# Scaling the Roots Mechanical Reinforcement in Plantation of Cunninghamia R. Br in Southwest China

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Selection of Trees and Roots Sampling

#### 2.3. Soil Properties

^{o}and a cone mass of 76 g. The soil density at field moisture content was determined by performing a modified Proctor’s test [34]. Further, the sieved sample’s grain size fraction was evaluated using a laser particle size analyzer. The gradation curve for soil samples is shown in Figure 2. The physical properties of the collected soil at the selected trees are given in Table 2. The average depth of the humus layer was 5 cm at the selected tree locations.

#### 2.4. Excavation Methodology and Measurement of Root Traits

- The area under the crown of the candidate’s trees for excavation was properly cleaned. All the shrubs and other loose materials were removed.
- An excavation zone for each tree was established with a different diameter ranging between 2.70 m to 3.0 m (boundary marked with red color, Figure 3a).
- The sub-zones dimension was decided by ground slope conditions, tree stem diameter, and distribution of roots. On average, the length of one subzone in the horizontal direction was 20 cm. The excavation zones were carefully marked on the ground with white chalk powder.
- After marking the excavation area, incremental step by step excavation of the sub-zones was done both lateral and in the vertical direction. During excavation, the roots of the shrubs were removed with the excavated soil as the stem of all the shrubs were cut down during the surface cleaning process. Further, the texture of the roots facilitated us whether it belonged to the shrubs or selected tree.
- For each vertical excavation, 10 cm increments were selected below the ground surface until the roots maximum growth depth was reached. In each excavated zone, the roots, which were protruding from the vertical profile (a × h Figure 3b), were counted, and the diameter of each counted root was measured using a digital Vernier caliper. Only those roots were considered, which were in the cross-sectional area (a × h (Figure 3b)), assuming all these roots play a role in providing additional root cohesion. If a root was branched inside the excavated area, the branched roots were not counted, as only the roots crossing the cross-sectional area (a × h) will play a role in root cohesion at that profile [36]. From these roots counting and roots diameter, the roots area (${\mathrm{A}}_{\mathrm{r}})$ was calculated. This ${\mathrm{A}}_{\mathrm{r}}$was used in equation −1 to calculate the roots area ratio (RAR). This calculation of RAR is consistent with the study of [7,18].
- Once the excavation for the vertical increment of 10 cm was completed, all the roots in this trench were cut down and properly bagged in plastic bags for roots biomass calculations before starting excavation for the next 10 cm in the same subzone.
- After excavation of the topsoil layer to a depth of 10 cm (Figure 3b), the next excavation was carried out 10 cm deeper with excavation in the lateral direction unchanged.
- For all the tree excavations, they were carried out in the upslope direction. The orientation of the tree roots was generally upslope and increased soil stability [37]. However, the trees developed different root architecture systems on different sides [38]; therefore, excavation was performed on the same side for all the trees for consistency in result comparison.

#### 2.5. Developing Indices for Root Architectural System

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#### 2.6. Root Tensile Strength

^{®}Servohydraulic Test Systems (MTS Systems Corporation, Eden Prairie, MN, USA) at Southwest Jiaotong University, Chengdu, China (Figure 4). The machine used 3 main systems to perform the test (1) generation of traction force by the hydraulic system, (2) displacement and load measurement, and (3) acquisition of data. All the roots were tested at a strain rate of 10 mm/min. During testing, some roots samples failed by pulling out from the resin reinforcement, and some failed near the clamps. Such results were discarded, and only those tests in which the sample break near the middle was accepted and used for data analysis. The average rate of success for tensile tests was 53%. The reason for such a low rate of success was the pull out of roots from the resin during tests, in addition to the breakage of the root near the clamp. As in some samples, the bond between the root and resin was not developed properly. Further, in some root samples, the resin was broken by the clamping system of the machine. Similar issues in root tensile testing were also reported by Nilaweera and Nutalaya [41] and Bischati et al. [20]. The maximum tensile force to break the root (${\mathrm{f}}_{\mathrm{max}}$) was obtained from the test, while the tensile strength (${\mathrm{t}}_{\mathrm{r}}$) was calculated as proposed by Bischetti et al. [20].

