Multi-criteria analysis of rehabilitation techniques for traditional timber frame walls 1 in Pombalino buildings (Lisbon)

This research aims to evaluate the intervention techniques currently adopted for the 14 traditional timber frame wall, using a case study in downtown Lisbon. 15 Different rehabilitation solutions were identified and evaluated through a multi-criteria 16 decision analysis using dedicated software (M-Macbeth, Measuring Attractiveness by a 17 Categorical-Based Evaluation technique ). 18 Five evaluation criteria, i.e. material compatibility and permanence, structural reliability 19 and authenticity, and visual-tactile appearance, were selected for this specific context. A 20 multidisciplinary panel of experts in conservation science were consulted for defining the 21 performance descriptors, evaluation levels, and weightings of these criteria. 22 Results show that Macbeth is a useful decision-aid capable of handling multiple outputs 23 generated from qualitative expert judgments. Lastly, the predominance of five best-scoring interventions within three design-related scenarios is discussed.

Results show that Macbeth is a useful decision-aid capable of handling multiple outputs 23 generated from qualitative expert judgments. Lastly, the predominance of five best-scoring 24 interventions within three design-related scenarios is discussed. In the absence of a consistent European legislative framework, the authors referred to seven 149 types of seismic upgrades as defined by FEMA [25]. 150 The intervention sub-categories specified in Table 1 were evaluated by Coías [9] in 151 reference to the Pombalino buildings, taking into account budgetary and feasibility 152 constraints. Global structural strengthening (intervention strategy n.4) is recommended 153 when the components show inadequate ductility and strength to resist large lateral 154 deformation. As alternatives to strengthening and stiffening, mass reduction, seismic 155 isolation, and supplemental energy dissipation (1a, 5a, 5b) are not considered feasible for 156 this type of construction system. 157 Considering that extra floors in Pombalino buildings are fully integrated in the external 158 configuration of the original construction for a number of reasons (e.g. alignment of the 159 openings, roof/dormer geometry, architectural features), their demolition (1a) would incur a 160 loss of the architectural value of the building, as well as a reduction of floor area and 161 inconvenience to the users. This is also incompatible with the decision-makers' interests, 162 due to a considerable decrease in the financial value of the investment. 163 This research regards interventions for structural stiffening and strengthening in timber-164 frame walls (TF)(3a, 4a, 4b, 4c). Although conceived as a load-bearing structure that is 165 included in a composite system interlocked with other components, TF was analysed 166 independently from the timber joists and the external walls in order to focus attention on 167 specific interventions for this component. 168 This work regards TF determined as retrofittable through visual grading and non-169 destructive testing (NDT). As a precondition for being repaired or strengthened, the timber 9 framework will guarantee some residual capacity if the level of conservation, the effective 171 cross-section, and deformations are acceptable [20]. It should also be pointed out that all 172 interventions involve the removal of the surface finish, which should be preceded by a 173 detailed documentation of the pre-intervention status quo [18]. 174 A set of specific interventions was identified for each of the four sub-components: timber 175 framework, infill, joints, and surface finish (Fig. 3, Table 2). 176 Individual options identified for those sub-components were regrouped into 131 177 combinations, which were in turn divided into eleven groups according to the type of the 178 intervention on the wall structure (F+I)( Table 3).  In order to streamline the large number of possible combinations, the following separate 206 interventions are equated in Table 3: 207  F3a=F3b: due to comparable mechanical behaviour; 208  I1=I2a: different mechanical performances of these types of infill (brick or rubble 209 masonry versus clay bricks or roof tiles) are not significant, since both include 210 hydraulic lime mortar, which produces a similar response for the shear transfer 211 mechanism and dissipative capacity.  Macbeth was chosen by the authors for its ability to incorporate a large number of 232 preferences (or amount of subjective information) built through pairwise comparison 233 judgments [4]. It can thus be tailored in order to match the specific requirements of the 234 analysts, through a co-participative decision-making process. It also resolves contradictions 235 12 between interests of single actors or with inconsistent scores by providing a complete 236 ranking based on an additive aggregation approach [4]. 237 In this research, a panel of experts (i.e. chemists, architects, and timber engineers) judged 238 the performance of alternatives for each sub-component of the wall; this set of criteria-wise 239 performances was numerically ranked in terms of attractiveness. 240 Macbeth is a user-friendly tool, since it can deal with inconsistent judgments in the 241 pairwise comparison matrix and suggest solutions. This software is also intuitive, due to the 242 graphical user interfaces (e.g. thermometer), and interactive, due to the possibility of 243 analysing the sensitivity of every output based on variations of judgements, performances, 244 and scores or weights [4,5]. 245 However, this interactive model is time-consuming as it requires more questions than other 246 elicitation methods (e.g. the swing weighting), especially when dealing with a high number 247 of alternatives, criteria, and performance levels. Once the qualitative performance descriptors of each criterion were established (Table 4), 289 the experts determined the respective performance evaluation levels (high, moderate, low, 290 or very low)( Table 5), whose interval values were defined through Macbeth pairwise 291 questioning procedure. 292 In order to obtain numerical values, it was necessary to more clearly define the distances 293 involved between the various evaluation levels. These would vary for judgments about 294 different subcomponents. The experts defined the difference of attractiveness between two 295 levels of performance by selecting the most suitable adjective among seven semantic 296 categories included in the Macbeth method (no, very week, week, moderate, strong, very 297 strong, or extreme). 298 It was therefore possible to determine under the Material Compatibility criterion, for 299 example, that the difference in attractiveness between High and Moderate evaluations was 300 "very strong" in reference to Framework Infill and Joints, while when considering surface 301 finish the difference between High and Moderate was seen as "weak". These qualitative 302 expert judgments were translated into cardinal values by M-Macbeth (Figs. 4, 5). 303 The difference of attractiveness between the sub-components of TF was determined 304 through the same pairwise procedure for all criteria except for the visual-tactile appearance 305 (VTA). In fact, VTA is related only to the surface finish, and thus the evaluations were 306 performed directly for the whole wall (Fig. 7). 307 Additionally, the threshold between what constitutes repair versus strengthening measures 308 is proposed below by using the weighted assessment of the combinations in the SR 309 criterion. The threshold value (t r-s ) was determined by calculating the weighted average of 310 the evaluation level defined as "low" (EL p ) of the SR criterion, as shown in eq. 1: 311 where WF i is the weighting of each sub-type of intervention (rehabilitation technique) used 313 to determine each partial value score of the evaluation under SR criterion. 314 The result for t r-s can be rounded up to 30 (eq. 2): 315 where 41, 25, and 15 are the value scores of the evaluation level 'low' attributed 317 respectively to F+I, J, and S (Fig. 4), whereas 0.35, 0.55, and 0.10 are the weightings 318 respectively attributed to F+I, J, and S (Fig.6, Table 6, numbers in bold). 319 The next step of this analysis consisted of the assignment of a relative weight to each 320 criterion. This step involved setting up separate Macbeth models corresponding to three 321 design-related models (Fig. 8, Value tree). These are listed according in ascending order of 322 intrusiveness of the intervention, depending in turn on the degree of authenticity and on the 323 level of structural safety of the building (Table 7). 324 Finally, each scenario, to which the value scores of the options are associated, can be 325 selected by the decision-maker (building owner or users) on the basis of the state of 326 conservation of the building components (Table 7). 327 328 4. Results and discussion 329

