**3. Factors affecting the earth erosion phenomenon**

Main factors affecting the erosion phenomenon are: a) the erodibility of the soil; b) the water velocity inside the soil mass or the water velocity on a river; c) geometry of the earth structure through its size and shape.

*Erodibility* can be defined as the relationship between the velocity of the water flowing over the soil and the corresponding erosion rate experienced by the soil. This definition of erodibility presents some problems because water velocity is a vector quantity which varies everywhere in the flow and is theoretically zero at the soil-water interface. It is preferable to quantify the action of the water on soil by using the shear stress applied by the water on the soil at the water-soil interface. Thus, erodibility of a soil can be defined by the relationship between the erosion rate *Z* and the shear stress *τ* at the soil-water interface (Briaud, 2008):

$$\dot{Z} = f\left(\tau\right) \tag{1}$$

Fig. 4. Proposed erosion categories for soils and rocks based on shear stress (Briaud, 2008)

Internal Erosion Due to Water Flow Through Earth Dams and Earth Structures 289

on the construction of the earth structure; for instance, if the permeability of the soil layers varies from one another, there might exist a mayor seepage concentration on those layers of higher permeability; c) the type of preventive measures in the downstream side of an earth structure, such as graded filters designed to prevent displacement of the fine particles; d) the compaction control along the installation of pipeline conduits; along such installations, many initial leaks and piping effects have been reported in the literature (Flores-Berrones et al., 2011); e) existence of hydraulic fracture in certain zones of an earth structure, where the water pore pressure becomes larger than the minor principal stresses (Peck, 1976); f) as it was already mentioned, the high plasticity soils, such as clays of high plasticity, are less

vulnerable to erosion than cohesionless soils.

Fig. 5. Constant water head permeameter

produce a slope failure.

**4. Analysis of seepage forces and their effect in slope stability** 

more complicated when seismic forces have to be considered.

possible to obtain the hydraulic gradient at any point of the flow region.

There are several practical cases where it is necessary to consider the forces produced by the water flow for the slope stability analysis of an earth structure. In the case of earth dams and levees, the water flow conditions that might occur and have to be consider for slope stability analysis are the following: a) transient flow that occurs during the first filling or a rapid drawdown conditions; b) constant flow which occurs sometimes after the reservoir is operating under regular water flow conditions; c) anisotropic water flow when the horizontal permeability is different than the vertical one. These three conditions might be

The water flow effects on the stability of an earth structure are the following: a) internal soil erosion o piping by removing and transporting soil particles, starting a duct that might increase rapidly, producing a complete failure; b) water pressure increase that will decrease the effective stresses and therefore decrease in the shear strength of the soil; c) increment on the water flow forces due to gravity might significantly decrease the safety factor and

Using either the graphical or numerical analysis, as it is explained later in this chapter, it is

For the most common practical cases that exist in earth dams and levees, Flores Berrones et al. (2003) have demonstrated that the water flow analysis can be reduced to a two dimensional

system, so equation (4) is the one that must be considered for steady-state conditions:

2 2 2 2 <sup>0</sup> *h h x y* 

(4)

As explained later in section 7.1, this erosion function can be obtained by using a laboratory device called the erosion function apparatus ‒EFA‒ (Briaud et al., 2001). Recently, based on erosion testing experience, *erosion categories* have been proposed in terms of water velocity or shear stress. Erodibility as a function of water velocity is less representative and leads to more uncertainties than using shear stress, as mentioned above. Then, Figure 4 shows these proposed erosion categories for soils and rocks based on shear stress (Briaud, 2008). According to this figure, it seems that grain size controls coarse grained soil erosion and plasticity seems to have a significant influence on fine grain soil erosion.

Additionally, some of the most important properties influencing erodibility of soils are listed in Table 2.


Table 2. Soil properties influencing erodibility (Briaud, 2008)

On the other hand, the velocity of the water flow through the soil mass depends on the hydraulic conductivity of the soil and the hydraulic gradient. According to several experimental tests, the water flow through fine soils is considered to be *laminar* (water particles move parallel each other), and such flow follows the Darcy's law, giving the following expression:

$$V = ki \tag{2}$$

Where *V* = discharge velocity, *k* = hydraulic conductivity and *i* = hydraulic gradient.

