**"Ultrasound test for root wood elastomechanical characterization,"**

*BioRes.*13(3), 5818-5835.

#### Abstract

The objective of this study was to verify the applicability and preliminary results of an ultrasound methodology for the complete characterization of root wood. The tests utilized six species: *Swietenia macrophylla*, *Gallesia integrifólia*,* Swietenia sp., Schinus molle, **Handroanthus heptaphyllus*, and *Acrocarpus fraxinifolius*. The results show expected elastic ratios between properties, indicating that although the properties can differ numerically from roots and other parts of the tree, the orthotropic wood behavior is maintained. The root densities were higher than those reported in the literature for trunk wood, but direct relationships among high density and stiffness or strength properties were not observed. The ultrasound tests allowed 12 elastic constants of root wood to be obtained and were feasible for root dimensions because only one specimen was required.

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#### Full Article

**Ultrasound Test for Root Wood Elastomechanical Characterization**

Nina Maria Ornelas Cavalcanti,^{a} Raquel Goncalves,^{a,}* Sergio Brazolin,^{b }Cinthya Bertoldo,^{a} and Monica Ruy ^{a}

The objective of this study was to verify the applicability and preliminary results of an ultrasound methodology for the complete characterization of root wood. The tests utilized six species: *Swietenia macrophylla*, *Gallesia integrifólia*, Swietenia sp., Schinus molle, *Handroanthus heptaphyllus*, and *Acrocarpus fraxinifolius*. The results show expected elastic ratios between properties, indicating that although the properties can differ numerically from roots and other parts of the tree, the orthotropic wood behavior is maintained. The root densities were higher than those reported in the literature for trunk wood, but direct relationships among high density and stiffness or strength properties were not observed. The ultrasound tests allowed 12 elastic constants of root wood to be obtained and were feasible for root dimensions because only one specimen was required.

*Keywords: Ultrasound test; Static compression test; Wood root strength; Wood root stiffness*

*Contact information: a: Laboratory of Nondestructive Testing – LabEND, School of Agricultural Engineering, FEAGRI University of Campinas – UNICAMP, Campinas, Brazil; b: Center for Forest Resource Technologies, Institute for Technological Research – IPT, São Paulo, Brazil;*

** Corresponding author: raquel@feagri.unicamp.br*

**INTRODUCTION**

Roots are essential elements for the stability of trees and are important for biomechanical studies focused on tree risk analysis. However, few studies have focused on the physical, mechanical, and anatomical properties of roots. Fortunel *et al*. (2014), Amoah *et al*. (2012), and Vurdu (1977) are examples of these studies. This lack of research is primarily because of the difficulty of accessing roots and the lack of commercial interest (Fortunel *et al*. 2014; Lemay *et al*. 2018). Because of this knowledge gap, the properties of roots are generally assumed to be equivalent to those of the trunk; however, this assumption may be incorrect.

Root characteristics differ from trunk, stem, and branch characteristics in three main ways: geotropism, coating film, and branching mode (Drénou 2006). The geotropism of roots is positive (roots grow down), whereas the geotropism of stems is negative (stems grow up) (Drénou 2006). The film coating on all aerial organs of terrestrial plants is hydrophobic, and such films reduce the evaporation of water into the environment, thereby maintaining moisture in the tissues (Drénou 2006). Compared with the branching mode of the roots, a more regular branching shape is observed in the trunk; moreover, the meristem of the roots is influenced by external tension, while the trunk presents a single terminal meristem (Drénou 2006). In addition to the differences highlighted by Drénou (2006), there are several additional anatomical differences (Vurdu 1977; Fortunel *et al*. 2014). Characteristics of vessels, fibers, and parenchyma are examples of anatomical differences among root, branch, and stem in studies cited by Fortunel *et al*. (2014), while fiber length and proportions of elements (rays, longitudinal parenchyma, fibers, and vessels) are examples in the research presented by Vurdu (1977). Considering these aspects, the physical and mechanical properties of roots may also differ from those of trunks and branches. Additionally, even in the case of wood from the trunk, limited information is available on the mechanical properties of species used more frequently in urban areas because such species do not have commercial appeal.