A set of incomparability and consistency of pairwise evaluations 330
A set of incomparability, arising from possible diverging judgments of the experts on the 331 different criteria [1] can be identified, for example in relation to a pairwise comparison of 332 the global scores of material compatibility (MC) versus structural reliability (SR) (Fig. 9, 333 Table 8). In fact, the individual scores of these solutions reach the highest value for MC 334 and low values for SR. This reflects the different weightings attributed respectively by 335 timber engineers and by chemists (section 3.3) to the repair measures on the joints (J1a or 336 J1b) in the calculation of the global assessment for these criteria. When evaluating MC, the 337 intervention on the joints is weighted by a very low value (0.08), whereas it is weighted by 338 a high value (0.55) when referring to the structural reliability (Table 6). 339 Another incomparability arises in the case of lack of replacement of the infill (F1+I3, Table  340 3): in the set of solutions between TF58 and TF81, MC ranges from 86 to 79, whereas VTA 341 equals 11, as shown in Table 8 (left). 342 On the other hand, the evaluations of MC and of SA show consistent outputs (Table 8, left). 343

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The best-scoring solutions for MC also score the best for SA (e.g. TF01-TF03, Group 1). 344 However, this consistency is not found when the surface finish is made of cement mortar 345 (S1b), or of cement-based mortar with metal mesh and acrylic render (S2). In these cases, 346 the solutions achieve only moderate scores for SA, due to the low weighting (0.10) applied 347 to the surface finish under SA. Conversely, the low scores for MC result from the high 348 weighting attributed to surface finish (0.50)( Table 6). 349 350

Predominance of five best solutions in three selected scenarios 351
In order to provide a preliminary screening of the results, all combinations characterized by 352 a low global weighted score in all three scenarios (lower than 50) were discarded; 74 353 options were thus excluded from the following analysis. The high weighting of material compatibility (MC) in all scenarios (Table 7) results in the 363 best-scoring solutions all belonging to Group 1 (Figs. 9, 10). 364 The best set of solutions to adopt within these three selected scenarios is highlighted in 365 Table 9. 366 These five best-scoring solutions consist of similar interventions on timber framework, 367 infill, and surface, whereas they differ on four types of intervention for the joints. 368 Therefore, under the same interventions on the wooden components and surface finish, 369 additional criteria can be taken into account for the comparison of these best solutions, i.e. 370 the average costs and time required to repair or strengthen the joints.

Research limitations and forthcoming perspectives 383
The main limitations of this study regard different aspects: problem structuring, scope of 384 application, gaps in scientific understanding (or dissemination of experimental data) related 385 to the original components, and potential disconnect between the evaluation in theory and 386 the real result of the interventions (arising from questions of quality of workmanship). 387