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Some Comments on the Entropy-Based Criteria for Piping

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Some Comments on the Entropy-Based Criteria for Piping Entropy 2015, 17, 2281-2303; doi:10.3390/e17042281 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Some Comments on the Entropy-Based Criteria for Piping Emöke Imre 1,*, Laszlo Nagy 2, Janos Lőrincz 3, Negar Rahemi 4, Tom Schanz 4, Vijay P. Singh 5 and Stephen Fityus 6 1 Ybl Miklós, Faculty of Architecture and Civil Engineering, Szent István University, Thokoly 74, Budapest 1146, Hungary 2 Geotechnical Department, Budapest University of Technology and Economics, Budapest 1111, Hungary; E-Mail: [email protected] 3 Tengizchevroil, Farnborough, Hampshire GU14 7BF, UK; E-Mail: [email protected] 4 Department of Geotechnical Engineering, Ruhr-University Bochum, Universitätsstrasse 150, 44780 Bochum, Germany; E-Mails: [email protected] (N.R.); [email protected] (T.S.) 5 Department of Biological & Agricultural Engineering, Zachry Department of Civil Engineering, Water Management & Hydrological Science, Texas A&M University, 321 Scoates Hall, MS 2117, College Station, TX 77843, USA; E-Mail: [email protected] 6 School of Engineering, University of Newcastle, Callaghan 2308, Australia; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected] or [email protected]; Tel.: +36-14631447; Fax: +36-14633006. Academic Editor: Kevin H. Knuth Received: 23 October 2014 / Accepted: 9 April 2015 / Published: 15 April 2015 Abstract: This paper is an extension of previous work which characterises soil behaviours using the grading entropy diagram. The present work looks at the piping process in granular soils, by considering some new data from flood-protection dikes. The piping process is divided into three parts here: particle movement at the micro scale to segregate free water; sand boil development (which is the initiation of the pipe), and pipe growth. In the first part of the process, which occurs during the rising flood, the increase in shear stress along the dike base may cause segregation of water into micro pipes if the subsoil in the dike base is relatively loose. This occurs at the maximum dike base shear stress level (ratio of shear stress and strength) zone which is close to the toe. In the second part of the process, the shear strain increment causes a sudden, asymmetric slide and cracking of the dike leading to the localized excess pore pressure, liquefaction and the formation of a sand Entropy 2015, 17 2282 boil. In the third part of the process, the soil erosion initiated through the sand boil continues, and the pipe grows. The piping in the Hungarian dikes often occurs in a two- layer system; where the base layer is coarser with higher permeability and the cover layer is finer with lower permeability. The new data presented here show that the soils ejected from the sand boils are generally silty sands and sands, which are prone to both erosion (on the basis of the entropy criterion) and liquefaction. They originate from the cover layer which is basically identical to the soil used in the Dutch backward erosion experiments. Keywords: grading entropy; entropy based erosion; piping; liquefaction 1. Introduction There is a characteristic two-layer soil condition below many of the flood protection dikes in Hungary, in which a lower permeability, fine sandy silt cover-layer overlies a saturated, higher permeability sandy gravel base material. In several situations, these have been affected by piping [1–6]. It is unclear, however, if the upper layer or the base layer is washed out during dike failure. The piping phenomena in Hungarian dikes can be classified into three categories on the basis of the speed of the process in the flood experiences of Hungary (Figure 1, [5–7]). In each case, the formation of sand boils, close to the toe (usually at deepest points of the surface or in a weak point of the surface such as a palaeochannel), is a common feature among piping failures. In the stretch of the Danube River between Rajka and Horany, the distance of the toe to a palaeochannel is 0–10 m in 29%, 11–50 m in 62% and 51–200 m in 9% of cases [5]. mitigation by (a) (b) unstable cover layer permeable base soil (c) Figure 1. Piping in two-layer system (a) and (b) slow piping: (a) Sand boil with sand transport, and crack due to localized collapse, and (b) the mitigation of slow piping by hydraulic surcharging on the land-side (after [7]). (c) Fast piping on thick and loose cover layer, deposited in an old meander with arching; this process also starts with a sand boil (adapted from [3]). Entropy 2015, 17 2283 In the first category, a sand boil forms at the land-side toe. Pipe development is slow and evident from small seepages and outwash of soil. If the pipe reaches the surface of the high