TREE BIOMECHANICS AND THE TRANSITION FROM JUVENILE … · Data for Bagassa: ONF Guyane 2016 . Properties of tree building material (result of xylem maturation: fibre cell wall thickening)

TREE BIOMECHANICS AND THE TRANSITION FROM JUVENILE TO

MATURE WOOD Bernard Thibaut, CNRS

IAWS ANNUAL CONFERENCE

PARIS, 2016, 1-3 JUNE

Wood Science for the Future

1

Juvenility in tree construction

• Juvenility regards the beginning of tree construction, when the tree is still young – Architectural juvenility for tree geometry

– Xylem juvenility for wood as building material • Two kind of juvenile behaviour are possible:

– Ontogenetic juvenility depending only on the ageing of buds and cambium – Environmental juvenility depending on the evolution of external constraints on tree

growth during the first ages

• Main aspects for structural tree biomechanics: – Flexure and buckling due to wind and self weight – Geometry of the structure and building material

• Growth and xylem maturation – Xylem growth = cell division + cell expansion (until the end of primary wall making).

Xylem growth contributes to tree geometry

– Xylem maturation = fibre cell wall thickening (until the end of secondary wall making). Xylem maturation contributes to properties of the building material

2

Geometry of the tree structure (result of xylem growth: cell division + cell expansion)

2 m

1 m

3 1

m

2

4 m

4

25 cm

1

5 c

m

5

Heuret et al 2003

2 – 3 – 4: Setting of the architectural model during juvenile phase

Geometrical parameters: - Height (H), Diameter at breast height (DBH) - Slenderness: H/DBH, taper, form factor - Crown height and diameter 3

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Sle

nd

ern

ess

(H/D

)

Diameter at breast height (cm)

OA

FD

FDg

BG

Juvenile growth in tropical forest

OA: dominated species (Oxandra a.) FD: 6 dominant species FDg: Tachigali & Goupia BG: Bagassa g. in plantation

Slenderness (H/DBH), adaption to growing context

4

Huge variations in observed slenderness associated with wind surface area (Aw) changes

Gambler H/D=200

Aw=1

Slender H/D=100 Aw=3,5

Quiet H/D=70 Aw=9,5

Super quiet H/D=36 Aw=27

Forest trees Prairie tree

Increasing available light and wind action

5

A simple model for trunk cylindrical growth

0

50

100

150

200

250

300

350

400

0 20 40 60

Sle

nd

ern

es

Ht/

DB

H


SG

G

S

Q

SQ

0

1000

2000

3000

4000

5000

6000

7000

0 20 40 60

Tota

l he

igh

t (c

m)


SG

G

S

Q

SQ

0

500

1000

1500

2000

2500

3000

3500

4000

0 20 40 60

Tota

l hei

ght

(cm

)


Douglas fir

Bagassa g.

Slender model

Model H(D)=a*(1-exp(-b*D)

a=6600 (asymptotic height in cm) Super gambler: b=0,054; H(6,7cm)=20m Gambler: b=0,036; H(10cm)=20m Slender: b=0,018; H(20cm)=20m Quiet: b=0,012; H(30cm)=20m Super: quiet b=0,006; H(60cm)=20m

2 parameters: a (Maximum height) and H(0)/D(0) (slenderness value at origin = a*b) 6

Data for Douglas Fir: N. Décourt 1967 Data for Bagassa: ONF Guyane 2016

Properties of tree building material (result of xylem maturation: fibre cell wall thickening)

l

r

t

MFA

Balsa: Density = 0,15 Swartzia: Density = 1,2

Density proxy of the ratio: wall thickness/cell diameter

0

20

40

60

80

100

120

140

0,00 0,50 1,00 1,50Co

mp

ress

ion

str

engt

h M

pa

Density g/cm3

Compression strength vs density

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 MFA °

Spe

cifi

c m

od

ulu

s 1

0 6

m2/s

2

Model Spruce

Scots pine Maritime pine

Specific modulus proxy of cell wall property in axial direction (linked to MFA and matrix chemistry)

7

Growth stresses & fibre maturation process

Step 1 Cell division creates a very soft new

xylem layer

Step 2 Maturation of fibres induces layer shrinkage (maturation strain) in L

direction while it stiffens

Step 3 Tensile forces created in the new layer are

equilibrated by compression in the core xylem

8

Tensile stress in the new xylem layer depends on maturation strain, density and specific modulus