Ultrasound techniques have been increasingly studied and applied in mechanical sorting applications, wood characterization and inspection (Brashaw *et al*. 2009), and for studying the acoustic tomography of trees (Arciniegas *et al*. 2014; Palma *et al*. 2018). The use of ultrasound in the characterization of wood has considerable advantages over conventional compression tests because only one specimen is required to obtain 12 elastic constants, whereas six specimens are required for compression tests (Gonçalves *et al*. 2014). This advantage is even more important in the case of urban trees because obtaining samples from such trees should only be performed when necessary and with the proper authorization. In addition, certain species of trees are very rare. In the case of roots, this question is even more complex because obtaining root specimen material is more difficult than obtaining trunk and branch specimen material, as the roots are underground.

Considering the importance and scarcity of data on root wood properties, the objective of this study was to verify the applicability and present the preliminary results of an ultrasound methodology for the complete characterization of root wood in six species.

**EXPERIMENTAL**

**Materials**

Root segments from *Swietenia macrophylla*, *Gallesia integrifólia*, Swietenia sp., Schinus molle, *Handroanthus heptaphyllus*, and *Acrocarpus fraxinifolius* were obtained during a micro-burst phenomenon that occurred in Campinas, São Paulo, Brazil, in June 2016. From each tree, a healthy root segment (without biodeterioration) corresponding to the lateral supporting root was identified immediately below the base of the trunk, as shown in Fig. 1. The root segments were placed in plastic bags and stored in a freezer to maintain the moisture content. From each root saturated segment, polyhedral and cubic specimens were cut and were placed in bags and stored in a freezer.

**Fig. 1.** Illustration of the root segment (a) and the measurement (b), root excavation for the removal process (c) to obtain ultrasonic (polyhedral, d) and static parallel (prismatic, e) specimens

The polyhedral specimens, with 26 faces and 50-mm edges (Fig. 1), were subjected to ultrasound tests. For the compression tests, the prismatic specimens, with dimensions corresponding to standard proportions (height = three times the edge of transversal sections), as indicated in the Brazilian Standard NBR 7190 (1997), were adopted. To facilitate the bonding of the strain gauges, a minimum nominal size of 30 mm × 30 mm × 90 mm was adopted whenever possible. The number of specimens acquired for the tests, as shown in Table 1, varied according to the availability of whole materials for the preparation process.

**Table 1.** Root Wood Sampling for Ultrasonic and Compression Tests

**Obtaining the Elastic Parameters of Root Wood by Ultrasound**

The complete characterization of root wood by ultrasound was performed using a methodology previously adopted by research groups (Gonçalves *et al*. 2014; Vázquez *et al*. 2015) for the characterization of timber. Using the ultrasound test, the elements of the stiffness matrix [C] were determined and inverted to derive the compliance matrix [S], which was then used to calculate 12 elastic parameters of the wood (three longitudinal moduli of elasticity, three shear moduli, and six Poisson ratios). For these calculations, the material was considered to be orthotropic. Equations 1 through 9 describe the relationships between the terms of the stiffness matrix (obtained by wave propagation methods) and the compliance matrix (obtained by static methods). The nomenclature is related to the symmetric axes of the wood with orthotropic behavior: 1 = longitudinal (L), 2 = radial (R), 3 = tangential (T), 44 = planes 2 and 3 (RT), 55 = planes 1 and 3 (LT), and 66 = planes 1 and 2 (LR),

C_{11} = C_{LL} = (1 – _{RT}. _{TR}). [E_{R}. E_{T}. S]^{-1 }(1)

