Modelling the Material Resistance of Wood—Part 2: Validation and Optimization of the Meyer-Veltrup Model

: Service life planning with timber requires reliable models for quantifying the effects of exposure-related parameters and the material-inherent resistance of wood against biotic agents. The Meyer-Veltrup model was the ﬁrst attempt to account for inherent protective properties and the wetting ability of wood to quantify resistance of wood in a quantitative manner. Based on test data on brown, white, and soft rot as well as moisture dynamics, the decay rates of different untreated wood species were predicted relative to the reference species of Norway spruce ( Picea abies ). The present study aimed to but previously deﬁned maximum thresholds had to be adjusted (i.e., maximum values of factors accounting for wetting ability and inherent protective properties) to 18 instead of 5 compared to Norway spruce. As expected, both the enlarged span in durability and the use of numerous and partly very divergent data sources (i.e., test methods, test locations, and types of data presentation) led to a decrease in the predictive power of the model compared to the original. In addition to the need to enlarge the database quantity and improve its quality, in particular for treated wood, it might be advantageous to use separate models for untreated and treated wood as long as the effect of additional impact variables (e.g., treatment quality) can be accounted for. Nevertheless, the adapted Meyer-Veltrup model will serve as an instrument to quantify material resistance for a wide range of wood-based materials as an input for comprehensive service life prediction software.


