Modelling the Material Resistance of Wood—Part 2: Validation and Optimization of the Meyer-Veltrup Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Meyer-Veltrup Model
2.2. Data Acquisition
2.3. Test Methods for Determining the Modifying Factors kinh and kwa
2.4. Evaluation Procedure and Model Fitting
3. Results and Discussion
3.1. Untreated Timber
3.2. Modified Timber
3.3. Preservative-Treated Timber
3.4. Model Fitting
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Wood Species | Common Name | Origin | References |
---|---|---|---|
Acer platanoides/A. pseudoplatanus | Norway maple/Sycamore | Europe | [18,30,31,32,33,34] |
Alnus glutinosa | Black alder | Europe | [18,31,34,35,36] |
Betula pendula/B. pubescens | Silver birch/Downy birch | Europe | [18,31,35,36] |
Dicorynia guianensis | Basralocus | S. America | [31,34,37,38,39] |
Fagus sylvatica | European beech | Europe | [15,18,19,31,32,33,34,35,36,39,40,41,42,43,44,45,46,47,48,49] |
Fraxinus excelsior | European ash | Europe | [18,19,31,35,36] |
Intsia bijuga | Merbau | Africa | [18,31,50,51] |
Lophira alata | Bongossi | Africa | [31,34,37,38,39,40,52,53] |
Peltogyne spp. | Amaranth | C. America | [30,34,38] |
Populus tremula | Aspen | Europe | [15,18,32,33,35,36] |
Quercus robur/Q. petraea | European oak | Europe | [15,18,19,30,31,34,35,36,38,39,40,41,43,44,46,49,52,53,54,55,56,57,58,59,60] |
Robinia pseudoacacia | Black locust | Europe | [18,31,34,36,39,49,52,53,57,61] |
Salix caprea | Goat willow | Europe | [18] |
Sorbus aucuparia | Rowan | Europe | [18,21] |
Tectona grandis | Teak | Asia | [18,31,34,35,36,38,39,62] |
Tilia cordata | Lime | Europe | [18] |
Ulmus glabra | Wych elm | Europe | [18,55] |
Wood Species | Common Name | Origin | References |
---|---|---|---|
Abies alba | Silver fir | Europe | [18,57] |
Juniperus communis | Juniper | Europe | [18,21] |
Larix decidua | European larch | Europe | [18,19,31,35,36,39,42,45,48,49,55,56,57,63] |
Larix sibirica | Siberian larch | Europe | [15,18,31,41,42,60,64,65] |
Picea sitchensis | Sitka spruce | Europe | [18] |
Pinus spp. | Southern pine sw | N. America | [18,33,61,66] |
Pinus radiata | Radiata pine sw | New Zealand | [18,31,34] |
Pinus sylvestris | Scots pine | Europe | [15,18,19,31,39,41,42,43,45,49,55,57,59,60,63,65,67,68] |
Scots pine sw | [18,19,31,33,34,39,41,42,43,45,48,49,56,57,61,63,68,69] | ||
Pseudotsuga menziesii | Douglas-fir | N. America, Europe, New Zealand | [15,18,31,34,38,39,40,42,43,45,57,59,63,70,71,72,73] |
Douglas-fir sw | [18,42,66,72] | ||
Thuja plicata | Western red-cedar | N. America | [15,18,30,31,39,58,63,71,73] |
Europe | [18,55] |
