Soil & Rock Physical Parameters and Levee Design

I have already raised the question of whether the Corps of Engineers did soil borings (cores sampling) to determing the elastic parameters of the soils below the levees. The independent study by the Engineering committee headed by Dr. Seed criticizes the analysis and decision making based upon those samples. In the previous blog entry I have illustrated the hydrostatic effects of the storm surge on the strenght of the soils. Now I will raise the issue of anisotropy. Soils and rocks are not homogeneous bodies. Their heterogeneity is not usually random but rather consists of thin quasi homogeneous layers of differing properties. These layers can be characterized by the terms, Coarse, Medium, and Fine Sand, Silt, Clay, Calcareous (shell), and Organic (peat). Each of these layers has a different set of elastic parameters (strength). The layers are often very thin (less than a mm). The effect of this layering is to introduce anisotropy into the elastic parameters. Anisotropy causes the strength of the soils or rocks to vary with direction of measurement. The usual directions of interest are parallel and perpendicular to the bedding planes. Differences on the order of 20% between the parallel and perpendicular velocities have been reported in the Geophysical Literature. The orientation of the elastic parameters is such that the weakest direction is parallel to the bedding and thus in the horizontal direction. I propose that the Corps of Engineers familiarize themselve with the effects of anisotropy as well as overpressure and make sure that their lab measurements on soil borings measure all of the effects and further, that their levee models include these effects. I believe that the Katrina failure of some of the canals was predictable if correct and complete modeling based on detailed soil boring analysis was done during design.

EXAMPLE FROM THE LITERATURE

The Corps of Engineers Soil Strength Analysis taken from the Independent Analysis headed by Dr. Seed is below. The analysis and decisions made based on the analysis have been criticized in the report. Errors of under estimation of the weakest soil strength of the order of 100% are visible on the graph. The decisions made from this analysis undoubtably contributed to the disaster. All Engineers know that a chain is only as strong as its weakest link. Their graph is below.



I have contributed some addition considerations. My analysis of the hydrostatic effects of the surge imply a 20-30% weakening of these measurements at the depth of failure . Anisotropy considerations add a 5-25% weakening of the shear parameter in the horizontal direction parallel to the bedding planes of the soil. Most core measurements are made perpendicular to the bedding planes unless additional core preparation is done to get a sample that can be measured parallel to the bedding planes. My conclusion is that the U.S. Corps of Engineers modeled the levy response to a storm surge using soil strengths a least 150% higher than reality and that this was a major factor in the levee failure.

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.