Introduction
Service life planning and performance prediction of wood are mutually linked. The first comprehensive approaches were in the Australian TimberLife project [1] and in different European research projects such as WoodExter [2], WoodBuild [3], and DuraTB [4]. The latter proposed engineering guidelines accounting for exposure-and resistance-related parameters that can be captured in terms of a dosage, which is a well-defined relationship with a response such as the biological depolymerization of wood. Among the numerous wood-destroying organisms, decay fungi play a vital role globally, since their spores are ubiquitous and can infest wood even under extreme climatic conditions [5,6].
The material-inherent resistance of wood against wood-destroying fungi is the product of chemical ingredients with inhibitory effects on fungal activity (e.g., extractives) and its repellency to moisture. Both can originate either from the natural chemical constitution and anatomy of the wood tissue itself or from man-made improvement through cell wall modification, water-repellant, and/or preservative treatments. The resulting mode of protective action is usually a combination of wood's inherent resistance and its wetting ability.
The durability of wood and wood-based materials against wood-destroying fungi is usually tested through incubation with monocultures of basidiomycetes under sterile conditions in the laboratory or exposure in field tests with or without ground contact. The moisture content and temperature of wood are kept at a favorable level for most decay fungi under standardized laboratory conditions. Permanent wetting of the wood samples is provided by high aqueous-containing nutritious media such as malt agar (e.g., EN 113-2 [7]) or moist soil substrate in so-called soil-block tests (e.g., AWPA E10-16 [8]). Similarly, wood specimens that are buried to half of their length in soil-contact field tests (e.g., AWPA E7-15 [9] and EN 252 [10]) and in so-called semi-field tests performed with unsterile soil under laboratory conditions (terrestrial microcosms, e.g., ENV 807 [11]; CEN/TS 15083-2 [12], and AWPA E14-16 [13]) are permanently wet. Permanent wetting of test specimens may reduce the mode of protective action by leaching biocidal components. Moreover, this permanently wet condition poorly represents above-ground applications where the wood is exposed to cyclical wetting and drying. Under such conditions, the moisture performance of wood has a greater influence on service life. Wood materials that are low in biocidal components but exhibit high water-repellency, usually perform worse than expected compared with outdoor above-ground conditions where they can dry out and are consequently not constantly wet. Occasionally, this is called "torture testing" [14] since it does not necessarily reflect the anticipated use conditions. Above-ground field tests deliver durability data under quite realistic hazard conditions, but respective test data are sparsely available [15]. Numerous above-ground test methods have been reported, but very few are standardized [16]. Furthermore, they cover a wide range of above-ground use conditions representing different moisture-induced decay risks. In summary, the durability classification of wood rarely considers moisture performance. The European standard EN 350 [17]-at least in its current form-indicates that permeability to water should be considered. Permeability is defined as the "ease with which water penetrates a wood-based matrix (wood of a particular species, wood-based material) and is released by evaporation" [17]. Accordingly, the permeability to water and the rate of release can provide information relevant for wood's expected service life. However, guidance on the incorporation of this material property in the classification of biological durability of wood is still lacking, but essential for more accurately predicting the service life of timber structures.
Meyer-Veltrup et al. [18] approached predicting the service life of wood above-ground considering the combined effects of wetting ability and durability data. A comprehensive dataset was obtained from laboratory durability tests and still ongoing field tests in three different countries. In addition, four different wetting ability tests were performed with the same material. A dose-response concept was used to predict decay rates for specimens exposed above-ground using various indicating factors. The Meyer-Veltrup model was developed and optimized considering the resistance of wood to brown, white, and soft rot, as well as relevant types of water uptake and release.
Decay rates from above-ground field tests at different test sites in Norway were predicted with the model. In a second step, the model was validated using data from laboratory and field tests performed in Germany and Sweden. The model was next validated using data from laboratory and field tests by different authors [18][19][20]. Material resistance data were determined for additional wood species [21][22][23] and wood treatments [19,24].
The model was found to be fairly reliable and slightly conservative, and it had the advantage of being implemented into existing engineering design guidelines. Several reality checks revealed a sufficient model fit when linked with a climate exposure model and a decay prediction model [25], as reported for timber bridge structures [4]. However, Brischke et al. [26] reported that the general good fit of the Meyer-Veltrup model did not apply to preservative-treated wood or wood-based materials due to a lack of data on their inherent resistance and/or wetting ability. In addition, at the time, the optimized model did not include extremely durable materials. The most durable materials included in the original research were black locust, English oak, teak, and merbau [18]. The maximum value of modifying factors accounting for inherent protective properties (k inh ) and wetting ability of wood (k wa ) were set to 5.0 as this gave the best fit with above-ground field test data. The maximum threshold might need to be higher for preservative-treated and modified wood. On the other hand, further factors may help account for treatment quality, preservative concentration and retention, modification level, superficial treatments, and coatings. However, it is difficult to quantify these factors, though attempts have been made to model such factors [27].
This study aimed to collect data on the inherent protective properties and the wetting ability of wood to further validate and optimize the Meyer-Veltrup model for material resistance. The range of wood-based materials included preservative-treated and modified woods tested under laboratory and above-ground field conditions in different parts of the world. To better utilize existing durability test data generated in different parts of the world but using different reference wood species, factors for different resistance parameters determined in Part 1 of this publication were applied in this study.

The Meyer-Veltrup Model
A model approach according to Meyer-Veltrup et al. [18] was applied to predict the above-ground field performance of the examined timbers. The model includes both the climatic exposure and the resistance of the material. Acceptance for a chosen design and material was expressed as: The exposure was expressed as an exposure dose (D Ed ) determined by daily averages of wood temperature (T) and wood moisture content (MC). The material property was expressed as a resistance dose (D Rd ). The dose would be expressed in days (d) with optimum moisture and temperature conditions for fungal decay as (see [28] and Equation (2)).
where: D Ed is the exposure dose (d); D Rd is the material resistance dose (d).
The exposure dose D Ed depends on an annual dose at a specific geographical location and several factors describing the effect of driving rain, local climate, sheltering, distance from the ground, and design details. A detailed description of the development of the exposure module of the model is given by [3]. The present study focused on the resistance dose module of the model, which is the resistance, expressed as material resistance dose D Rd . The latter is the product of a critical dose D crit and two factors considering the wetting ability of wood (k wa ) and its inherent durability (k inh ). The approach is described by Equation (3) according to [28]: where: D Rd is the material resistance dose (d); D crit is the critical dose (d) corresponding to decay rating 1 (EN 252 [10]); k wa is a factor accounting for the wetting ability of the material (-) relative to a reference wood species; k inh is a factor accounting for the inherent protective properties of the material against decay (-) relative to a reference wood species.
The critical dose (D crit ) was evaluated for Scots pine sapwood and Douglas fir heartwood according to [28]. The critical dose corresponding to decay rating "1" was more or less independent from the wood species. Instead, differences between species and/or treatments were better expressed by their moisture dynamics and decay inhibiting properties. For Scots pine sapwood and Douglas-fir heartwood, the critical dose was around 325 days with favorable conditions for fungal decay [28], as previously determined in horizontal double-layer experiments performed at several locations in Europe for up to eight years [29].