#### 2.7. Root Additional Cohesion

#### 2.8. Statistical Analysis

^{2}and p-value were calculated to show the goodness of fit, considering a significance level of 0.05. The Kolmogorov–Smirnov’s (K.-S.) test was applied to confirm the homogeneity and normality of the variance using a significance level of 0.05. The data of roots distribution, roots area ratio, roots biomass, and roots cohesion were analyzed using analysis of variance (ANOVA) tests with pairwise Tukey’s Studentized test to determine the variation between the selected trees according to distance from the tree and depth. To evaluate the differences in tensile strength of roots and the number of roots between the investigated trees, analysis of covariance (ANCOVA) with HSD (honestly significant difference) was applied. The values were presented as mean value ± standard error.

## 3. Results

#### 3.1. Roots System and Spatial Distribution of Roots

#### 3.2. Distribution of Root Indices with Depth

^{3}(tree stem diameter = 468 mm) to 0.00068 roots/cm

^{3}(tree stem diameter = 220 mm), in the second layer (20–30 cm) this value ranged from 0.0012 roots/cm

^{3}(tree stem diameter = 468 mm) to 0.0007 roots/cm

^{3}(tree stem diameter = 220 mm); in the third layer (20–30 cm) this value was from 0.0011 roots/cm

^{3}(tree stem diameter = 468 mm) to 0.0004 roots/cm

^{3}(tree stem diameter = 220 mm), in the fourth layer (30–40 cm) this value ranged from 0.00083 roots/cm

^{3}(tree stem diameter = 468 mm) to 0.0005 roots/cm

^{3}(tree stem diameter = 450 mm), while in the deepest layer (40–50 mm) this value was 0.0007 roots/cm

^{3}(tree stem diameter = 450 mm). Similarly, the variability of roots biomass along with depth was also quite large. The RB was more in the top 10 cm, and after that, the decrease of biomass for all investigated trees was significant. The value of maximum biomass was observed as 0.0049 g/cm

^{3}(tree stem diameter = 468 mm).

#### 3.3. Distribution of Root Indices with Horizontal Distance from the Tree Stem

#### 3.4. Root Tensile Strength

_{r}) and root diameter is shown in Figure 9. The mean root tensile strength for 220 mm diameter tree was 11.8 ± 2.1 MPa, for 320 mm diameter tree was 14.1 ± 2.4 MPa, for 450 mm diameter tree was 15.9 ± 2 MPa, and for 468 mm diameter tree was 19.9 ± 2.2 MPa. A significant decrease was observed in the tensile strength of the roots with an increasing root diameter (Table 4), such as from 40 MPa (0.76 mm diameter root) to 3 MPa (9.98 mm diameter root) for 220 mm tree diameter, 107 MPa (0.5 mm diameter root) to 3 MPa (9.81 mm diameter root) for 320 mm tree diameter, 77 MPa (0.6 mm root diameter) to 5 MPa (9.98 mm root diameter) for 450 mm diameter tree, 70 MPa (0.67 mm root diameter) to 6 MPa (8.53 mm root diameter) for 468 mm diameter tree. The observed relationship attributes to the variation in the structure of the roots because coarse roots have relatively less cellulose content per unit mass compared to fine roots [49].

_{r}= 20.369d

^{−0.522}(R

^{2}= 0.37, p < 0.001) for 220 mm diameter tree, t

_{r}= 26.47d

^{−0.636}(R

^{2}= 0.47, p < 0.001) for 320 mm diameter tree, t

_{r}= 28.933d

^{−0.644}(R

^{2}= 0.52, p < 0.001) for 450 mm diameter tree and t

_{r}= 30.639d

^{−0.522}(R

^{2}= 0.36, p < 0.001) for 468 mm diameter tree. The maximum tensile force (F

_{max}) obtained from the tensile test showed the trend of increase with increasing root diameter. The power-law regression method was used for fitting the positive correlation between F

