ROLE OF SAND BOIL FORMATION IN LEVEE FAILURE

V. P. Singh, C. S. P. Ojha, D. D. Adrian and S. Ozkan

Department of Civil Engineering, Louisiana State University

Baton Rouge, LA 70808, U. S. A. (cesing@lsu.edu) 

G. E. Sills

Geotechnical Branch, U. S. Army Corps of Engineers

Vicksburg District, 4155 Clay Street, CELMK-ED-G

Vicksburg, MS 39183, U. S. A.

Abstract: Flood-induced seepage may lead to development of piping underneath the base of levees. The piping causes cavities which may grow, resulting in sudden levee settling and failure. The flow of water in the piping, called seepage, occurs due to hydrostatic head gradient between the two sides of a levee. This flow causes migration of soil particles to the exit point of the flow path where the particles deposit and form a sand boil. The size of the sand boil reflects the integrated effect of seepage characteristics, porous medium characteristics and hydraulics of flow behind and underneath the levee. On the other hand, the development of piping has been reported to be useful to withstand the increase in head beyond critical head conditions. Thus, a levee design may be benefited by considering the geomechanics and hydraulics of piping and sand boil formation. This study makes a critical review of the existing literature and then proposes an analytical framework for determination of the significance of sand boils on levee failures. It also evaluates the effect of porous medium characteristics on the sand boil formation.

Keywords: critical head, hydraulic conductivity, porosity, sand boil, seepage

1    INTRODUCTION

The use of levees to protect land areas from floods has been common in many parts of the world. The continued use of thumb rules of Bligh (1910) and  Lane (1935) in many parts of the world indicates that the importance of  levees  has been recognized for a long time. These thumb rules provide guidelines for selecting a range of length-to-critical-head ratio for different types of soils, including clay, silt, sand, and gravel. Depending on the site-specific conditions, these levees may rest on the beds of varying permeability. In levees, a phenomenon called “piping” is a common occurrence and is generally accompanied by the formation of sand boils. Basically, starting from the point of sand boil formation, a pipe-like opening develops below the levee base, as shown in Figure 1 and it proceeds towards the stream. If this process continues, the failure of levee becomes inevitable. 

Thurnbull and Mansur (1961) offered a summary of the flood-induced seepage under levees based on their experience with the U. S. Army Corps of Engineers. Peter (1974, 1982) examined the conditions of piping phenomenon in the subsoil and near levees in the Mississippi region in the United States  and in the Danube region in former Czechoslovakia, Hungary, and Yugoslavia. Van Zyl and Harr (1982) discussed different types of seepage erosion, including piping.  Khilar et al. (1985) developed criteria for piping in clayey soils. Schuster and Sabol (1994) and Budh and Gobin (1995) also addressed the problem of seepage erosion and presented case studies.

Fig. 1    Definition sketch for sand boil formation

Excluding the thumb rules of Bligh (1910) and  Lane (1935), which were proposed for specific soil types and which did not explicitly account for porosity variations, a key component of piping models has been the use of a porosity/permeability term in defining the critical head limits, which should always be respected for the safety of the levee. Sellmeijer (1988), Sellmeijer and Koenders (1991), and Weijers and Sellmeijer (1993) developed models for sand beds. However, their studies on sand beds report partial success while showing the variation of critical head with porosity. Schuster and Sabol (1994) used horizontal and vertical permeabilities as the basis for modifying empirical rules of Lane (1935) for estimation of critical head.

To study the role of porosity, use is made of the models of Terzaghi as cited in (Peter, 1982), and Khilar et al. (1988) for sand beds. While doing so, an attempt is also made to investigate the role of porosity within the framework of a Darcy’s law-based critical head model for avoiding occurrence of sand boil.

2    CRITICAL HEAD MODELS

Fig. 1 shows the definition sketch of a levee, along with the points of sand boil formation and development of piping or slit channel. Considering the equilibrium of forces in the soil, Terzaghi as cited by Peter (1982) proposed the following equation:

                           (1)

where i_c = critical head gradient, g_s= the specific weight of soil,  g_w = the specific weight of  water, and e = clean bed porosity.

