Reliability Analysis of the Influence of Woody Vegetation on Levee Performance

Woody vegetation, which is present on a large portion of California’s levees, has become a source of concern regarding its potential detrimental effects on the long term performance of the levees. While trees are known to provide habitat for many species and to have positive effects, such as root reinforcement, on slope stability, concerns have been expressed regarding potential detrimental effects to the levee structure due to tree weight at the top of slopes, wind loading and uprooting of trees, potential for increased seepage through and below the levees, and restricted access for levee maintenance. The California Levee Vegetation Research Program (CLVRP) was thus created to conduct original scientific research to inform vegetation policy issues affecting the State and federal levee systems in California. For example, CLVRP-sponsored studies have obtained quantitative data on the size, density, and extent of tree roots on levees for different species of trees commonly found on levees, and explored known or perceived direct influences the trees may have on long term levee performance. The main objective of the research presented in this report was to use the data developed by CLVRP in order to quantify the incremental effect of vegetation on levee performance using a probabilistic/stochastic analysis. A model levee based on conditions in the Pocket area of Sacramento, California was used in all analyses reported here, and judgment should be used in applying these results to other levee system conditions. The First Order Reliability Method (FORM) was used to evaluate the incremental contribution to structural deficiency posed by vegetation by calculating slope stability and seepage through and under the model levees in the presence and absence of vegetation. The principal strength of the reliability analysis approach is that it can directly account for the inherent variability, i.e. stochastic nature, of the input variables and the associated degree of uncertainty about their actual values. The results are then presented in terms of the probability of exceeding a specific criterion, i.e. an undesirable outcome often referred to as “failure.” Thus, “failure” as used here refers to an undesirable outcome such as a sand boil but does not necessarily imply a breach through the entire levee section. The computed probabilities for different scenarios can then be compared to assess the incremental changes due to different assumptions or modes of failure and they then allow the evaluation of incremental changes in the associated risk of failure or damage. Most importantly, for practical engineering and asset management applications, FORM provides information on the sensitivity of the solution to the input variables or, in other words, the level of influence (importance) that these variables have on the outcome of the analysis. The sensitivity results are an integral and unique aspect of FORM and offer an advantage, in comparison to other reliability methods (e.g., First-Order Second Moment or Monte Carlo Simulation). Although reliability methods have previously been used to evaluate levees in general, the analyses and results presented herein are unique by directly considering uncertainty in hydraulic conductivity on seepage and by directly considering the effect of woody vegetation, i.e. trees and tree roots, on levee stability, using FORM. Overall, the FORM analyses are capable of providing significant insight into the factors controlling levee performance and can be used in combination with the standard deterministic methods commonly used in engineering practice. To evaluate the effects of woody vegetation, data from CLVRP-sponsored studies were used to create a new three-dimensional (3D) biomass model for quantifying the influence of root reinforcement, tree weight and wind loading. The biomass model provides a detailed description of the lateral and vertical spread of roots in the subsurface, which were then incorporated into levee seepage and stability analyses. The 3D description of the biomass distribution and the analytical procedures used to incorporate it in levee analyses represent significant improvements over previously used methods for evaluating woody vegetation effects on levees. The main results and conclusions of the analyses performed in this study can be summarized as follows: 1. Slope stability analyses with and without woody vegetation show that the overall effect of a tree and its root system depends on the assumptions about the location of the potential failure surface. This study shows that standard techniques for evaluating the effect of trees on slope stability tend to produce a misleading assessment, i.e. overestimating positive effects of trees on slope stability. In typical past analyses, the critical sliding surface (the surface with the lowest Factor of Safety, FS) without vegetation has been used to assess the influence of vegetation by simply including the tree effects (root reinforcement, tree weight and wind loads). Such analyses tend to show that the tree roots help anchor that sliding surface and increase the FS. However, our analyses show that when a new search is performed for the failure surface with the lowest FS after adding in tree effects, a different critical sliding surface will be found that tends to bypass the root system (Section 6.4). 