permeability base material, it generally stops. Otherwise, piping can be mitigated by surcharging the water level above the land-side end of the pipe, thereby decreasing the hydraulic gradient to a non-critical magnitude. In the second category, continued outwash leads to the development of cavities or “pipes” in the soil which ultimately progress to failure. Not many of such cases are known in Hungary. Part of these pipes forms in the cover layer (probably similar to that described in the Dutch tests [8–10]), but another part of the pipe is likely to continue into the base layer. In the third category, the failure is extremely quick, with collapse occurring almost at the same time as the sand boils appear adjacent to the landside toe. In one case (July 15, 1954 at Ásványráró [3,5]), a 0.5 m diameter geyser suddenly appeared at 5 m from the landside toe, throwing off the cover layer. Within 2 seconds, the pipe reached the riverside. A funnel developed at the waterline and the dike collapsed. In this case, the silty sand layer was extremely loose and thick. A similar case occurred in 1965 in Csicsó [5]. The process is still not well-understood despite several large scale tests having been conducted ([5,8–11]). This technical note is an extension of a previous work [12] to provide some clarification regarding the failure mechanism in cases of piping. It combines a short description of an entropy based internal stability criterion (see further details in [13]) and the description of the piping failure mechanism in Hungarian dikes, with some additional research. In this paper, it is hypothesized that piping is the result of a more complex process where local soil densification, due to the increasing shear stress and decreasing shear resistance, and possibly even due to the shear waves caused by crack formation during lateral spreading, may play a key role in pipe formation, by ensuring kinematic conditions for the outwash. The suggested process is intimately linked to a local volume decrease in soils with void ratios greater than that at the critical state, in the vicinity of the maximum shear stress point, which is close to the dike toe. The various piping categories differ in the size of these vicinities, depending on the relative density of the soils and the shear strength of the base and cover layers. The idea that the special Hungarian two-layered subsoil conditions may result in a larger hydraulic gradient and a smaller shear resistance than expected in situations of homogeneous soils is also explored. In previous work [12], it was proposed that the soils washed-out from beneath the dikes originate from the cover layer, on the basis of only four samples. In this paper, the idea is tested further using measured data for 20 additional washed-out soil samples. These are presented using the entropy diagram, and compared with the soils from the natural base strata at some dike failure sites. Moreover, the failure mechanism is explained by analyzing the stress and volumetric strain variations in the dike base during flooding in the Hungarian experience. The hypothesised complex process is confirmed in this paper by analyzing the liquefaction susceptibility of materials taken from the sand boil, consideration of the hydraulic conditions of seepage with dynamic water-front effects, and analysis of a theory of lateral spreading, showing that a sudden cracking displacement with some additional dynamic effects due to the decrease in the soil friction during the movement of the soil body is likely to occur. Entropy 2015, 17 2284 2. Elements of the Analysis 2.1. Review of the Grading Entropy Based Rules 2.1.1. Statistical Cells (Fractions and Elementary Cells) Grading entropy is a measure which reflects the range and frequency of different sized particles in a soil [13–16]. This is most simply determined from a mechanical sieve analysis. A cell system of particle sizes is used as the basis to apply the statistical entropy theory of a discrete distribution and the successive sieve hole diameters generally have a multiplier of two. The double statistical cell system is used, defined by an arbitrary elementary cell width, d0, and a non-uniform sized cell system (“fraction system”) defined on the pattern of the classical sieve aperture diameters. The diameter range for fraction j (j = 1, 2, 3 …, N; see Table 1) is: jj-1≥> 22,dd00 d (1) For granular soils, the smallest particles are caused by crushing which can produce particles not less than the size of some microns. For plastic soils, the diameters can be much smaller, however, the concept is not significantly influenced by the selection of the elementary cell width d0. Table 1. Definitions of fractions and cells, where d0 is the elementary cell width. Fraction j 1 ... 23 24 22 23 23 24 Limits d0 to 2 d0 ..
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