Wood Species | Common Name | Origin | Modification | References |
---|---|---|---|---|
Fagus sylvatica | European beech | Europe | HT | [19,48,74] |
Picea abies | Norway spruce | Europe | HT | [19,32,41,48,59,61,68,75] |
Pinus sylvestris | Scots pine | Europe | HT | [18,33,34,41,56,59,60,61,68,75,76] |
Fraxinus excelsior | European ash | Europe | OHT | [18] |
Picea abies | Norway spruce | Europe | OHT | [18,57] |
Pinus spp. | Southern pine sw | USA | AC | [18] |
Pinus sylvestris/P. radiata | Scots pine sw/Radiata pine sw | Europe/New Zealand | AC | [18,34,41,60,61,76,77] |
Acer platanoides | Norway maple | Europe | FA | [18,32,78] |
Pinus spp. | Southern pine sw | USA | FA | [18,32] |
Pinus sylvestris | Scots pine sw | Europe | FA | [18,60,79] |
Pinus sylvestris | Scots pine sw | Europe | DMDHEU | [18,24,34,76,80] |
Wood Species | Preservative/Treatment | References |
---|---|---|
Pinus sylvestris sw | CCA 2 kg/m3 | [18,61,65] |
CCA 4 kg/m3 | [18,32,33,41,76,79] | |
CCA 9 kg/m3 | [32,33,41,61,68,79] | |
Picea abies | Cu (II) sulphate low: 0.35% aqueous solution | [81] |
Cu (II) sulphate high: 1.4% aqueous solution | ||
CuEA low: 0.098% Cu; 0.51% EA | ||
CuEA high: 0.39% Cu; 2.05% EA | ||
CuEAOA low: 0.098% Cu; 0.51% EA; 0.07% OA | ||
CuEAOA high: 0.39% Cu; 2.05% EA; 0.29% OA | ||
CuEAOAQuat low: 0.098% Cu; 0.51% EA; 0.07% OA; 0.098% Quat | ||
CuEAOAQuat high: 0.39% Cu; 2.05% EA; 0.29% OA; 0.39% Quat | ||
BoronEAOAQuat low: 0.098% B; 0.51% EA; 0.07% OA; 0.098% Quat | ||
BoronEAOAQuat high: 0.39% B; 2.05% EA; 0.29 OA; 0.39% Quat | ||
Picea abies, Pinus sylvestris sw, Larix decidua | Cu (II) carbonate: 0.25%, dipping 8-h 1 and 24-h | [82] |
Cu (II) carbonate: 0.25%, vacuum 1 | ||
Cu (II) carbonate: 0.25%, vacuum + pressure | ||
Cu (II) carbonate: 0.5%, dipping 8-h1 and 24-h | ||
Cu (II) carbonate: 0.5%, vacuum | ||
Cu (II) carbonate: 0.5%, vacuum + pressure | ||
Pinus sylvestris sw | Metal-free organic | [18,32] |
Wood Species | kinh | kwa | vrel. | |||||
---|---|---|---|---|---|---|---|---|
br | wr | Soil | LWU | VU | WR | CWU | ||
Acer platanoides/A. pseudoplatanus | 2.54 | 0.94 | 1.02 | 0.80 | 1.14 | 1.07 | 1.02 | 0.90 |
Alnus glutinosa | 1.09 | 1.04 | 0.72 | 0.87 | 1.14 | 1.16 | 1.06 | 1.35 |
Betula pendula/B. pubescens | 1.01 | 0.93 | 0.88 | 0.76 | 1.16 | 1.33 | 0.36 | 0.95 |
Dicorynia guianensis | 15.30 | 16.54 | 5.11 | 1.43 | 1.35 | 1.25 | 1.06 | 0.19 |
Fagus sylvatica | 1.26 | 0.70 | 0.61 | 0.73 | 1.15 | 1.30 | 1.44 | 1.17 |
Fraxinus excelsior | 6.62 | 0.75 | 1.30 | 1.01 | 1.17 | 1.07 | 0.74 | 0.39 |
Intsia bijuga | 16.19 | 9.93 | 16.33 | 1.72 | 1.63 | 0.55 | 4.62 | 0.25 |
Lophira alata | 13.26 | 14.64 | 10.52 | 1.54 | 1.58 | 1.28 | 1.24 | 0.19 |
