Closure to “Laboratory Modeling of the Mechanisms of Piping Erosion Initiation” by Mandie S. Fleshman and John D. Rice

The authors would like to thank the discusser for his interest in the paper. We are familiar with the discusser’s previous work and are pleased he has shown interest in our research and paper. The discusser mentions quicksand tanks and the modeling of heave of sandy soils, pointing out that critical gradients measured in these laboratory tests were consistent with gradients calculated using Eq. (1) of the paper. The discusser also comments on the USACE’s field experience with vertical critical gradients needed to initiate boils (presented in Fig. 2 of the paper) along with his own data and attributes the lower observed gradients to concentrations of flow caused by imperfections in the soil. The authors agree with this assessment, illustrating the concentration of flow into a blanket defect in Fig. 1. However, the authors’ intent was not to model the heave mechanism but to model the initiation of soil movement into a void such as what takes place at the base of a defect in an overlying blanket (defect in the blanket as shown in Fig. 1). Soil movement in this case would not occur due to the heave mechanism but through deformation of the soil mass and individual grain movement into the void. It should also be pointed out that heaving of sand in liquefaction tanks and formation of sand boils through a blanket defect occur due to very different mechanisms. Terzaghi and Peck (1948) showed that heave of sand occurs due to upward seepage forces acting against the buoyant weight of the soil. Eq. (1) of the paper is based on Terzaghi’s theory and produces gradients similar to the liquefaction tests referenced by the discusser. The formation of sand boils through a blanket defect is a much more complex phenomena, consisting of migration of sand grains (individually or in mass) through the defect. The mechanisms of initiating this movement are complex and are the focus of our laboratory testing and the subject paper. The discusser asserts that the vertical gradients measured in the study are higher than those estimated by Eq. (1) due to the highfriction interface on the sides of the sample holder along with interference from the instrumentation in the sample holder. The authors agree with this assertion but would like to point out that the friction on the sampler sides was intentional in order to prevent heave and model the deformation of the soil mass and individual grain movement at the top of the sampler. [In fact, preliminary tests were performed at the initiation of this study without the silicon coating and correlated well with gradients predicted by Eq. (1).] This was done in order to assess how piping will initiate into a void of limited size; such as a defect in an overlying blanket (Fig. 1) or a hole in a conduit, to name a few. The friction on the sides of the sampler was meant to model friction with the adjacent soil that is overlain and retained by blanket material, thus, preventing heave of the soil mass below the void. Our model differs from the conditions depicted in Fig. 1 in that the gradient across the sample is uniform in lieu of the converging and concentrating flow conditions shown in Fig. 1. This too was intentional so that the gradients at which the various stages of observed behavior occur could be assessed. After presenting the results of the tests, the authors discuss how the results and observations from our experiments relate to field conditions (see “Application to Field Conditions” section of the paper). In this section we present a scenario and describe how the four stages of soil movement observed in our experiments could be manifested in the field and illustrate this in Fig. 11. Obviously, because the soil is eroding and deforming into a defect of limited size, heave of the soil mass does not occur and friction between the moving soil and the adjacent retained soil does exist. The discusser also mentions the limited size and height to diameter ratio of our sample holder and points out that it is much greater than that used in the quicksand tests. He also points out that soils with higher friction angles reflect the friction effect with higher gradients required to develop the stages of piping development. Again, because we are modeling erosion into a defect of limited size we are not modeling the heave mechanism for which a small height to diameter ratio would be desired. The authors do understand that the size of the opening will affect the ability of the soil to arch across the void and will, thus, affect the behavior. Because of this we have performed tests using samplers with larger diameters as part of our ongoing research. These tests are allowing us to assess the effects of soil arching on the mechanisms discussed in the paper. We are also performing tests on inclined samples to assess the effects inclined seepage exit faces may have on this erosion mechanism. The results of these tests will be presented in subsequent papers that are under development. In conclusion, the experiments presented in the paper were designed to model a mechanism of internal erosion quite different from the heave mechanism that is referenced by the discusser. Our experiments resulted in vertical gradients that are higher than those observed in “quicksand tests” and the average gradients observed in the field. However, the increased gradients do not include the effects of converging flow that would also be observed with the mechanism being studied. Such converging flow would tend to increase the gradients at the point of erosion. It is the opinion of the authors that the vertical gradients observed by the USACE in the field are average gradients that are concentrated and increase substantially as the flow approaches the defects. The concentrated gradients act on the soil that is supported by side friction and arching that results in greater resistance to movement than the heave equations would predict. Thus, the wide range of average gradients presented by the USACE is the result of the effects of the flow concentration and the arching effects cancelling out to varying degrees. The discusser expresses concern that the results presented are “seriously inconsistent in the nonconservative direction.” The authors concur that if the results were applied to the wrong conditions they would be very nonconservative. However, a discussion of scenarios of where and how the results are applicable are presented in the paper and should prevent the inappropriate use of our results. The challenge does come in applying our results to a field situation. To address this challenge we are collaborating with a numerical modeling specialist who will be modeling our experiments with