_{max}and root diameter (d), which gives F

_{max}= 18.89d

^{1.3644}(R

^{2}= 0.80, p < 0.001) for 220 mm diameter tree, F

_{max}= 15.98d

^{1.4776}(R

^{2}= 0.82, p <0.001) for 320 mm diameter tree, F

_{max}= 22.71d

^{1.3588}(R

^{2}= 0.83, p < 0.001) for 450 mm diameter tree and F

_{max}= 24.05d

^{1.4775}(R

^{2}= 0.81, p < 0.001) for 468 mm diameter tree. The roots tensile data and correlation developed showed that increase in tree stem diameter from 220 mm to 468 mm resulted in an average increase in root tensile resistance of 33%.

#### 3.5. Variation of Root Cohesion with Depth

_{r}was observed in the top 20 cm layer. Below this depth, the c

_{r}value decreased with the depth significantly. This decline in c

_{r}with depth and stem diameter was also reported by other studies [4,20,23,53,54].

_{r}) value in the first layer (0–10 cm) for the selected trees was observed as 78 KPa (tree stem diameter = 468 mm) to 42 kPa (tree stem diameter = 220 mm), while this value in the second layer (10–20 cm) ranged from 77 kPa (tree stem diameter = 468 mm) to 39 kPa (tree stem diameter = 220 mm), in the third layer (20–30 cm) this ranged from 44 kPa (tree stem diameter = 468 mm) to 12 kPa (tree stem diameter = 220 mm), in the fourth layer (30–40 cm) it was 14 kPa (tree stem diameter = 468 mm) to 5 kPa (tree stem diameter = 220 mm), while in the deepest layer (40–50 cm) it was from 16 kPa (tree stem diameter = 468 mm) to 9 kPa (tree stem diameter = 450 mm).

#### 3.6. Variation of Root Cohesion with Horizontal Distance from the Tree Stem

_{r}) and FBM (c

_{fbm}), showed a decrease significantly with the distance from the tree stem (Figure 11). The value of the root cohesion was high in the lateral distance of 60 cm from the tree stem, and after that, this value decreased significantly. The average maximum value of root cohesion for the tree with a stem diameter of 468 cm was 155 kPa at a distance of 20 cm, for the tree with a stem diameter of 450 mm, this value was 118 kPa at a distance of 60 cm, while for the tree with a stem diameter of 320 mm this value was 61 kPa at a distance of 20 cm, for a tree with a stem diameter of 220 mm was 42 kPa, and after that, it decreased systemically for all investigated trees.

## 4. Discussion

#### 4.1. Roots Traits and Architectural Indices

#### 4.2. Roots Tensile Strength

#### 4.3. Roots Cohesion

_{r}values in this study are consistent with those reported by Genet et al. [17] and Moresi et al. [7], but higher than the mean values reported by other authors, estimated by using the same methodology [5,74,75]. Nevertheless, Schmidt et al. [23] observed that the mean c

_{r}could be high as 100 kPa due to lateral roots for natural forests having a RAR value between 0.001 to 0.1%. Overestimation is also involved in RAR estimation since all the roots were considered orientated perpendicularly to the soil shearing zone. However, it does not represent the realistic conditions of the field. It is very important to take orientation into account. Moreover, this influence is against safety and, therefore, of primordial importance. Since laboratory investigations have revealed that reinforcement provided by perpendicularly orientated fibers to the shearing zone can be compared to that provided by fiber randomly orientated [76]. The range of roots diameter plays an important role in the calculation of RAR, which differs from study to study. More explanation regarding the higher value of c

_{r}is the assumption of the WWM model that during shearing of the soil, the tensile strength of the roots is fully mobilized, and roots failure occurs at breaking at once. In actual conditions, during shearing of soil root composite, roots break progressively because of having different tensile strength [16,75].

