Radial Expansion and Flattening in Woody Tree Roots: Assessing the Limits

As tree roots elongate and increase in diameter, they must generate sufficient pressure to displace the surrounding soil (Reichert et al. 2021). This pressure is limited both by the ability of root cells to exert force through turgor pressure (Azam et al. 2013) and by the root’s capacity to generate a reactionary force. Without this reactionary force, the root may be pushed backward instead of extending further into the soil (Eavis 1967). To counteract this, root hairs help anchor the root and prevent backward movement. In compacted soils, root hairs become both longer and more abundant. Under extreme compaction, roots often increase in diameter due to their heightened sensitivity to axial rather than radial pressure (Bengough 2012; Tomobe et al. 2023). Consequently, it is believed that constraints on radial expansion may actually promote axial elongation, enabling roots to grow more effectively through dense soils (Eavis 1967; Bengough and Mullins 1991).

While radial root growth can generate higher pressures than axial growth, it is still ultimately constrained. In an early study, Zwieniecki and Newton (1995) split rock profiles to examine morphological changes in roots growing within narrow fissures. When growth was restricted in two directions, the root cortex became severely deformed, adopting a wing-like shape, while the stele remained cylindrical and unaffected by the surrounding environment. This morphological plasticity was observed only in certain species. Conifers such as Pinus ponderosa (Dougl. ex Laws.) and Pseudotsuga menziesii (Mirb.) did not produce roots in the most confined spaces.

Understanding the mechanical limits of axial and radial root growth has both ecological and practical implications. From an ecological perspective, researchers have studied these limits to better understand plant colonization and soil development in compacted and confined rooting environments (Bello-Bello et al. 2022). From an applied perspective, the ability to penetrate compacted soils has been examined to project yield in traditional forest management (Reichert et al. 2021), and the ability to expand radially has been studied to address infrastructure conflicts in urban forest environments (Grabosky et al. 2011).

While axial root growth has been more commonly studied (Bengough and Mullins 1991; Atwell 1993; Clark et al. 2003), fewer investigations have examined the pressures generated by radial root growth (Tracy et al. 2011; Potocka and Szymanowska-Pułka 2018). In an early experiment, Misra et al. (1986) tested whether radial expansion of pea, cotton, and sunflower seedling roots could generate enough pressure to break surrounding chalk walls of varying thicknesses. This work was later supported by Kolb et al. (2012), who directed emerging chickpea radicles between pairs of photo-elastic discs to assess the radial forces exerted along the sides of the root.

Studies of the pressures associated with radial root growth in mature woody roots are even more limited than those focused on seedlings. Grabosky et al. (2011) examined roots that had grown between two layers of foam placed beneath a sidewalk over a ten-year period. To estimate the pressure exerted by the roots, they recreated the observed indentations using a press and measured the resulting stress with a load cell.

Our objective was to determine the limits of radial root expansion in woody roots. While advancing understanding of woody root development, this also holds practical implications for engineers seeking to prevent pavement lifting in urban areas—a costly ecosystem disservice (McPherson 2000; Roman et al. 2021). As noted by Zwieniecki and Newton (1995), extremely confining rooting environments can alter root morphology, flattening roots where they exceed radial expansion thresholds. Although Misra et al. (1986) addressed this question in seedling roots of nonwoody species, and Grabosky et al. (2011) focused on woody roots, the latter did not explore this threshold. Identifying such a threshold could help engineers design urban infrastructure that resists cracking or lifting and encourages root flattening—a more desirable alternative to root loss from infrastructure repair or replacement (Benson et al. 2019).

Mean initial diameter for Q. virginiana roots was 32.00 mm (SD = 11.38), with values ranging from 10.08 mm to 52.28 mm. Taxodium distichum roots were smaller on average, with a mean diameter of 19.55 mm (SD = 8.79) and a range of 5.38 mm to 35.86 mm. One oak root was excluded due to clamp failure during the study period. Additionally, 3 T. distichum roots were not harvested at the conclusion of the study because they began producing knees within the airspace of the observation boxes. These roots were preserved in situ for continued monitoring using timelapse photography. In total, 8 of the 30 T. distichum roots developed knees in the airspace adjacent to the clamps. This supports early observations by Whitford (1956), who noted that knees were more likely to form in areas with greater aeration compared to the rest of the root zone.