Data Acquisition
Data on material resistance based upon laboratory and field wood durability tests and different wetting ability tests were gathered from scientific publications, research reports, and technical guidelines. In addition, raw data in terms of mass loss, decay ratings, or moisture-related characteristics were provided by the authors. Information about the materials included in this study is summarized in Tables 1-4 as well as the respective data sources used to calculate the modifying factors k wa and k inh , and decay rates in in-and above-ground tests are indicated in Tables 5-8. Results from the in-ground field tests were used to supplement laboratory tests when accounting for soft rot resistance to calculate the respective factor k inh .    Table 5. Factors accounting for the protective inherent properties (k inh ) and moisture performance (wetting ability, k wa ), and relative decay rate in above-ground field tests of untreated hardwood species. (br = brown rot; wr = white rot; LWU = liquid water uptake; VU = vapor uptake; WR = water release; CWU = capillary water uptake; v rel. = relative decay rate).  Table 6. Factors accounting for the protective inherent properties (k inh ) and moisture performance (wetting ability, k wa ), and relative decay rate in above-ground field tests of untreated softwood species. (br = brown rot; wr = white rot; LWU = liquid water uptake; VU = vapor uptake; WR = water release; CWU = capillary water uptake; v rel. = relative decay rate; sw = sapwood).  Table 7. Factors accounting for the protective inherent properties (k inh ) and moisture performance (wetting ability, k wa ), and relative decay rate in above-ground field tests of modified timbers. (br = brown rot; wr = white rot; LWU = liquid water uptake; VU = vapor uptake; WR = water release; CWU = capillary water uptake; v rel. = relative decay rate; TM = thermal modification; OHT = oil-heat treatment; AC = acetylation; FA = furfurylation; DMDHEU = treatment with 1.3-dimethylol-4.5-dihydroxyethyleneurea).  Table 8. Factors accounting for the protective inherent properties (k inh ) and moisture performance (wetting ability, k wa ), and relative decay rate in above-ground field tests of preservative-treated timbers. (br = brown rot; wr = white rot; LWU = liquid water uptake; VU = vapor uptake; WR = water release; CWU = capillary water uptake; v rel. = relative decay rate; CCA = chromated copper arsenate; Cu = copper; EA = ethanolamine; OA = octanoic acid; Quat = quaternary ammonium compounds; P.s. = Pinus sylvestris; P.a. = Picea abies; L.d. = Larix decidua).