Peltogyne spp. | 16.48 | 18.00 | 5.11 | 2.41 | 1.31 | 2.17 | 1.39 | 0.25 |
Populus tremula | 1.24 | 0.99 | 0.94 | 0.91 | 1.13 | 1.09 | 0.65 | 1.04 |
Quercus robur/Q. petraea | 14.62 | 8.04 | 2.77 | 1.70 | 1.34 | 1.70 | 0.88 | 0.47 |
Robinia pseudoacacia | 12.20 | 12.34 | 2.67 | 2.67 | 2.15 | 1.24 | 1.65 | 0.24 |
Salix caprea | 1.37 | 1.16 | 1.46 | 1.16 | 1.36 | 0.85 | 0.60 | 0.50 |
Sorbus aucuparia | 1.27 | 1.25 | 1.46 | 0.94 | 1.00 | 1.07 | 0.44 | 0.56 |
Tectona grandis | 18.00 | 16.96 | 7.83 | 2.08 | 2.43 | 1.04 | 1.17 | 0.16 |
Tilia cordata | 0.89 | 1.04 | 1.39 | 0.92 | 1.43 | 0.83 | 0.38 | 0.86 |
Ulmus glabra | 7.33 | 1.12 | 1.66 | 1.14 | 1.31 | 0.91 | 0.49 | 0.39 |
Wood Species | kinh | kwa | vrel. | |||||
---|---|---|---|---|---|---|---|---|
br | wr | soil | LWU | VU | WR | CWU | ||
Abies alba | 1.33 | 1.22 | 1.24 | 0.91 | 1.09 | 0.96 | 0.68 | 1.14 |
Juniperus communis | 13.05 | 13.11 | 7.53 | 1.30 | 1.43 | 0.77 | 1.20 | 0.32 |
Larix decidua | 4.13 | 6.15 | 2.30 | 1.81 | 1.39 | 0.98 | 1.87 | 0.34 |
Larix sibirica | 3.32 | 1.55 | 4.86 | 1.01 | 1.30 | 1.05 | 0.46 | 0.45 |
Picea sitchensis | 1.09 | 1.82 | 1.14 | 1.17 | 1.03 | 1.03 | 3.92 | 0.86 |
Pinus spp. sw (Southern pine) | 2.38 | 10.88 | 0.87 | 0.89 | 1.01 | 0.69 | 0.58 | 0.76 |
Pinus radiata sw | 1.95 | 0.89 | 1.16 | 0.63 | 0.92 | 1.29 | 0.85 | 0.98 |
Pinus sylvestris | 2.98 | 6.85 | 1.86 | 1.06 | 1.21 | 0.89 | 1.37 | 0.47 |
P. sylvestris sw | 0.97 | 0.91 | 1.14 | 1.00 | 1.08 | 0.88 | 1.03 | 0.83 |
Pseudotsuga menziesii | 3.46 | 9.30 | 3.34 | 1.61 | 1.25 | 0.93 | 2.84 | 0.55 |
P. menziesii sw | 1.63 | 4.66 | 1.43 | 1.14 | 1.11 | 0.92 | 1.01 | 0.83 |
Thuja plicata (N.-America) | 16.73 | 11.67 | 2.63 | 1.13 | 1.61 | 0.59 | 0.27 | 0.42 |
T. plicata (Europe) | 18.00 | 11.10 | 1.31 | 0.78 | 1.29 | 0.81 | 0.56 | 0.35 |
Wood Species and Treatment | kinh | kwa | vrel. | |||||
---|---|---|---|---|---|---|---|---|
br | wr | Soil | LWU | VU | WR | CWU | ||
F. sylvatica—TM | 9.60 | 7.60 | 4.68 | 1.79 | 2.86 | 0.43 | 3.24 | 0.02 |
P. abies—TM | 8.67 | 4.95 | 2.98 | 6.99 | 2.09 | 6.44 | 1.40 | 0.34 |
P. sylvestris—TM | 8.74 | 9.72 | 5.36 | 1.87 | 1.80 | 1.70 | 1.47 | 0.53 |
F. excelsior—OHT | 18.00 | 9.71 | 11.79 | 1.99 | 2.91 | 0.60 | 1.60 | 0.07 |
P. abies—OHT | 18.00 | 18.00 | 9.66 | 1.73 | 2.35 | 0.51 | 0.88 | 0.16 |
Pinus spp. sw (Southern pine)—AC | 18.00 | 18.00 | 17.78 | 1.32 | 2.86 | 0.31 | 0.76 | 0.04 |
P. sylvestris P. radiata sw—AC | 18.00 | 18.00 | 16.69 | 1.57 | 3.01 | 1.43 | 1.28 | 0.07 |
A. platanoides—FA | 14.72 | 10.09 | 3.86 | 1.89 | 2.92 | 0.23 | 1.08 | 0.05 |