9

Maturation strain is depending on MFA and chemistry (strongly different in reaction wood)

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

- 10 20 30 40 50

Normal wood

Tension wood

Compression wood

MFA °

Maturation strain µdef

MFA = 4°

MFA = 24°

Simarouba Data from 3 angiosperms and 3 gymnosperms

Juvenility in xylem properties

0

0,2

0,4

0,6

0,8

0 10 20 30

Bas

ic d

ensi

ty g

/cm

3

Radius cm

Basic density vs

radius for TRP

0

10

20

30

40

0 10 20 30

Spec

ific

mo

du

lus

Radius cm

Specific modulus vs

radius for TRP

0,0

0,2

0,4

0,6

0,8

1,0

0 5 10 15 20

Den

sity

g/c

m3

Radius cm

Density vs radius

0

5

10

15

20

25

30

0 5 10 15 20

Spec

ific

mo

du

lus

Radius cm

Specific modulus vs radius

Beech Beech TRP TRP

Typical radial pattern (Lachenbruch 2011) Typical pattern for European Beech (Slender type)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0 1 2 3 4 5

Den

sity

g/c

m3

Radius cm

Density vs radius

0

5

10

15

20

25

30

0 1 2 3 4 5

Den

sity

g/c

m3

Radius cm

Specific modulus vs radius

Oxandra a. understory species

Oxandra a. understory species

Typical pattern for an understory species in French Guyana (Gambler type) 10

Simple models for xylem properties (excluding reaction wood)

from different data bases: CTFT (Sallenave), Wood handbook (Kretschmann), Bridge project (Beauchêne), Reaction wood project (Gril) and papers on

growth stresses (Yamamoto and others)

• Compressive strength proportional to basic density

• Green density proportional to the power 0,52 of basic density

• MOE proportional to both basic density and specific modulus

• Maturation strain: linear variation with specific modulus

• Maximum flexure strain in flexion: linear variation with specific modulus

• Pre-stressing at trunk periphery proportional to maturation strain, basic density and specific modulus

11

Basic growth simulation

• 5 different types of geometrical growth (H/DBH varying from 33 to 330 for H=20m)

• Constant xylem properties (basic density and specific modulus)

• 3 different values of basic density from 300 to 900 Kg/m3

• 3 different values of specific modulus from 15 to 30 106*m2/s2

• Radial increment of 5mm

• Inclusion of tensile pre-stressing in the compressive strength limit

• Buckling safety factor using Greenhill theory

• Calculus of: – Dry biomass (DBM)

– Maximum flexure resistance (RCM)

– Ratio of resistance on biomass (RCM/DBM)

– Buckling safety factor (BSF)

12

Evolution of buckling security factor with diameter

There is a critical diameter at minimum buckling security factor (Sterk & Bongers 1998) This diameter is lower for very slender trees and BSF is higher for strong wood (high MOE)

For slender trees there is a rather large zone in juvenile phase with a security factor above 2 13

Q: quiet; S: Slender; G: Gambler; SG: Super gambler

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0 20 40 60

BSF

DBH cm

Buckling security factor (BSF) vs DBH

Q

S

G

SG

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0 20 40 60

BSF

DBH cm

Buckling security factor (BSF) vs DBH

Q

S

G

SG

Juvenile zone

Basic density = 600 Kg/m3

Specific modulus = 22*106 m2/s2

Standard wood

Basic density = 900 Kg/m3

Specific modulus = 30*106 m2/s2

Strong wood

0

500

1000

1500

0 0,5 1

Dry biomass vs basic density

Q

S

G0

50

100

150

200

10 15 20 25 30

Wind resistance related to dry

biomass vs specific modulusQ

S

G

0,5

1,0

1,5

2,0

2,5

3,0

10 15 20 25 30

Buckling security factor

vs specific modulusQ .9Q .6Q .3S .9S .6S .3G .9G .6G .3

Q: quiet; .9, .6, .3: basic density S: slender; .9, .6, .3: basic density G: gambler; .9, .6, .3: basic density

Slenderness (Q to G type) is by far the most influencing factor (reg. coeff. > 90%)

Within a type: -Dry biomass depends only on basic density -Resistance to wind relative to dry biomass depends only on specific modulus -Buckling security factor depends mainly on specific modulus but also on basic density

Main results from simulation on structural behaviour

14

Impact of typical radial pattern (TRP)