C_{22} = C_{RR} = (1 –_{LT}. _{TL}). [E_{L}. E_{T}. S]^{-1 }(2)

C_{33} = C_{TT} = (1 – _{LR}. _{RL}). [E_{L}. E_{R}. S]^{-1} (3)

C_{12} = C_{LR} = (_{RL} + _{RT}. _{TL}). [E_{R}. E_{T}. S]^{-1} (4)

C_{13} = C_{LT} = (_{TL} + _{LR}. _{RT}). [E_{R}. E_{L}. S]^{-1} (5)

C_{23} = C_{RT} = (_{TR} + _{TL}. _{LR}). [E_{L}. E_{T}. S]^{-1} (6)

C_{44} = G_{RT} (7)

C_{55} = G_{LT} (8)

C_{66} = G_{LR} (9)

where *C* is the term of the stiffness matrix, is the Poisson ratio,* E* is the longitudinal modulus of elasticity (MPa), *G* is the shear modulus (MPa), and *S* = [ 1 – _{LR}. _{RL} – _{RT}. _{TR} – _{LT}. _{TL} – 2_{RL}. _{TR. TL}].

To obtain the diagonal of the stiffness matrix (*C*_{ij}), ultrasound wave propagation in the L, R, and T axes was used. For the first three terms of this diagonal, a longitudinal wave transducer was used because propagation and polarization must be in the same direction (LL, RR, and TT). To determine the terms *C*_{44}, *C*_{55}, and *C*_{66} (planes RT, LT, and LR, respectively), shear transducers were used because propagation must occur in one direction, and polarization must occur in a perpendicular direction. These six terms were obtained using general Eq. 10, which was deduced using the Kelvin-Christoffel tensor. The Christoffel equation (Eq. 10) allowed the relation of the elastic constants and the ultrasound propagation velocities that form the basis of ultrasound application studies to determine the properties of orthotropic materials,

*C*_{ii} = .*V*_{ii}^{2} (10)

where i = 1, 2, 3, 4, 5, and 6, is the material density (kg.m^{-3}), and *V* is the velocity of wave propagation (m.s^{-1}).

Equations 11 through 13 were used to obtain the three off-diagonal terms (*C*_{12}, *C*_{23}, and *C*_{13}). For this derivation, the wave had to propagate outside the symmetric axes, and quasi-longitudinal and quasi-transversal propagations were obtained,

(*C*_{12 }+ *C*_{66}) *n*_{1 }*n*_{2} = [(*C*_{11} *n*_{1}^{2} + *C*_{66} *n*_{2}^{2 }– *V* ^{2}) (*C*_{66} *n*_{1}^{2} + *C*_{22} *n*_{2}^{2} – *V*^{2})]^{1/2 }(11)

(*C*_{23 }+ *C*_{44}) *n*_{2 }*n*_{3} = [(*C*_{22} *n*_{2}^{2} + *C*_{44} *n*_{3}^{2 }– *V* ^{2}) (*C*_{44} *n*_{2}^{2} + *C*_{33} *n*_{3}^{2} – *V*^{2})]^{1/2 }(12)

(*C*_{13 }+ *C*_{55}) *n*_{1 }*n*_{3} = [(*C*_{11} *n*_{1}^{2} + *C*_{55} *n*_{3}^{2 }– *V* ^{2}) (*C*_{55} *n*_{1}^{2} + *C*_{33} *n*_{3}^{2} – *V*^{2})]^{1/2 }(13)

where is the propagation of the ultrasonic wave angle (outside the symmetry axes), *n*_{1} is the cos , *n*_{2} = sen e *n*_{3} = 0 when is considered with respect to axis 1 (Plane 12), *n*_{1} = cos , *n*_{3} = sen e *n*_{2} = 0 when is considered with respect to axis 1 (Plane 13), and *n*_{2} = cos , *n*_{3} = sen e *n*_{1} = 0 when is considered with respect to axis 2 (Plane 23).