Test Methods for Determining the Modifying Factors k inh and k wa
Meyer-Veltrup et al. [18] determined the modifying factors k inh and k wa on the basis of different laboratory durability test methods against brown, white, and soft rot-causing fungi and different moisture performance tests accounting for liquid water uptake during submersion, water vapor uptake at high relative humidity (RH), desorption tests at low RH (approx. 0%), and capillary water uptake (CWU) of end-grain surfaces. The test protocols are described in detail in Part 1 of this publication [83]. In each case, the reference wood species was Norway spruce (Picea abies). This study enlarged the pool of datasets and also included results where Scots pine sapwood (Pinus sylvestris) and European beech (Fagus sylvatica) were used as reference species. Factors accounting for the relationship between the material resistance and its respective components for the three reference species were applied as described in Part 1 [83] of this publication. In addition to standard basidiomycete tests with brown and white rot fungi (e.g., EN 113-2 [7]) and soil contact soft rot tests under laboratory (e.g., ENV 807 [11]) and field conditions (e.g., EN 252 [10]), results from basidiomycete mini-block tests [84] were considered. Results from submersion and floating tests according to CEN/TS 16818 [85] were considered for calculating k wa factors in addition to the tests described in Part 1 [83].
A decay rating of specimens in and above-ground was performed regularly (usually once per year) with the help of a pick test. The depth and distribution of decay were determined and rated using the five-step scheme according to EN 252 [10] as follows: 0 = sound, 1 = slight attack, 2 = moderate attack, 3 = severe attack, and 4 = failure. Some studies used the American and/or Australian rating system (10 to 0), which were transformed to the EN 252 scale as suggested by Stirling et al. [88].
The normal process requires that all specimens of a specific material must have reached decay rating 4 to determine mean lifetime. This was not the case for all materials. Therefore, the mean decay rate v mean was calculated according to [18] as follows (Equation (4)): where: v mean is the mean decay rate of specimens (a −1 ); v i is the decay rate of single specimens (a −1 ); R is the decay rating according to EN 252 [10]; t is the exposure time (a); n is the number of replicate specimens (-). For further modeling, a relative decay rate was calculated with Norway spruce as a reference species (Equation (5)) to become independent of the respective test location and test method. When other wood species than Norway spruce were used as reference, species-or genus-specific factors were established for correcting the values according to the relationships between reference species and Norway spruce.
where: v rel. is the relative decay rate (-); v species x is the decay rate of species x (a −1 ); v reference is the decay rate of a reference, here: Norway spruce, (a −1 ).

Evaluation Procedure and Model Fitting
Negative mass losses (ML), i.e., mass gains, in laboratory decay tests were considered to be equal to zero for further calculations. To avoid unrealistically high relative values (factors), a threshold (Thr) was set to 18.0 for both factors, leaving the values in the following range: 0 < k wa ≤ Thr and 0 < k inh ≤ Thr according to the best fit of the model based on the method of least squares.
The above-ground performance of wood was the target measure in this study. Performance was quantified by calculating the resistance dose (D Rd ) according to Equation (3) above, averaged for all available datasets per material (Tables 5-8), and used for optimizing the resistance model using a power regression function and the method of least squares.
To identify the most suitable indicators, different factors and factor combinations (based on results from the wetting ability and durability tests) were used to correlate the relative resistance dose D Rd,rel. (Equation (6)) with the relative mean decay rate (v rel. ). Therefore, both measures were set relative to the reference species Norway spruce. To calculate k inh from laboratory basidiomycete tests (Equation (7)), ML was factorized and either used as mean of ML caused by brown and white rot (br:wr,mean) or as worst case, i.e., the maximum relative ML representing white, brown, and soft rot, and exposure to soil, and thus the minimum k inh (min). Factors obtained in laboratory soil bed tests and in-ground field tests were averaged or k inh was calculated from soft rot tests with soil contact (k inh,soil ). D Rd, rel. = D Rd, species x D Rd, re f erence (6) where: D Rd,rel. is the relative resistance dose (-); D Rd,species x is the resistance dose of species x (a −1 ); D Rd is the resistance dose of the reference, here: Norway spruce, (a −1 ).
where: k inh is the factor accounting for the inherent protective properties of the material against decay (-); k inh,soil, i is the factor accounting for the inherent protective properties of the material against decay in tests with soil contact (-); k inh,non-soil, j is the factor accounting for the inherent protective properties of the material against decay in tests without soil contact (-); n is the number of tests.

