UC Berkeley

Much of the Central Valley of California is protected from flooding by levees, which can fail in numerous ways. Vegetation, including large trees, has been allowed to grow over many miles of levee, and although there is no case history of a tree leading directly to levee failure, vegetation is considered a low-level risk factor that could lead to failure. Due to the complexity and inherent variability of trees and their root systems, the influence of vegetation is generally not considered in engineering evaluations of levees. Thus, the objective of this research was to quantify the incremental effect on levee performance due to trees, through an assessment of root reinforcement, weight and wind loads in the context of seepage and stability analyses.

The model levee selected for analyses represents typical conditions found in the Pocket neighborhood of Sacramento. The levee is 5.2 m (17 ft) high with 2.5:1 H:V slopes and it is a sandy embankment underlain by a relatively low hydraulic conductivity cohesive blanket layer and sandy aquifer with an open hydraulic connection to the Sacramento River. Steady-state seepage analyses were used to evaluate pore pressures that concentrate in the blanket layer and reduce effective stress, controlling blanket layer strength. Stability of the levee slope was evaluated using Spencer's Method of slices to compute factor of safety (FS).

Previous work evaluating vegetation effects for slope stability analyses focuses on the root reinforcement of shallow sliding surfaces on steep slopes. If more complex slope failures are considered the spatial distribution of roots and their properties is often simplified. To properly assess the influence of vegetation the three-dimensional distribution of roots must be incorporated into a stability model. This is accomplished by the development of a biomass model that estimates key tree parameters from trunk diameter at breast height, including maximum lateral and vertical limits and the spatial distribution of root density and volume. The biomass model is supported by published allometric data for woody vegetation, with an emphasis placed on data from the Central Valley, and is incorporated into the stability model.

Reinforcement of roots in the slope is incorporated as an increase in soil cohesion and quantified proportionally to root area ratio, as estimated by the biomass model. Strength of individual roots is implicitly included by applying a probability distribution to root reinforcement representing the range of likely values; root diameter, orientation and tensile strength are not included explicitly in the biomass or slope stability models. When effective soil cohesion due to root reinforcement is unrealistically high, or prevents a solution for FS from being reached by the slope stability model, limits on maximum values are defined which can be related to the expected reinforcement capacity of roots due to pullout and breakage (i.e., insufficient root-soil friction and root rupture, respectively). The root ball represents the highest density of a root system and is considered to be the area where weight and wind loads are transferred to the soil. Measurements of root pits from windthrow events are used to define the size of the root ball. Wind loads are implemented as horizontal and vertical forces that are equivalent to the ultimate moment that a tree can carry prior to uprooting. To address the three-dimensional interaction of slope failures and root distribution, two-dimensional analyses are used that incorporate tree spacing in the plane-strain direction to determine average values of vegetation effects.

Variability and complexity of seepage, strength and vegetation parameters considered herein are well-suited to evaluation with probabilistic analysis. Probability distributions are selected for fifteen parameters and the first-order reliability method (FORM) is used to evaluate probability that FS<1.0 for seepage and stability. The FORM algorithm is specifically tailored to provide an invariant solution for the class of problems considered, at the cost of increasing computation time and complexity in numerical software. In addition to probability, FORM output includes an estimate of the most likely conditions at failure (the design point) and importance and sensitivity measures that rank the relative impact that each parameter input has on the solution. Fragility curves are developed by completing a FORM analysis at multiple levels of water level, illustrating the aleatory uncertainty in levee stability. Sensitivity measures are used to quantify the epistemic uncertainty in levee stability, represented by a one standard deviation confidence interval for fragility or FS.

Overall, vegetation effects are found to have a relatively small impact on levee stability with respect to seepage and strength parameters, producing dFS on the order of +/-0.1 for most cases. Incremental effects are generally positive, although tree location and position can be chosen to produce adverse conditions. Root reinforcement has the biggest effect on stability, with breakage and pullout limits for effective cohesion playing a significant role in the magnitude of the change in FS (dFS). When vegetation is applied to a potential sliding surface dFS is generally over estimated if a new minimum FS surface search is not performed. Non-circular surfaces are necessary to find a sliding surface geometry that is capable of avoiding the root reinforcement zone that can cause a misleadingly high estimate of FS. Tree weight increases linearly from dFS<0 with a tree at the levee crest to dFS>0 as the tree is moved downslope. Wind loads generally have small effect in comparison to the sliding mass of a slope failure and are found to produce |dFS| less than approximately +/-0.1 for the upslope and downslope direction.

Reliability results are consistent with deterministic analyses of levee stability. Importance measures indicate vegetation random variables have a small effect on stability in comparison to seepage and strength parameters. The most likely conditions expected for a slope failure occurrence (i.e., the design point) are essentially identical between reliability analyses with and without vegetation. An exception is the increased importance of root density and effective cohesion when a tree is located near the entry or exit point of a sliding surface; however, searches for alternative sliding surfaces that minimize factor of safety illustrate the ease with which slope failures can avoid high density root zones. Fragility curves decrease when vegetation effects are included but remain within the one standard deviation confidence bounds on fragility, illustrating the uncertainty in strength and seepage parameters has a bigger effect on levee performance than the effect of vegetation overall.