Pinus spp. sw (Southern pine)—FA | 10.88 | 12.67 | 6.54 | 1.73 | 2.23 | 0.40 | 1.45 | 0.12 |
P. sylvestris sw—FA | 18.00 | 18.00 | 7.53 | 2.79 | 3.30 | 0.23 | 1.54 | 0.27 |
Wood Species and Treatment | kinh | kwa | vrel. | |||||
---|---|---|---|---|---|---|---|---|
br | wr | Soil | LWU | VU | WR | CWU | ||
P. sylvestris, CCA, 2 kg/m3 | 18.00 | 18.00 | 5.12 | 0.92 | 0.97 | 0.87 | 2.49 | 0.10 |
P. sylvestris, CCA, 4 kg/m3 | 18.00 | 18.00 | 7.79 | 1.34 | 0.92 | 1.22 | 1.35 | 0.13 |
P. sylvestris, CCA, 9 kg/m3 | 9.66 | 18.00 | 11.87 | 0.83 | 1.02 | 0.88 | 1.02 | 0.06 |
P. abies, Cu (II) sulph. low | 6.75 | 10.37 | 1.82 | 0.90 | 0.80 | 0.97 | 1.04 | 0.69 |
P. abies, Cu (II) sulph. high | 8.77 | 10.54 | 2.66 | 0.89 | 0.77 | 1.31 | 0.81 | 0.63 |
P. abies, CuEA low | 7.13 | 8.94 | 2.37 | 0.88 | 0.90 | 1.28 | 0.94 | 0.61 |
P. abies, CuEA high | 8.00 | 7.15 | 2.00 | 0.97 | 0.92 | 0.90 | 1.10 | 0.65 |
P. abies, CuEAOA low | 6.48 | 8.80 | 1.72 | 1.04 | 0.98 | 1.16 | 0.91 | 0.11 |
P. abies, CuEAOA high | 7.34 | 6.12 | 1.98 | 0.98 | 0.93 | 1.06 | 1.50 | 0.57 |
P. abies, CuEAOAQuat low | 13.87 | 9.95 | 1.45 | 0.87 | 1.03 | 0.94 | 0.83 | 0.21 |
P. abies, CuEAOAQuat high | 16.42 | 7.78 | 1.84 | 0.90 | 1.10 | 0.75 | 1.16 | 0.01 |
P. abies, BorEAOAQuat low | 12.53 | 9.76 | 0.85 | 0.99 | 0.89 | 0.95 | 1.41 | 0.86 |
P. abies, BorEAOAQuat high | 13.00 | 8.30 | 0.88 | 1.08 | 0.75 | 1.08 | 4.28 | 0.61 |
P. abies, Cu 0.25%, dip. 8-h | 11.43 | 16.02 | 1.47 | 1.19 | 0.83 | 0.51 | 0.79 | 0.58 |
P. abies, Cu 0.25%, dip. 24-h | 13.71 | 18.00 | 1.71 | 1.17 | 0.74 | 0.78 | 0.71 | 0.46 |
P. abies, Cu 0.25%, vac. | 18.00 | 18.00 | 3.57 | 1.14 | 0.73 | 0.77 | 0.81 | 0.17 |
P. abies, Cu 0.25%, vac. + press. | 16.01 | 15.30 | 4.50 | 1.20 | 0.83 | 0.45 | 0.75 | 0.03 |
P. abies, Cu 0.5%, dip. 8-h | 13.76 | 18.00 | 1.54 | 1.21 | 0.81 | 0.36 | 1.01 | 0.39 |
P. abies, Cu 0.5%, dip. 24-h | 14.48 | 18.00 | 2.94 | 1.16 | 0.83 | 0.33 | 1.02 | 0.42 |
P. abies, Cu 0.5%, vac. | 15.35 | 15.25 | 3.18 | 1.25 | 0.80 | 0.32 | 0.97 | 0.13 |
P. abies, Cu 0.5%, vac. + press. | 15.19 | 15.07 | 3.60 | 1.29 | 0.72 | 0.45 | 0.88 | 0.15 |
P. sylvestris, Cu 0.25%, dip. 8-h | 13.27 | 10.20 | 1.39 | 1.31 | 0.90 | 0.36 | 4.96 | 0.16 |
P. sylvestris, Cu 0.25%, dip. 24-h | 13.69 | 11.08 | 2.38 | 1.34 | 0.88 | 0.30 | 1.86 | 0.09 |
P. sylvestris, Cu 0.25%, vac. | 18.00 | 18.00 | 2.01 | 1.28 | 0.80 | 0.53 | 2.64 | 0.09 |
P. sylvestris, Cu 0.25%, vac. + press. | 18.00 | 17.64 | 3.03 | 1.14 | 0.76 | 0.33 | 1.81 | 0.00 |
P. sylvestris, Cu 0.5%, dip. 8-h | 13.83 | 14.45 | 2.55 | 1.20 | 0.77 | 0.26 | 2.63 | 0.13 |
P. sylvestris, Cu 0.5%, dip. 24-h | 16.94 | 15.84 | 2.75 | 1.21 | 0.76 | 0.32 | 2.23 | 0.09 |