Untreated Timber
The results from the different moisture performance and durability tests are given in Tables 5-8 and are expressed as factors k wa and k inh . The results differed markedly between wood species, treatments, and test methods. The factor accounting for protective inherent properties k inh varied among the hardwoods between 0.61 (beech, soil) and 18.0 (Amaranth, white rot, and teak, brown rot, Table 5), i.e., the Thr for both factors, k inh and k wa (see Section 2.4. Evaluation Procedure and Model fitting). The factors accounting for moisture performance (wetting ability, k wa ) showed less variation, i.e., between 0.38 (lime, CWU) and 2.43 (teak, liquid water uptake (LWU)). Similarly, k inh varied more than k wa among the softwood species (Table 6).
The relative decay rate (v rel. ) was between 0.16 (teak) and 1.35 (alder) among the hardwoods and between 0.32 (juniper) and 1.14 (silver fir) among the softwoods. The wider range in biological durability of hardwood species compared to softwoods is consistent with previous reports [15,89].

Modified Timber
In general, both factors, k inh and k wa , of differently modified timber were higher compared to respective untreated wood species and showed lower v rel. in above-ground durability tests ( Table 7). The factor k wa varied between 0.43 and 3.24 for heat-treated beech, which also showed the lowest v rel . In contrast, thermally modified Norway spruce and Scots pine also showed rather high k inh (2.98-9.39), but suffered from comparatively high v rel. , i.e., 0.34 and 0.53, respectively. The latter might at least partly be explained through the increased brittleness of thermally modified wood [89], which can be mistaken for fungal decay, since the effect of high temperatures and brown rot decay on wood's structural integrity is very similar [90,91]. Thus, the severity of fungal decay in thermally modified wood can easily be overestimated.

Preservative-Treated Timber
The preservative-treated timbers generally showed high k inh values, often close to or at Thr = 18.0. In contrast, the wetting ability factors were at least partly negatively affected by the treatments. In particular, many copper-treated woods showed low k wa values in desorption tests, i.e., 0.18 at minimum, which can be explained by increased sorption of wood after impregnation with aqueous salt solutions [92] and by the presence of quaternary ammonium compounds. These chemicals are known as surfactants and can therefore lower the surface tension between treated wood and water [93].
The summary table suggests that k inh is dependent on the wood species (i.e., initial durability, permeability), the type and concentration of the wood preservative, and the impregnation process (Table 8). Furthermore, one needs to consider the type of decay and respective test fungi, such as copper-tolerant brown rot fungi, which make co-biocides play an important role in copper-containing preservatives [94]. This became particularly evident for wood treated with preservatives containing only copper as the active ingredient. In addition, the unexpectedly high v rel. might be attributed to the leaching of active ingredients such as boron, which led to high k inh values in laboratory tests without pre-aging.
Copper-based treatments are generally effective in the laboratory against fungal monocultures. Even shell treatments can be sufficient to prevent hyphal penetration to the central part of the specimens. However, surface cracks are formed when larger specimens are exposed outdoors, which enables access to the specimen core by decay fungi. In addition, leaching of active ingredients contributes to the higher susceptibility of wood to decay as well. However, copper mobility has also been shown to protect checks that expose untreated wood from the germination of basidiospores from copper-tolerant fungi [95,96]. Copper-ethanolamine-treated wood was considerably less effective against soft rot fungi than CCA-treated wood. On the one hand, this is likely the result of increased copper leaching during exposure to terrestrial microcosm. Up to 80% of the copper from the specimens is leached during such tests due to humic acids in compost soil and other acids excreted by fungi and bacteria [97]. On the other hand, arsenic also serves as an efficient co-biocide against soft rot fungi.