The hydraulic conductivity of the soil is determined through laboratory or field tests; for clean sands and gravel mixtures the hydraulic conductivity varies from 10-1 to 10-3 cm/sec, whereas for very fine sands to homogeneous clays the *k* value varies from 10-4 to 10-9 cm/sec (Lambe, 1951). The hydraulic gradient is given by the difference of the water head *h*1 at the entrance and the water head *h*2 at the exit of a soil section, where there exist a water flow, divided by the length *L* of the flow path. Using the information provided by Figure 5, the hydraulic gradient is given by the following expression:

$$i = (\mathbb{I}\_1 \text{--} \mathbb{I}\_2) / \,\mathrm{L} = \Delta \mathrm{h} / \,\mathrm{L} \tag{3}$$

As it can be observed in Eq. (3), the hydraulic gradient is dimensionless. Later in this chapter, we demonstrate the existence of a hydraulic gradient that makes the effective stresses among soil particles become zero, in such a way that the friction resistance forces against erosion become nullified. The smallest hydraulic gradient that nullifies such stresses is called *critical* and its value usually ranges between 1 ±0.20.

Some other factors affecting the internal soil erosion or piping in soils are: a) the degree of compaction of the soil layers on the earth structure; b) the homogeneity and quality control on the construction of the earth structure; for instance, if the permeability of the soil layers varies from one another, there might exist a mayor seepage concentration on those layers of higher permeability; c) the type of preventive measures in the downstream side of an earth structure, such as graded filters designed to prevent displacement of the fine particles; d) the compaction control along the installation of pipeline conduits; along such installations, many initial leaks and piping effects have been reported in the literature (Flores-Berrones et al., 2011); e) existence of hydraulic fracture in certain zones of an earth structure, where the water pore pressure becomes larger than the minor principal stresses (Peck, 1976); f) as it was already mentioned, the high plasticity soils, such as clays of high plasticity, are less vulnerable to erosion than cohesionless soils.

288 Soil Erosion Studies

As explained later in section 7.1, this erosion function can be obtained by using a laboratory device called the erosion function apparatus ‒EFA‒ (Briaud et al., 2001). Recently, based on erosion testing experience, *erosion categories* have been proposed in terms of water velocity or shear stress. Erodibility as a function of water velocity is less representative and leads to more uncertainties than using shear stress, as mentioned above. Then, Figure 4 shows these proposed erosion categories for soils and rocks based on shear stress (Briaud, 2008). According to this figure, it seems that grain size controls coarse grained soil erosion and

Additionally, some of the most important properties influencing erodibility of soils are

On the other hand, the velocity of the water flow through the soil mass depends on the hydraulic conductivity of the soil and the hydraulic gradient. According to several experimental tests, the water flow through fine soils is considered to be *laminar* (water particles move parallel each other), and such flow follows the Darcy's law, giving the

 *V* = *ki* (2)

The hydraulic conductivity of the soil is determined through laboratory or field tests; for clean sands and gravel mixtures the hydraulic conductivity varies from 10-1 to 10-3 cm/sec, whereas for very fine sands to homogeneous clays the *k* value varies from 10-4 to 10-9 cm/sec (Lambe, 1951). The hydraulic gradient is given by the difference of the water head *h*1 at the entrance and the water head *h*2 at the exit of a soil section, where there exist a water flow, divided by the length *L* of the flow path. Using the information provided by Figure 5, the

 *i* = (*h*1 –*h*2)/*L* = ∆*h*/*L* (3) As it can be observed in Eq. (3), the hydraulic gradient is dimensionless. Later in this chapter, we demonstrate the existence of a hydraulic gradient that makes the effective stresses among soil particles become zero, in such a way that the friction resistance forces against erosion become nullified. The smallest hydraulic gradient that nullifies such stresses

Some other factors affecting the internal soil erosion or piping in soils are: a) the degree of compaction of the soil layers on the earth structure; b) the homogeneity and quality control

Where *V* = discharge velocity, *k* = hydraulic conductivity and *i* = hydraulic gradient.

plasticity seems to have a significant influence on fine grain soil erosion.

Soil water content Soil dispersion ratio Soil unit weight Soil cation exchange cap Soil plasticity index Soil sodium absorption rat

Soil void ratio Soil temperature Soil swell Water temperature Soil mean grain size Water salinity Soil percent passing #200 Water pH

Table 2. Soil properties influencing erodibility (Briaud, 2008)

hydraulic gradient is given by the following expression:

is called *critical* and its value usually ranges between 1 ±0.20.

Soil undrained shear stress Soil pH

listed in Table 2.

Soil clay minerals

following expression:
