7-year old cladding is code b with 5% probability. A 4-year old cladding has a 35 % probability of being code b, a 4% probability of being code c and 5% probability of being code d. A 95-year old cladding will, with a 99% probability, need replacement. 3.2 Building quality space On the y-axis of the graph in figure 3 the probability of a given building element to be code a, b, c or d respectively can be seen. The space Q{, }on the y- axis represents the universe of all building elements in the whole building. Any

5 specific element, q, is situated somewhere between and on the y-axis of the graph dependent on its quality. If we accept the hypothesis that element deterioration follows an affine curve to L min, L max or L Ø in figure, and if we know the exact position of an element on the y-axis of the graph, we can read the time of passage from one code to another. If q is a specific element, q Q, the value q= represents a good building with a long life span as all transitions from one code to another are taking place after very long time. It corresponds to L max in figure. An element corresponding to the value q= in contrast represents the worst case. It corresponds to L min in figure. The value q=.5 corresponds to L Ø. We call the space Q={,} the "Quality Space". In practice it is impossible to determine the position of a specific element exactly in the space Q, but it is possible to define or assess a region in which it is likely to be found. An element of poor quality for example belongs to q {.5,} while an element of good quality belongs to q {,.5}. 3.3 Conditional probabilities If we know that q {, B}, conditional probabilities give P( code i q {, B} ) = P(code i) / B. () If q {B, } () becomes: P( code i q {B, } ) = (P(code i)-b) / (-B). (2) i {a, b, c, d}. Q B P(a) P(b) P(c) P(d) Age in years Fig. 4: If we know that a building is found in a subspace q= {, B} then P(code i q) = P(code i) / B As we can see from figure 4, the interval of probable transition from code a to code b is from the 2 th to the 26 th year, i.e. an interval of 4 years. Knowing that q {, B} restrains the time of transition to the interval from the 8 th to the 26 th year i.e. an interval of 8 years. The new probable period for transition from b to c is from the 34 th to the 5 th year and the new probable period of transition from c to d is from the 5 th to the 95 th year. As it appears, the knowledge of q {, B} considerably restrains dispersion on the probable residual service life.

6 3.4 Determination of the probable residual service life During the building survey - EPIQR diagnosis - the surveyor determines the deterioration code of the 5 building elements. Further, information about the building age is available from the general information about the building. Combining the information about degradation code and age, it is possible to determine a subspace q to which the element belongs, see figure 5. To do this, a line, arrow, is drawn from the element age to intersect with the curve between the area of the elements degradation code to the neighbouring area(s). Then draw a line, arrow 2, from the intersection point to the y-axis to determine point B. For instance, as shown in the figure for degradation code c, the arrow is intersecting the curve between areas for code b and code c. The quality subspace becomes q ={B, }, see figure 5, as the deterioration code has changed from b to c. (In case there are two intersections two vertical lines are drawn and the sub-space is determined as the distance from the lower to the higher value of y). As we have chosen a probabilistic approach, the probable residual service life, L, is not a single figure but corresponds to an interval. To find the probable residual service life the point where the probability of having code d is 5% is determined, i.e. where y = (+B)/2 intersects the next transition curve (the curve that separates P(c) and P(d)). A line, arrow 3, is drawn vertically from this point to intersect with the x- axis. The difference between this point and the age of the element give the probable residual service life L mean. On the curve the upper and lower limits of the probable interval of L are determined as the intersections of the curve with y = B and Y = respectively. Q B P(a 2 P(b) 3 P(c P(d) L mean Residual service life, L = 7 ± 5 year Fig. 5: Residual service life for a 3 year old cladding with code c

7 3.4. Example The cladding of a 3 year old building has been allocated code c. The quality sub-space becomes q = {B, }, see figure 5. This means that the cladding is of bad quality. On the graph in figure 5 it can be read that at time t = 35 years, i.e. five years after the diagnosis date, P(at least c, t = 3) =.94. Also it can be seen that B =.76. Using equation (2): P(code c, t=35 code c at t=3) = (P(at least c, t=3)-b) / (-B) = ( ) / ( -.76) =.75. The a priori probable deterioration code of a 3-year-old cladding in 5 years from now is % code a, 49% code b, 45% code c, 6% code d. Knowing that today, 3 years after construction, the cladding is at code c, the probability for code c in 5 years from now becomes 75% and for code d 25% (codes a and b are excluded). 3.5 Evolution of refurbishment investment budget After determining the present state and the quality subspace of an element, the a posteriori probability of having code a, b, c, or d for the 5 years that follow the diagnosis can be determined. With a number of random draws on the probability curves for the 5 elements (Monte-Carlo procedure) and calculating the cost for the resulting code combinations, we can obtain the probability distribution of the global refurbishment cost. t= t=5 Q B random number Fig. 6: Random number generation of the deterioration codes for the 5 years following diagnosis Every random number gives a deterioration code for each year for an element. With the costs corresponding to the codes, we calculate the global refurbishment cost of a random building situated in the sub-space {q, q2, q3,.q5} {Q, Q2, Q3,..Q5}. If a sufficient number of random buildings situated in the building quality subspace are drawn, the probability distribution of their refurbishment cost will approach the real probability distribution. Also the mean and the standard deviation of the cost distribution can be calculated. The minimum global cost on the curve can be interpreted as the refurbishment cost of elements with a long service life, i.e. good quality materials, protected location etc.

8 $ Year Fig. 7: Illustrative example of an expected curve of the evolution of the refurbishment investment budget 4 Conclusions The residual service life of building elements is an important piece of information for refurbishment decisions that should be economically as well as sustainable. In order to determine residual service life correctly the current deterioration state of the elements must be taken into account. It is also necessary to adopt a system with distinct classes to describe deterioration, and the classes should have a physical meaning which can be observed and distinguished in practice. The EPIQR qualitative deterioration codes a, b, c, d is an example of a tool which offers a good basis for the modelling of the degradation over time. MEDIC calculates the residual service life of a building element not as a deterministic unique value but as a probability distribution. To do so it combines a priori information collected on a large number of buildings with specific information on the examined building in order to calculate an a posteriori probability distribution with less dispersion. The residual service life of building elements is not only used as a decision criterion in refurbishment scenarios but is also an important factor in Life Cycle Analysis. The evolution of the global refurbishment cost of the building is valuable information for investment planning. It can help the owner of a single building to decide which is the most judicious moment to undertake refurbishment, or the owner of a large building stock to organise refurbishment operations and determine his short and long term financial needs.

9 5 References Genre J-L (995), MEBI - Méthode d'evaluation de Budgets d'investissements, LESO-PB, EPFL, Lausanne. Mayer P. et al., (995), Vieillissement des éléments de construction et coûts d entretien, Swiss Federal Office for Economic Policy, Program PI BAT, Zurich Mayer Paul, Kurt Christen, Financial Optimisation of the Time Interval between Renovation of a Building, ETH Zurich (to be published). Brandt, E., Wittchen, K.B., A. Faist, Genre, J-L. (998), EPIQR A new surveying tool for maintenance and refurbishment, Proceedings 8 th Conference on Durability of Building Materials and Components, Vancouver, Canada (to be published).