Model Fitting
The most suitable factors and factor combinations, respectively based on results from the wetting ability and durability tests, can be extracted from Table 9 where the coefficients of determination R 2 for the various combinations are summarized. One of the best fits (R 2 = 0.336; Figure 1c) between v rel. (Equation (5)) and the relative resistance dose (D Rd , rel ) (Equation (6)) was achieved by using the mean value of the four k wa factors multiplied with the k inh factors based on soil contact tests and k inh factors based on non-soil contact tests weighted equally (Equation (7)). This pair of factors led to the best fit already in the initial material resistance model presented by Meyer-Veltrup et al. [18]. However, the fit itself was poor and a slightly better fit (R 2 up to 0.376) was reached when k wa was calculated based on CWU data and combined with k inh , either based on mean, minimum, or equally weighted values from soil and non-soil tests. However, the latter was mostly attributed to a series of tests performed with softwood species treated with different copper systems (Table 8); these showed highly varying CWU and thus contributed to higher prominence of a relationship between the relative D Rd and v rel ., which as such was only poorly fitted (see Figure 1b). Relationship between calculated relative D Rd and relative mean decay rate of specimens exposed in various above-ground field tests. The basis was 30 untreated timbers (a), 45 modified and preservative treated timbers (b), and both groups together (c). The k inh factors based on soil contact tests and those based on non-soil contact tests (i.e., monocultures of brown and white rot fungi) were weighted equally; k wa factors of all wetting ability tests were weighted equally. Table 9. Coefficient of determination R 2 for the relationship between the relative resistance dose D Rd and the relative mean decay rate (v rel. ) in above-ground durability tests. D Rd was calculated based on different combinations of factors accounting for protective inherent properties (k inh ) and moisture performance (wetting ability, k wa ) using data from the references provided in Tables 5-8. First line: R 2 at a threshold of 17, second line R 2 with the threshold in brackets that gave the best fit. (br = brown rot; wr = white rot; LWU = liquid water uptake; VU = vapor uptake; WR = water release; CWU = capillary water uptake). In contrast to the differently treated materials, a good fit between relative D Rd and v rel. was observed for the untreated timbers (R 2 = 0.823) at a threshold for k inh and k wa of Thr = 3. Meyer-Veltrup et al. [18] only used untreated wood for the initial model which had an even better fit (R 2 = 0.912), but covered a smaller range of durability. In this study, several very durable tropical hardwood species were considered, such as Bongossi, Amaranth, merbau, Basralocus, and teak. Furthermore, a larger variety of data sources representing different test methods, test locations, and inspection and assessment techniques were considered and helped explain that both D Rd and v rel . scatter more compared to the previous model. However, the model was robust even when including several very durable wood species from a variety of data sources (R 2 = 0.823).

Conclusions
The Meyer-Veltrup model predicts relative decay rates (v rel. ) based on a material resistance dose representing the inherent protective properties of wood and its wetting ability. The optimized Meyer-Veltrup model presented in this paper produced reliable decay rate estimates for a range of new species and treatments. However, the predictive power of the model was stronger for untreated than for modified and preservative-treated wood. Both modified and treated wood add influence factors to the model, such as type and concentration of the preservative, varying levels of treatment intensity (e.g., weight present gain or treatment temperatures), process conditions, and an increased variability within and between treatment batches. It is assumed that material-and treatment-specific parameters of water-repellant treated and coated wood will also affect the reliability of the model. To further increase the accuracy and fit of the model, more data are needed, which should: (1) match laboratory indicators and field performance, and (2) cover further parameters, which are specific for treated wood and were lacking (i.e., unavailable) in the recent study.
Assessing data quality remains a major challenge when utilizing test data, especially for treated material. Due to the lack of directly matched data for a specific material, it is unavoidable to group sets of data that are similar but still show some discrepancies. In Part 3 of this paper [98], we will utilize the presented modeling approach and provide estimates of relative decay rates based on: (1) above-ground field tests at many different locations, and (2) relative D Rd values from an intensive global survey on durability data. Author Contributions: G.A. and C.B. were mainly responsible for the conceptualization, methodology used, data evaluation, data validation, and formal analysis. Investigations and data curation were conducted by all authors. The original draft of this article was prepared by C.B. who was also responsible for the review and editing process of this article. C.B. provided the visualization. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement:
The entire set of raw data presented in this study is available on request from the corresponding author.