Buckling safety factor keeps close to 2 in the juvenile phase, with an improvement in other responses

0,0

1,0

2,0

3,0

4,0

5,0

0 20 40 60

Bu

cklin

g se

curi

ty f

acto

r

Diameter at breast height cm

Buckling safety factor vs diameter

S .6-22

S - TRP

0

20

40

60

80

100

120

140

160

0 20 40 60

WR

/DB

M


Wind resistance relative to dry biomass

S .6 - 22

S - TRP

S .6-22; FC

S - TRP; FC

050

100150200250300350400

0 5 10 15 20

Dry

bio

mas

s K

g


Dry biomas vs diameter at breast height

S .6-22

S - TRP

0

0,2

0,4

0,6

0,8

0 10 20 30

Bas

ic d

en

sity

g/c

m3

Radius cm

Basic density vs

radius for TRP

0

10

20

30

40

0 10 20 30

Spe

cifi

c m

od

ulu

s

Radius cm

Specific modulus vs

radius for TRP

15

FC: correction using tree flexibility (maximum elastic deflexion before damage

Growth stress results and impact of TRP

Compression failure index: ratio between growth stress and compressive strength at the centre. - Growth stress level depends both on radius, basic density and specific modulus. - The risk of compression failure grows both with diameter and specific modulus.

- TRP lowers the risk of compression failure

-120

-100

-80

-60

-40

-20

0

20

0 10 20 30

Gro

wth

str

ess

Mp

a

Radius cm

Growth stress vs radius

SM=30

SM=22

SM=15

SM=TRP0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0 20 40 60

CFI

Diametercm

Compression failure index (CFI) vs diameter

Série1

Série2

Série3

Série4

16

Conclusion

• Mechanical juvenility seems to be mainly adaptive

• The most important parameters in mechanical adaption are geometrical

• Slenderness (total height/diameter at breast height) of the young tree is a good indicator for adaption, its range is high, from 30 to 300

• Physical and mechanical properties are second order parameters

• Basic density combined to slenderness is the key for dry biomass at a given tree height

• Specific modulus (square of sound speed in dry wood) combined to slenderness is the key for wind resistance relative to dry biomass

• Both specific modulus and basic density combined to slenderness are keys for buckling security

• There is a critical diameter (minimum BSF), rather low for very slender trees which needs rather high values of basic density and specific modulus (Sterk & Bongers 1998)

• For usual slender forest trees, buckling risk is low in the juvenile phase

• Gradients in basic density and specific modulus in the juvenile phase:

– keeps buckling risk at reasonable value

– lowers dry biomass,

– Improves the resistance to wind relative to dry biomass

– Lowers growth stresses at heart and thus the risk of compression failure in trunk centre

17

Thanks for your attention

Aknowlegments

• Many results used to build the model come from recent Master (P. Tabarant) and PhD works (G. Jaouen, R. Lehnebach, J. Bossu) in EcoFoG laboratory (French Guyana) under the supervision of T. Alméras, J. Beauchêne, B. Clair, M. Fournier, P. Heuret or E. Nicolini.

• Many also come from long term systematic measurements of wood properties in Nancy (LERFOB) and Montpellier (CIRAD) associated to numerous projects concerning wood quality of often less known species and growth stresses in trees, thanks to J. Gérard, JM. Leban, F. Mothe or A. Thibaut

• Most of the ideas, theories and calculations come from the work of M. Fournier, J. Dlouha, G. Jaouen & T. Alméras (Journal of experimental botany 2013).

• I was inspired both by these recent works and by discussions with B. Gardiner, B. Lachenbruch and F. Telewski to try this general but simplistic approach.

19

H/D=200 H=0,2*H L=0,1*H

S=0,02pi*H2 1

Hv=0,9*h Mv=0,018*H3

1

H/D=100 H=0,4*H L=0,2*H

S=0,08pi*H2 4

Hv=0,8*h Mv=0,064*H3

3,55

H/D=70 H=0,6*H L=0,4*H

S=0,24pi*H2 12

Hv=0,7*h Mv=0,172*H3

9,55

H/D=36 H=0,85*H L=1,0*H

S=0,85pi*H2 42,5

Hv=0,575*h Mv= 0,489 *H3

27,15 20

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TREE BIOMECHANICS AND THE TRANSITION FROM JUVENILE … · Data for Bagassa: ONF Guyane 2016 . Properties of tree building material (result of xylem maturation: fibre cell wall thickening)