At the conclusion of the study, 36 roots had exhibited flattening while 20 had not. Initial logistic regression models included both species and applied stress (MPa) as predictors of root flattening. However, species was not a significant predictor (P = 0.139) and was removed from the final model. The simplified model using stress alone showed a statistically significant relationship with root flattening (P = 0.038). Model performance metrics included an area under the curve (AUC) of 0.696 and a Nagelkerke R² of 0.144. The overall classification accuracy was 71.43%, with better performance in identifying flattened roots (88.89%) than nonflattened roots (40.00%).

The prediction curve from our logistic regression model (Figure 3) was used to estimate the stress required to trigger root flattening at increasing levels of confidence. The goal of this analysis was to determine the stress level at which all roots could be expected to flatten. However, because the logistic function approaches but never actually reaches 100%, we used values very close to 100% to estimate this upper threshold.

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Figure 3.

Probability of root flattening as stress (MPa) increases. Predictions are derived from a logistic regression model. Data from Q. virginiana Mill. and T. distichum (L.) Rich. are combined due to a nonsignificant species effect.

To do this, we first took the logistic regression prediction function:

We then rearranged it to determine the value of x (stress in MPa) that corresponds to a desired probability p of flattening:

The goal of our study was to determine the stress required to achieve near 100% confidence in root flattening, as this value could inform engineering solutions for sidewalk lifting. While exact 100% confidence is mathematically unattainable, we can approach it closely. By calculating the pressure needed to reach 99.99% certainty of root flattening, we arrive at the following stress threshold:

The use of 99.99% was our first choice, but it is admittedly somewhat arbitrary. For comparison, a stress of 0.173 MPa corresponded to a 99% likelihood of flattening, while 0.251 MPa was needed for 99.9% and 0.329 MPa for 99.99%.

Our estimated stress thresholds for root flattening (0.173 MPa to 0.329 MPa) fall within the lower to middle range of values reported in other studies (Table 1). Compared to previous work on seedling radicles, our results are lower than the 0.50 MPa threshold observed by Misra et al. (1986) for Pisum sativum but overlap with thresholds reported for Gossypium hirsutum (0.29 MPa) and Helianthus annuus (0.24 MPa). They also align closely with the values observed in Cicer arietinum (0.30 MPa ± 0.15 MPa) by Kolb et al. (2012). Relative to other studies of woody roots, our values are slightly lower than those reported by Grabosky et al. (2011) for Platanus × hispanica (0.35 MPa to 0.40 MPa), potentially reflecting species differences or the longer time frame over which stress accumulated in our study.

The pressure thresholds identified in this study (0.173 MPa to 0.329 MPa) provide design criteria for engineering interventions aimed at minimizing root-related sidewalk lifting and pavement damage. For example, engineers could design reinforced sidewalk systems with anchors that maintain pressures above these thresholds in the root zone, encouraging horizontal root flattening rather than vertical displacement of pavement slabs. Alternatively, slab thickness could be increased to prevent cracking and increase the downward pressure due to increased weight.

While this study provides valuable insights into root radial expansion, several limitations should be acknowledged. First, our findings are based on only two species (Q. virginiana and T. distichum), which may not be representative of the broader range of woody species found in urban environments. Given the morphological and physiological diversity among tree species, stress thresholds for root flattening may vary across taxa. Second, our study was limited to relatively small diameter roots, with mean diameters of 32.00 mm (1.26 inches) for Q. virginiana and 19.55 mm (0.77 inches) for T. distichum. Larger structural roots may exhibit different biomechanical properties. Third, the duration of stress application varied between species (21 months for Q. virginiana and 13 months for T. distichum), and our overall study period may not capture the full range of long-term responses to mechanical constraint. Future research should expand to include a broader range of species, root sizes, and exposure durations to better understand the generalizability of these findings.

This study provides one of the first empirical estimates of the pressure threshold at which mature woody roots begin to deform in response to radial constraint. By quantifying the stress required to induce root flattening in Q. virginiana and T. distichum, we contribute to a growing body of work aimed at understanding root biomechanics under confining soil conditions. Our results suggest that root deformation occurs at relatively modest pressures (0.173 MPa to 0.329 MPa), particularly compared to values reported for seedling radicles or larger woody roots in different settings. These findings have practical implications for infrastructure design, particularly in the context of mitigating root-related pavement damage, which is a significant and costly ecosystem disservice. Future work should explore how species, soil type, and duration of constraint influence these thresholds and whether roots subjected to moderate pressure can be directed to flatten without compromising tree health or stability.

The authors reported no conflicts of interest.