Submitted:
07 January 2026
Posted:
09 January 2026
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Abstract
Keywords:
Introduction
Methodology
Results and Discussion
Conclusions
- The experimental results showed that roots of the tested species flatten at as low as 0.17 MPa, with high likelihood of flattening beyond 0.35 MPa.
- From the numerical simulations, the stresses in the pavement are strongly influenced by root placement depth, followed by pavement thickness, then base thickness. The thickness of the geotextile layer used was kept at 1 mm.
- Increasing pavement thickness from 7.5 cm to 10 cm can reduce stress by up to 20%, while increasing root depth from 5 cm to 40 cm can reduce stress by up to 60%. These findings highlight practical design levels for balancing cost and performance.
- Stresses due to a single root in the considered geometrics were at 550 kPa as a maximum, which is lower than 2 MPa, the flexural strength of typical concrete used in sidewalks. Nevertheless, the presence of multiple roots may increase the stresses imparted onto the pavement, which needs to be studied in further studies.
- Design schematics for both existing and new infrastructure were proposed, emphasizing controlled root placement and adequate separation from pavement to mitigate cracking risks while supporting long-term tree health.
Supplementary Materials
Funding
Credit Authorship Contribution Statement
Declaration of Competing Interest
Acknowledgments
References
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| Parameter | Value | Description |
| Hsb | 0.6 m | Subbase thickness |
| W | 4 m | Width of numerical domain (graphical) |
| Hgtx | 0.001 m | Geotextile thickness |
| Hb | 0.1 m | Base thickness |
| Hp | 0.1 m | Pavement thickness |
| Dr | 0.01 m | Initial root Diameter |
| D | 0 m | Depth of root from geotextile |
| E | 0.01 m | Growth increment of root |
| ρp | 2200 kg/m3 | Mass density of pavement |
| ρb | 1936 kg/m3 | Mass density of base |
| ρsb | 1661 kg/m3 | Mass density of subbase |
| ρr | 595 kg/m3 | Mass density of root |
| Ep | 34.26 x 107 kPa | Modulus of elasticity of pavement |
| Eb | 1.72 x 105 kPa | Modulus of elasticity of base |
| Esb | 6.89 x 104 kPa | Modulus of elasticity of subbase |
| Er | 173 kPa | Modulus of elasticity of root |
| Egtx | 1000 kPa | Modulus of elasticity of geotextile |
| Μ | 0.3 | Poisson’s ratio of all domains |
| Root position | Stress in pavement (kPa) | |||
| Surface thickness (cm) | Base thickness (cm) | Root depth in subbase (cm) | @ 0.35 MPa root confining stress | @ 0.50 MPa root confining stress |
| 7.5 | 10 | 0 | 375.57 | 536.52 |
| 7.5 | 10 | 2 | 236.58 | 337.98 |
| 7.5 | 10 | 4 | 147.9 | 211.29 |
| 8.75 | 10 | 0 | 331.41 | 473.44 |
| 8.75 | 10 | 2 | 216.22 | 308.89 |
| 8.75 | 10 | 4 | 138.72 | 198.17 |
| 10 | 10 | 0 | 294.59 | 420.84 |
| 10 | 10 | 2 | 197.22 | 281.75 |
| 10 | 10 | 4 | 129.33 | 184.75 |
| 7.5 | 12.5 | 0 | 358.96 | 512.8 |
| 7.5 | 12.5 | 2 | 226.47 | 323.53 |
| 7.5 | 12.5 | 4 | 140.08 | 200.11 |
| 8.75 | 12.5 | 0 | 318.27 | 454.67 |
| 8.75 | 12.5 | 2 | 207.88 | 296.96 |
| 8.75 | 12.5 | 4 | 132.39 | 189.12 |
| 10 | 12.5 | 0 | 284.65 | 406.65 |
| 10 | 12.5 | 2 | 191.23 | 273.19 |
| 10 | 12.5 | 4 | 124.16 | 177.37 |
| 7.5 | 15 | 0 | 339.85 | 485.5 |
| 7.5 | 15 | 2 | 217.59 | 310.85 |
| 7.5 | 15 | 4 | 132.3 | 189 |
| 8.75 | 15 | 0 | 304.77 | 435.38 |
| 8.75 | 15 | 2 | 201.47 | 287.82 |
| 8.75 | 15 | 4 | 125.47 | 180.67 |
| 10 | 15 | 0 | 276.86 | 395.52 |
| 10 | 15 | 2 | 186.61 | 266.58 |
| 10 | 15 | 4 | 118.96 | 169.94 |
| Parameter | Effect |
| Depth of Root Placement | In all nine considered scenarios, increasing the root depth from 0.05 m to 0.4 m led to a decrease in stresses by around 10% to 60%, respectively,. Regardless of pavement and base thickness |
| Pavement Thickness | For the same base thickness, increasing pavement thickness led to stress reduction of 11% (at 0.0875 m) and 20% (0.1 m) relative to the 0.075 cm pavement, when the root is placed at the top of the subbase. This reduction diminishes with increasing depth to 6% and 12%, respectively when the root is 0.4 cm deep in the subbase. |
| Base Thickness | For the same pavement thickness, increasing base thickness led to stress reduction of 3% (at 0.125 m) and 4.5% (at 0.15 m) relative to the 0.1 m base, when the root is placed at the top of the subbase. This reduction increases with increasing depth to 8% and 10%, respectively when the root is 0.4 cm deep in the subbase. |
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