## 5. Conclusions

- The tree stem diameter is having a significant impact on the roots indices and root cohesion. The roots indices and root cohesion increase with an increase in tree diameter.
- The tree diameter governs the average root cohesion estimated for the investigated trees. The variation of stem diameter from 220 mm to 460 mm results in increased cohesion from 23 kPa to 63 kPa.
- The maximum depth and lateral distance of the root system for the investigated tree are 50 cm and 300 cm, respectively.
- The values of roots architectural indices are significantly higher in the topsoil depth range (0–20 cm) of the root zone and near to the tree stem in the lateral distance range (0–100 cm).
- Root cohesion estimated by FBM shows the same trend of decrease as that of WWM. However, FBM estimated that cohesion values were less than that of WWM values by the reduction factor of 0.55–0.79.
- The tree with a large stem diameter has more number of fine to medium roots (roots diameter <10 mm) than a tree with smaller stem diameter.
- The same diameter roots class of trees with large stem diameter is having more tensile strength as compared to trees with a smaller diameter. The increase in tree diameter from 220 mm to 468 mm diameter results in the increase of roots tensile strength by 33%.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**(

**a**) Excavation zone marked on the ground with white chalk powder, (

**b**) incremental excavation (depth of each increment (h) was 10 cm for each zone).

**Figure 4.**Root sample and performance of the tensile test. (

**a**) Casting of root terminals in synthetic resins. The tensile force of the root was measured in z-direction, d = root diameter measurement, L

_{0}is the root initial length (

**b**) MTS Bionix

^{®}Servohydraulic Test System used for performing the tensile test.

**Figure 6.**Root distribution along with the horizontal distance from the tree stem (d = root diameter in mm).

**Figure 7.**Variation of roots indices with depth (

**a**) roots area ratio (RAR) (

**b**) roots distribution (RD), and (

**c**) roots biomass (RB).

**Figure 8.**Variation of roots indices with lateral distance from the tree stem (

**a**) RAR (

**b**) RD, and (

**c**) RB.

**Figure 10.**Variation of the root cohesion with depth (

**a**) Wu and Waldron Model (WWM) (c

_{r}) (

**b**) Fiber Bundle Model (FBM)(c

_{fbm}).

**Figure 11.**Distribution of root cohesion with horizontal distance from stem of the tree (

**a**) WWM (

**b**) FBM.

Tree Specie | Location | Altitude (m) | DBH (mm) |
---|---|---|---|

Cunninghamia R. Br | Latitude: 31°8′9.78″ N Longitude: 103°34′41.01″ E | 1805 | 220 ± 0.3 |

Latitude: 31°8′30.04″ N Longitude: 103°34′31.62′′E | 1806 | 450 ± 0.7 | |

Latitude:31°8′10.41″ N Longitude: 103°34′41.13′′E | 1834 | 468 ± 1 | |

Latitude:31° 8′28.97″ N Latitude:103°34′29.48″ E | 1843 | 320 ± 0.4 |

Parameter | Tree Diameter = 220 mm | Tree Diameter = 320 mm | Tree Diameter = 450 mm | Tree Diameter = 568 mm |
---|---|---|---|---|

Gravel Content (%) | 7 | 11 | 9 | 12 |

Sand Content (%) | 67 | 64 | 67 | 64 |

<74 μm grain size content (%) | 27 | 25 | 24 | 24 |

Moisture Content (%) | 20.56 | 20.08 | 20.66 | 20.06 |

Bulk Unit Weight gm/cm^{3} | 1.453 | 1.445 | 1.453 | 1.445 |

Liquid Limit (%) | 35.56 | 33.25 | 36.24 | 34.15 |

Plastic Limit (%) | 49.96 | 48.96 | 49.25 | 48.16 |

Plasticity Index | 14.31 | 15.71 | 13.01 | 14.01 |

Root Diameter (mm) | With Depth | With Horizontal Distance | ||
---|---|---|---|---|

