**8.3 Analysis considering both rapid filling and drawdown phenomena**

This example focuses on studying the effects on soil erosion due to transient flow within a levee as water level of a river increases and decreases because of the rain cycles in a tropical region. Simplified geometry of studied domain including foundation soil of the levee is illustrated in Figure 19. Properties of materials are specified in Table 3 (Lopez-Acosta et al., 2010).

Fig. 19. Simplified geometry and material number of the studied domain (Lopez-Acosta et al., 2010)

Internal Erosion Due to Water Flow Through Earth Dams and Earth Structures 303

In the same way, from Figures 21 and 22, it can also be observed that in general the highest values of flow velocity occur in the more pervious materials of the studied domain; in contrast, the highest values of hydraulic gradient arise in the less pervious materials of this domain. This is a suggestion that instability problems of levees could not be solved by constructing them with more impervious material, but rather building them with more or less pervious material or even placing drains in strategic areas of the body of levees (Lopez-Acosta et al., 2010). Some authors have indeed concluded that soils with a low hydraulic conductivity, such as clayey and silty soils, are more prone to slope failure than more

Based on previous results, it can be said that in the case of slope stability analysis, it should be considered on the one hand, the susceptibility to erosion of the material used for constructing the levee; but on the other one, the analysis must also consider measures to

Quite recently, some types of analyses based on probabilistic methods have been suggested for the study of levees in general. Hubel et al. (2010) presented a practical approach to assess combined levee erosion, seepage forces, and slope stability failure modes; they developed response curves for landside and waterside slope stability, as well as landside seepage failure modes for various hydrostatic water loads. In a similar context, the Army Corps of Engineers (Lee & Wibowo, 2007, as cited in Hubel et al., 2010) used the limit state approach

decrease the hydraulic gradients and seepage forces generated within the soil mass.

for estimating the probability of levee erosion that might induce a breaching failure.

Fig. 21. Hydraulic gradients (magnitude) for three different times during rapid filling and

drawdown (Lopez-Acosta et al., 2010)

pervious materials such as granular soils (Pradel & Raad, 1993).


Table 3. Properties of material layers (Lopez-Acosta et al., 2010)

Boundary conditions assumed for analyses were as follows:


Fig. 20. Boundary conditions assumed for analyses (Lopez-Acosta et al., 2010)

From results of analyses (Lopez-Acosta et al., 2010), it is interesting to note that during transient flow certain regions of higher hydraulic gradients and flow velocities are generated, as appreciated in Figures 21 and 22, respectively. Predominantly, the highest values of hydraulic gradients and velocities take place at the toe of downstream slope of levee. Specifically, the gradient values of those areas greater than the so-called critical gradient (>1) could facilitate *global piping* through the body of levee or through the foundation soil (Figure 21). These above mentioned highest values occur when maximum level of water surface is achieved (day 17 of filling). Additionally, it can be observed that during rapid filling velocity vectors are directed towards downstream (Figure 22a) and during rapid drawdown the direction of some of these vectors changes towards upstream (Figure 22b). Particularly, during rapid drawdown it can be observed that velocities and gradients generated near the upstream slope, as water level descends, are not negligible; in extreme conditions they could facilitate *local erosion* of material in those zones (Lopez-Acosta et al., 2010).

N° Material Hydraulic conductivity, *k* Void ratio, *e*

plasticity (OH) 0.00864 m/d (1×10-7 m/s) 0.90



1 Clay sand (SC) 0.0864 m/d (1×10-6 m/s) 0.43 2 Sandy clay of low plasticity (CL) 0.0864 m/d (1×10-6 m/s) 0.50

4 Clay sand (SC) 0.0864 m/d (1×10-6 m/s) 0.43 5 Silty sand (SM) 0.0864 m/d (1×10-6 m/s) 0.43 6 Organic clay of high plasticity (OH) 0.00864 m/d (1×10-7 m/s) 0.90 7 Clay levee 0.00864 m/d (1×10-7 m/s) 0.70

Table 3. Properties of material layers (Lopez-Acosta et al., 2010)

16.4m, in a period of 17 days (variation is illustrated in Figure 20).

Fig. 20. Boundary conditions assumed for analyses (Lopez-Acosta et al., 2010)

From results of analyses (Lopez-Acosta et al., 2010), it is interesting to note that during transient flow certain regions of higher hydraulic gradients and flow velocities are generated, as appreciated in Figures 21 and 22, respectively. Predominantly, the highest values of hydraulic gradients and velocities take place at the toe of downstream slope of levee. Specifically, the gradient values of those areas greater than the so-called critical gradient (>1) could facilitate *global piping* through the body of levee or through the foundation soil (Figure 21). These above mentioned highest values occur when maximum level of water surface is achieved (day 17 of filling). Additionally, it can be observed that during rapid filling velocity vectors are directed towards downstream (Figure 22a) and during rapid drawdown the direction of some of these vectors changes towards upstream (Figure 22b). Particularly, during rapid drawdown it can be observed that velocities and gradients generated near the upstream slope, as water level descends, are not negligible; in extreme conditions they could facilitate *local erosion* of material in those zones (Lopez-Acosta

11.3m, in a period of 27 days (variation is shown in Figure 20).

Boundary conditions assumed for analyses were as follows:

<sup>3</sup>Organic sandy-clay silt of high

et al., 2010).