Another model by Leva et al. as cited by Peter (1982), although not available in terms of the critical hydraulic gradient, does highlight the influence of porosity. Further details on this model can be had from Peter (1982). Among the models proposed in the last two decades, Khilar et al. (1985) presented the following equation as a measure of the critical gradient causing piping:

where K_h = hydraulic conductivity (cm/s), and t_c = critical tractive stress (dynes/cm²). For a particle of size d, the critical tractive stress t_c used by Khilar et. al. (1985) is expressed as

Here, t_c is in g/m² and d is in mm.  Lane as cited by Khilar et. al (1985) suggested the use of d₅₀ with c as 10 for granular materials. 

A well-known equation for estimating the saturated hydraulic conductivity is the Kozeny-Carman equation (Singh, 1997):

where d_m = some representative grain size diameter, r = fluid density, g = gravitational acceleration, and m = dynamic viscosity of the fluid.

There is also a class of equations which do not include any influence of porosity. One such equation is given by Harleman et al. (1963):

where d = a characteristic grain size and equals d₉₀ for non-granular materials (McWhorter and Sunada, 1981).

3    CRITICAL HEAD USING DARCY’S LAW

Considering the flow channel just at the base level, one can note that at its upstream, the available head is H. Let the critical head corresponding to a porosity e be H_crit and the associated head loss be h_f in a length L_. Corresponding to a critical condition, let the incipient or critical velocity be V_c.

With base as the datum and using Bernoulli’s theorem between the top surface of the upstream water body having zero velocity and the upstream atmospheric pressure, and the point A (see Fig. 1), where the velocity is V_s , the datum head is zero, and the pressure is assumed atmospheric, one can obtain the following expression for V_s:

Thus, using (6), one can write the following expression for incipient critical velocity V_c corresponding to the critical head H_crit :

For a given particle size and fluid properties, V_c will remain same. Eq. 7 can be also written as

Using Darcy’s law,

With use of (9), (8) can be expressed as

It can be seen from (10) that due to an increase in permeability, which is associated with sand boil formation, there is a decrease in the critical head for initiation of the motion of medium particles. Thus, a levee, which is exposed to sand boil development, is weak enough to resist the next flood for the same head.

4    DEPENDENCE ON POROSITY

It is evident that the dependence of critical head/critical gradient on porosity varies with the expression for K_h that is used. Considering (1), (2), (9) in conjunction with (4) and (5), one can express the  following generalized variation between i_c and e.

In (11), m and n are constants.  For example, with reference to Darcy’s law-based critical head model, m = 2 and n= 3. Similarly, with reference to (1), m = 1 and n = 0  Thus, one can see that depending on the use of a particular critical head gradient model and a specific relationship for intrinsic or hydraulic conductivity, the dependence of critical gradient on porosity may exhibit a range of behavior. Thus, an examination of porosity dependence may give useful insight into the critical head gradient model and the appropriate porosity functions associated therewith.

5    ANALYSIS OF DATA

Weijers and Sellmeijer (1993) present many graphs, which show the variation of critical head with porosity. In these graphs, the base length of the structure, particle diameter, and fluid properties remain the same. Using these data, one can obtain values of the observed ratio of critical heads. To assess the suitability of an appropriate porosity function, one can minimize the error function E defined in a least squares sense as:

where N = number of observations. Based on minimization of E, Table 1 lists the average error E associated with different optimization strategies.

                  Table 1    Details of error optimization

6    RESULTS AND DISCUSSION

With due consideration to the porosity function, it is reasonable to infer that in case of sands studied here, Darcy’s model is a better performer than the Terzaghi model. It is noted that the objective here is not to present a comparative evaluation of different models. However, when such evaluations are needed, the role of porosity cannot be overlooked.

The use of Darcy’s law is popular in flows through porous media and for this reason this was considered, although the flow conditions during piping may not always represent a laminar flow situation. However, a limited data analysis does indicate that   the Darcy law still has a potential for estimation of the critical head along with the Carman- Kozeny relationship for the permeability  in justifying the dependence of critical head on porosity.

7    CONCLUSIONS

The choice of an appropriate porosity function is found to influence the adequacy of piping models. The use of Darcy’s law is found useful in explaining the dependence of porosity on critical head for three different sets of data related to sands of different sizes and origin. The sand boil formation leads to an increase in hydraulic conductivity and thus lowers the critical head. However, this observation is based on negligible role of slit in the piping phenomenon.

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