F | p | F | p | |

d ≤ 1 | 14.17 | <0.001 | 16.752 | <0.001 |

1 < d ≤ 2 | 15.63 | <0.001 | 9.708 | 0.001 |

2 < d ≤ 5 | 20.68 | <0.001 | 10.31 | 0.001 |

5 < d ≤ 10 | 20.94 | <0.001 | 13.103 | <0.001 |

Tree Diameter (mm) | Root Diameter (mm) | Tensile Strength (MPa) | |||
---|---|---|---|---|---|

Min | Max | Max | Min | Mean ± Standard Error | |

220 | 0.76 | 9.98 | 40 | 3 | 11.8 ± 2.1 |

320 | 0.50 | 9.81 | 107 | 3 | 14.1 ± 2.4 |

450 | 0.60 | 9.98 | 77 | 5 | 15.9 ± 2 |

468 | 0.67 | 8.53 | 70 | 6 | 19.9 ± 2 |

**Table 5.**The power-law functions coefficients for tensile strength and tensile for with co-efficient of correlation.

Tree Diameter (mm) | Tensile Strength | Tensile Force | ||||
---|---|---|---|---|---|---|

a | b | R-Squared | a | b | R-Squared | |

220 | 20.369 | 0.522 | 0.37 | 18.890 | 1.364 | 0.80 |

320 | 26.470 | 0.636 | 0.47 | 15.980 | 1.478 | 0.82 |

450 | 28.930 | 0.644 | 0.52 | 22.710 | 1.476 | 0.83 |

468 | 30.640 | 0.523 | 0.36 | 24.050 | 1.478 | 0.81 |

Depth (cm) | Cunninghamia | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Tree Dia=220 mm | Tree Dia = 320 mm | Tree Dia = 450 mm | Tree Dia = 468 mm | |||||||||

c_{r} (kPa) | c_{fbm} (kPa) | c_{fbm}/c_{r} | c_{r} (kPa) | c_{fbm} (kPa) | c_{fbm}/c_{r} | c_{r} (kPa) | c_{fbm} (kPa) | c_{fbm}/c_{r} | c_{r} (kPa) | c_{fbm} (kPa) | c_{fbm}/c_{r} | |

10 | 42.36 | 30.03 | 0.71 | 51.69 | 35.02 | 0.68 | 67.43 | 46.20 | 0.69 | 78.23 | 62.0 | 0.79 |

20 | 39.17 | 25.46 | 0.65 | 47.16 | 30.97 | 0.66 | 60.95 | 43.38 | 0.71 | 77.4 | 54.1 | 0.70 |

30 | 11.85 | 10.54 | 0.89 | 13.59 | 6.91 | 0.51 | 40.03 | 16.64 | 0.42 | 44.1 | 33.6 | 0.76 |

40 | 4.52 | 3.32 | 0.74 | 4.86 | 3.40 | 0.70 | 13.94 | 7.26 | 0.52 | 10.9 | 7.5 | 0.69 |

50 | - | - | - | - | - | - | 16.38 | 4.54 | 0.28 | 8.9 | 3.9 | 0.44 |

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## Share and Cite

**MDPI and ACS Style**

Mehtab, A.; Jiang, Y.-J.; Su, L.-J.; Shamsher, S.; Li, J.-J.; Mahfuzur, R.
Scaling the Roots Mechanical Reinforcement in Plantation of *Cunninghamia* R. Br in Southwest China. *Forests* **2021**, *12*, 33.
https://doi.org/10.3390/f12010033

**AMA Style**

Mehtab A, Jiang Y-J, Su L-J, Shamsher S, Li J-J, Mahfuzur R.
Scaling the Roots Mechanical Reinforcement in Plantation of *Cunninghamia* R. Br in Southwest China. *Forests*. 2021; 12(1):33.
https://doi.org/10.3390/f12010033

**Chicago/Turabian Style**

Mehtab, Alam, Yuan-Jun Jiang, Li-Jun Su, Sadiq Shamsher, Jia-Jia Li, and Rahman Mahfuzur.
2021. "Scaling the Roots Mechanical Reinforcement in Plantation of *Cunninghamia* R. Br in Southwest China" *Forests* 12, no. 1: 33.
https://doi.org/10.3390/f12010033