Modeling Levee Failure

The modeling of stress and strain and the breaking or "failure" of solid bodies is a science that has at least 200 years of development behind it. It is an integral part of the training of Civil Engineers, Structural Geologists and Solid Earth Geophysicists. The forces involved are usually due to Gravity. The parameters of interest are the weight distribution of the object, and the strength of the materials in the object. The strength of the materials is broken into two independent parameters, the compressional strength and the shearing strength. Levees are primarily made of soil which is a porous and permeable solid which is water wet. The physical properties of water wet rocks both consolidated and unconsolidated are studied by Geophysicists for the purpose of determining their effects upon Seismic (sound) waves propagating through them. I am not an expert on near surface stress and strain modeling but I propose that the parameters that are used in such modeling are closely related to the elastic parameters of the water wet soils. This is the subject I wish to address in this blog entry. Both the shear and compressional elastic moduli are known to be a well behaved function of the "effective pressure". Effective pressure is the weight of the overburden (soil and rock above our depth of interest) minus the pressure of the fluid (water) in the pore spaces. Effective pressure is essentially the weight born by the solid frame of the rock or soil by grain to grain contact and is thus a primary factor in determining the elasticity of the entire rock. Laboratory measurements of the velocity of Seismic waves through a core specimen measured at different effective pressures are available in the Geophysical literature. Examples Below:


The velocity and elastic moduli increase with effective pressure which represents the normal variation seen with depth within the Earth. Note that the variation is the most rapid at the shallowest depth. In the case of the New Orleans levee failures, the depth at which failure occurred seems to be at about 20 feet. The effective pressure would then be about 20 - 9 = 11 psi. Now consider what happens when Katrina's storm surge raises sea level by 10 feet. The pressure at 20 feet of depth is now 20 - 15.5 = 4.5 psi. This is a very large relative change in effective pressure and may have had a profound effect on the soil's elastic parameters and contributed to their failure. My simple analysis shown in the figure above shows a reduction in the shear strength of 35% at a depth of 17 feet. I do not recall reading that the Corps or SWB did any soil borings and strength measurements. Dr. Seed in the independent Engineering report did mention noting a layer of organic peat material and measured the strength of it and found it very low. I believe that soil boring and core measurements of elasticity should be a part of all levee construction and further postulate that the effects of changes in the hydrostatic head (water level) need to be included in the modeling. Because the elastic parameters vary quite rapidly with depth in the near surface, I believe that this variation should be an integral part of the Levee Failure Model. In the measurement of the soil's elastic parameters, care needs to be taken to measure any anisotropy in those coefficients. We Geophysicists have become quite familiar with the phenomenon of elastic anisotropy in layered (banded, bedded) rocks. The direction parallel to the bedding planes usually being the minimum values (weakest strength).

Again, near surface stress and strain are not my area of expertise and others undoubtedly have more authority than I do in this area but I felt it necessary to raise the issue in consideration of the Katrina disaster and other recent levee failures.