2. Overall, the influence of vegetation, i.e. the effect of roots and tree weight on FS for slope stability can generally be considered to be less than +/-10% for a large tree in the most critical location on the embankment (i.e., positioned near the top of the sliding surface). The change in FS decreases as the mass of the potential slope failure increases (Sections 6.3 and 6.4). 3. Similarly, wind produces a change in FS for slope stability less than +/-10% for high loading conditions. Although wind can exert high loads on large trees, the actual load applied to a slope through the tree root system is reduced by the flexibility of the tree and limited by the maximum resistance of the root system, which would eventually pull out of the ground assuming high enough wind loads (i.e., windthrow failure). This study assumed the short duration of strong wind gusts does not provide a long-term increase in soil strength. It should be noted that when a tree is uprooted, the wind load is reduced to zero, but the influence of vegetation is not necessarily eliminated, as a root pit is formed that has the potential to negatively affect the through seepage or underseepage failure modes (Section 6.6). 4. 3D slope stability analysis illustrates slope failures are expected to have a width (measured parallel to the levee) more than twice the length measured along the slope. The 3D FS for this critical geometry is comparable to the FS from traditional 2D slope stability analysis; therefore, the inclusion of vegetation effects using 2D analyses is appropriate for the general assessment of slope stability as long as the position of the potential failures surface is recomputed when the effects of vegetation are added, as already mentioned (Section 6.5). 5. The effect of a potential root pit in the blanket layer (levee foundation) due to an uprooted tree was evaluated using heave/uplift as a surrogate for internal erosion piping of the foundation. The analyses show that a windthrow root pit reduces the blanket layer thickness and consequently its effect is always negative, thus increasing the probability of “failure” (Section 6.7). 6. Resistance of the sandy levee embankment to internal erosion (through seepage) was evaluated for the land side and assumed to depend only on slope angle and cohesive soil strength. As such, for the levee condition considered in this report, the size of a tree root pit was not considered for through seepage (but was considered for underseepage). The results show that even small amount of cohesion will have a significant positive effect in decreasing the potential for internal erosion. However, while roots of woody vegetation are accounted for in the form of a cohesion in slope stability analyses and they can similarly reduce the potential for internal erosion piping through a levee embankment this effect is highly localized. As a result, it is not prudent to count on the positive effect of woody vegetation in assessing the potential for failure by through seepage (Section 6). 7. Overall, while the presence of vegetation and tree roots does affect the FS (positively and negatively) and hence the probability of “failure” due to slope failure, by through seepage, and/or by underseepage, these effects are small relative to the effect of the uncertainty in the values of the basic properties of the levees, i.e. soil strength and hydraulic conductivity (permeability) (Sections 6.8 and 6.9). Quantifying the influence of vegetation is only one step in the decision making process. From the stand point of levee maintenance and management, the main challenge lies in the decision of whether or not to mitigate the detrimental effects and/or promote the beneficial effects of existing or planted levee vegetation. In a risk-prioritized paradigm, this decision must be made in consideration of the relative significance of other deficiencies, given the limited financial resources available for levee improvements. Levee improvements for flood protection should maximize the benefit-to-cost ratio, measured by a risk analysis, which combines probability of failure with an- ticipated consequences: a weak levee protecting moderately valuable assets may be more “risky” than a very strong levee protecting high value assets. The advantage of the probabilistic approach in using FORM-based reliability analysis in the risk-prioritized approach is that it provides direct quantitative comparison between the traditional geotechnical risk factors (e.g., seepage, slope stability) on a site-specific basis. These can then be incorporated in the traditional event tree analyses for evaluation of overall levee performance. For the conditions considered in this report, the incremental effects of woody vegetation on each failure mode, while not negligible, were less significant than the uncertainty associated with the different failure modes when vegetation effects were not considered.