P. sylvestris, Cu 0.5%, vac. | 17.23 | 18.00 | 3.59 | 1.22 | 0.67 | 0.53 | 1.60 | 0.03 |
P. sylvestris, Cu 0.5%, vac. + press. | 15.49 | 17.34 | 3.28 | 1.22 | 0.65 | 0.37 | 2.73 | 0.00 |
L. decidua, Cu 0.25%, dip. 24-h | 11.94 | 11.58 | 1.03 | 2.10 | 0.85 | 0.54 | 15.49 | 0.00 |
L. decidua, Cu 0.25%, vac. + press. | 17.99 | 18.00 | 1.10 | 1.85 | 0.84 | 0.28 | 5.63 | 0.17 |
L. decidua, Cu 0.5%, dip. 24-h | 13.84 | 14.53 | 1.14 | 2.02 | 0.94 | 0.18 | 4.30 | 0.09 |
L. decidua, Cu 0.5%, vac. | 17.60 | 18.00 | 0.87 | 2.03 | 0.93 | 0.28 | 17.00 | 0.06 |
L. decidua, Cu 0.5%, vac. + press. | 14.78 | 14.00 | 1.32 | 1.73 | 0.76 | 0.19 | 4.42 | 0.20 |
P. sylvestris, metal-free organic | 18.00 | 18.00 | 2.41 | 0.85 | 1.05 | 0.78 | 0.48 | 0.09 |
kinh | kwa | ||||||
---|---|---|---|---|---|---|---|
LWU | VU | WR | CWU | Mean 1 | Min 2 | 1 3 | |
Soil | 0.133 0.218 (2) | 0.059 0.072 (4) | 0.000 0.202 (1) | 0.291 0.295 (14) | 0.168 0.202 (3) | 0.010 >0.015 (∞) | 0.110 0.166 (3) |
br:wr,Mean | 0.298 0.299 (26) | 0.255 0.267 (34) | 0.076 0.112 (38) | 0.369 0.375 (36) | 0.341 - | 0.138 0.172 (36) | 0.311 0.313 (26) |
Min 2 | 0.150 0.241 (2) | 0.073 0.087 (4) | 0.000 >0.002 (∞) | 0.376 0.381 (36) | 0.189 0.217 (3) | 0.018 >0.021 (∞) | 0.133 0.190 (3) |
Soil:no Soil,Mean | 0.288 0.291 (27) | 0.220 0.241 (35) | 0.045 0.081 (38) | 0.377 0.383 (36) | 0.337 - | 0.109 0.148 (37) | 0.311 0.314 (26) |
Mean 1 | 0.295 0.297 (26) | 0.238 0.255 (35) | 0.058 0.095 (38) | 0.376 0.381 (36) | 0.342 - | 0.122 0.160 (37) | 0.315 0.317 (26) |
1 3 | 0.295 0.297 (34) | 0.000 0.035 (1) | 0.209 0.258 (1) | 0.176 0.177 (16) | 0.094 0.097 (15) | 0.110 0.126 (1) | - |
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Brischke, C.; Alfredsen, G.; Humar, M.; Conti, E.; Cookson, L.; Emmerich, L.; Flæte, P.O.; Fortino, S.; Francis, L.; Hundhausen, U.; et al. Modelling the Material Resistance of Wood—Part 2: Validation and Optimization of the Meyer-Veltrup Model. Forests 2021, 12, 576. https://doi.org/10.3390/f12050576
Brischke C, Alfredsen G, Humar M, Conti E, Cookson L, Emmerich L, Flæte PO, Fortino S, Francis L, Hundhausen U, et al. Modelling the Material Resistance of Wood—Part 2: Validation and Optimization of the Meyer-Veltrup Model. Forests. 2021; 12(5):576. https://doi.org/10.3390/f12050576
Chicago/Turabian StyleBrischke, Christian, Gry Alfredsen, Miha Humar, Elena Conti, Laurie Cookson, Lukas Emmerich, Per Otto Flæte, Stefania Fortino, Lesley Francis, Ulrich Hundhausen, and et al. 2021. "Modelling the Material Resistance of Wood—Part 2: Validation and Optimization of the Meyer-Veltrup Model" Forests 12, no. 5: 576. https://doi.org/10.3390/f12050576