In the same way, from Figures 21 and 22, it can also be observed that in general the highest values of flow velocity occur in the more pervious materials of the studied domain; in contrast, the highest values of hydraulic gradient arise in the less pervious materials of this domain. This is a suggestion that instability problems of levees could not be solved by constructing them with more impervious material, but rather building them with more or less pervious material or even placing drains in strategic areas of the body of levees (Lopez-Acosta et al., 2010). Some authors have indeed concluded that soils with a low hydraulic conductivity, such as clayey and silty soils, are more prone to slope failure than more pervious materials such as granular soils (Pradel & Raad, 1993).

Based on previous results, it can be said that in the case of slope stability analysis, it should be considered on the one hand, the susceptibility to erosion of the material used for constructing the levee; but on the other one, the analysis must also consider measures to decrease the hydraulic gradients and seepage forces generated within the soil mass.

Quite recently, some types of analyses based on probabilistic methods have been suggested for the study of levees in general. Hubel et al. (2010) presented a practical approach to assess combined levee erosion, seepage forces, and slope stability failure modes; they developed response curves for landside and waterside slope stability, as well as landside seepage failure modes for various hydrostatic water loads. In a similar context, the Army Corps of Engineers (Lee & Wibowo, 2007, as cited in Hubel et al., 2010) used the limit state approach for estimating the probability of levee erosion that might induce a breaching failure.

Fig. 21. Hydraulic gradients (magnitude) for three different times during rapid filling and drawdown (Lopez-Acosta et al., 2010)

Internal Erosion Due to Water Flow Through Earth Dams and Earth Structures 305

 The applicability of the concepts presented in this chapter was illustrated through some examples related to the analysis of soil erosion problems caused by rapid filling and

Alberro, J. (2006). *Effect of transient flows on the behavior of earth structures*, 8th Nabor Carrillo

Auvinet, G.; López-Acosta, N.P. & Pineda, A. R. (2008). *Final report of Integral Hydraulic* 

Auvinet, G. & Lopez-Acosta, N.P. (2010). Rapid drawdown condition in submerged slopes,

Briaud, J. L. (2008). Case histories in soil and rock erosion: Woodrow Wilson bridge, Brazos

Brinkgreve, R.B.J.; Al-Khoury, R. & Van Esch, J. M. (2006). *Plaxflow User Manual Version 1.4*,

Casagrande, A. (1968). *Notes of engineering 262 Course*, Vol. 1, Harvard University,

Cedergren, H. (1989). *Seepage, drainage and flow nets*, Third Edition, John Wiley & Sons Inc.,

Chapuis, R. P. & Gatien, T. (1986). An improved rotating cylinder technique for quantitative

Fell, R.; Wan, C. H. & Foster, M. (2003). *Progress report on methods for estimating the probability* 

Flores-Berrones, R. (2000). *Water flow through soils*, Avances en Hidráulica, Mexican Hydraulic Association and Mexican Institute of Water Technology, Mexico (in Spanish) Flores-Berrones, R.; Alva-Garcia, F. & Li Liu, X. (2003). Effect of water flow on slope stability. *Hydraulic Engineering in Mexico*, Vol. 18, No. 2, (April-June), pp. 35-52 (in Spanish) Flores-Berrones, R.; Ramirez Reynaga M. & Macari, E. J. (2011). Internal Erosion and

Freeze, R. A. (1971). Influence of the unsaturated flow domain on seepage through earth

Hanson, G. J. (1991). Development of a jet index to characterize erosion resistance of soils in

Huang, M. & Jia C-Q. (2009). Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage. *Computers and Geotechnics*, No. 36, pp. 93-101 Hubel, B. A.; Letter, Jr. J. V.; Goodhue, M. & Lee, L. T. (2010). A practical approach to asses

*Engineering*, Vol. 137, No. 2, (February 1, 2011), ASCE, pp. 150-160

earthen spillways. *Transaction ASAE*, Vol. 34, No. 5, pp. 2015-2020

dams. *Water Resources Research*, Vol. 7, No. 4, pp. 929-941

Lecture, Mexican Society of Geotechnical Engineering SMIG, Tuxtla Gutierrez,

*Project of Tabasco (PHIT)*, Research Report of Geotechnical Department, Institute of

In: *15 Presentations of friends and colleagues in tribute to Eng. Jesús Alberro Aramburu*, Edited by Institute of Engineering UNAM and the Mexican Society of Geotechnical Engineering (SMIG), pp. 167-189, ISBN 978-607-02-0866-9, Mexico (in Spanish) Briaud, J.-L.; Ting, F.; Chen, H. C.; Cao, Y.; Han, S.-W. & Kwak, K. (2001). Erosion function

apparatus for scour rate predictions. *Journal of Geotechnical and Geoenvironmental* 

river meander, Normandy cliffs and New Orleans levees. *Journal of Geotechnical and Geoenvironmental Engineering*, Vol. 134, No. 10, (October 1, 2008), ASCE, pp. 1424-1447

measurements of scour resistance of clays. *Canadian Geotechnical Journal*, No. 23, pp.

*of failure of embankment dams by internal erosion and piping*, The University of New

Rehabilitation of an Earth Dam. *Journal of Geotechnical and Geoenvironmental* 

combined levee erosion, seepage, and slope stability failure modes, Geotechnical

drawdown conditions in earth embankments.

Engineering UNAM, Mexico (in Spanish)

*Engineering*, Vol. 127, No. 2, pp. 105-113

Chiapas Mexico (in Spanish)

Balkema, The Netherlands

Cambridge, Massachusetts

South Wales, Sydney, Australia

New York

83-87

**10. References** 

Fig. 22. Velocity vectors (magnitude) for two different time intervals during rapid filling and drawdown (exaggerated scale) (Lopez-Acosta et al., 2010)
