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10 CHAPTER 2 ERODIBILITY OF COHESIVE SOILS 2.1 ERODIBILITY: A DEFINITION et al. (1999), but is summarized below. The factors influenc- ing the erodibility of cohesive soils according to the litera- Erodibility is a term used often in scour and erosion studies. ture survey are listed in Table 2.1. Although conflicting find- Erodibility may be represented as one number that charac- ings sometimes occur, the influence of various factors on terizes the rate at which a soil is eroded by the flowing water. cohesive soil erodibility is shown in Table 2.1. With this concept, erosion-resistant soils would have a low The critical shear stress of cohesionless soils is tied to erodibility index and erosion-sensitive soils would have a high the size of the particles and usually ranges from 0.1 N/m2 erodibility index. This concept is not appropriate; indeed the to 5 N/m2. The rate of erosion of cohesionless soils above water velocity in rivers can vary drastically from 0 m/s to the critical shear stress increases rapidly and can reach tens 5 m/s or more. Therefore erodibility cannot be represented by of thousands of millimeters per hour. The most erodible a single number but is a relationship between the velocity soils are fine sands and silts with mean grain sizes in the applied and the corresponding erosion rate experienced by 0.1 mm range (Figure 2.2). The critical shear stress of cohe- the soils. While this is an improved definition of erodibility, sive soils is not tied to the particle size but rather to a num- it still presents some problems because water velocity is a ber of factors as listed in Table 2.1. The critical shear stress vector quantity that varies everywhere in the flow. It is prefer- of cohesive soils, however, varies within the same range as able to quantify the action of the water on the soil by using cohesionless soils (0.1 N/m2 to 5 N/m2 for the most com- the shear stress applied by the water on the soil at the water- mon cases). Since the critical shear stress controls the max- soil interface. Erodibility is therefore defined here as the rela- imum depth of scour, as will be seen later, it is likely that tionship between the erosion rate z and the hydraulic shear the final depth of scour will be approximately the same in stress applied (Figure 2.1). This relationship is called the sands and in clays. One major difference between cohe- erosion function z (). The erodibility of a soil or a rock is rep- sionless and cohesive soils is the rate of erosion beyond the resented by the erosion function of that soil or rock. critical shear stress. In cohesive soils, this rate increases slowly and is measured in millimeters per hour. This slow 2.2 EROSION PROCESS rate makes it advantageous to consider that scour problems are time dependent and to find ways to accumulate the effect Soils are eroded particle by particle in the case of coarse- of the complete hydrograph rather than to consider a flood grained soils (cohesionless soils). In the case of fine-grained design alone. soils (cohesive soils), erosion can take place particle by parti- cle but also block of particles by block of particles. The bound- aries of these blocks are formed naturally in the soil matrix by 2.4 ERODIBILITY AND CORRELATION micro-fissures which result from various phenomena, such as TO SOIL AND ROCK PROPERTIES compression and extension. For coarse-grained soils, the resistance to erosion is influ- There is a critical shear stress c below which no erosion enced by the weight of the particles; for fine-grained soils, occurs and above which erosion starts. This concept, while resistance to erosion is influenced by a combination of weight convenient, may not be theoretically simple. Indeed, as seen and electromagnetic and electrostatic interparticle forces. on Figure 2.1, there is no obvious value for the critical shear Slow-motion videotape observations at the soil-water inter- stress. In this report, the critical shear stress is arbitrarily face indicate that the removal of particles or blocks of parti- defined as the shear stress that corresponds to an erosion rate cles is by a combination of rolling and plucking actions of the of 1 mm/hr. The critical shear stress is associated with the water on the soil. critical velocity vc. One can also define the initial slope Si = (dz /d)i at the origin of the erosion function. Both c and Si 2.3 EXISTING KNOWLEDGE ON ERODIBILITY are parameters that help describe the erosion function and, OF COHESIVE SOILS therefore, the erodibility of a material. In cohesionless soils (sands and gravels), the critical shear A complete discussion on the erodibility of cohesive soils stress has been empirically related to the mean grain size D50 and a literature review on that topic can be found in Briaud (Briaud et al., 2001).

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11 Figure 2.1. Erodibility function for a clay and a sand. c ( N m 2 ) = D50 ( mm) (2.1) function beyond that point because the erosion rate is not suf- ficiently slow to warrant a time-dependent analysis. For such soils, the erosion rate beyond the critical shear In cohesive soils (silts and clays) and rocks, Equation 2.1 stress is very rapid and one flood is long enough to reach the is not applicable (Figure 2.2) and the erosion rate is suffi- maximum scour depth. Therefore, there is a need to be able ciently slow that a time-dependent analysis is warranted. to predict the critical shear stress to know if there will be Therefore, it is necessary to obtain the complete erosion func- scour or no scour but there is little need to define the erosion tion. An attempt was made to correlate those parameters, c TABLE 2.1 Factors influencing the erodibility of cohesive soils When this parameter increases Erodibility Soil water content * Soil unit weight decreases Soil plasticity index decreases Soil undrained shear strength increases Soil void ratio increases Soil swell increases Soil mean grain size * Soil percent passing sieve #200 decreases Soil clay minerals * Soil dispersion ratio increases Soil cation exchange capacity * Soil sodium absorption ratio increases Soil pH * Soil temperature increases Water temperature increases Water chemical composition * Figure 2.2. Critical shear stress versus mean soil grain * unknown diameter.

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12 and Si, to common soil properties in the hope that simple TABLE 2.2 Database of EFA tests equations could be developed for everyday use. The pro- Woodrow Wilson Bridge (Washington) Tests 1 to 12 cess consisted of measuring the erosion function and com- South Carolina Bridge Tests 13 to 16 mon soil properties (i.e., water content, unit weight, plas- National Geotechnical Experimentation Site (Texas) Tests 17 to 26 ticity index, percent passing sieve no. 200, undrained shear Arizona Bridge (NTSB) Test 27 Indonesia samples Tests 28 to 33 strength). This led to a database of 91 EFA tests (Table 2.2), Porcelain clay (man-made) Tests 34 to 72 which was used to perform regression analyses and obtain Bedias Creek Bridge (Texas) Tests 73 to 77 correlation equations (Figures 2.3 to 2.6). All attempts Sims Bayou (Texas) Tests 78 to 80 Brazos River Bridge (Texas) Test 81 failed to reach a reasonable R2 value. Navasota River Bridge (Texas) Tests 82 and 83 The fact that in this project no relationship could be San Marcos River Bridge (Texas) Tests 84 to 86 found between the critical shear stress or the initial slope of San Jacinto River Bridge (Texas) Tests 87 to 89 Trinity River Bridge (Texas) Tests 90 and 91 the erosion function and common soil properties seems to be at odds with the accepted idea that different cohesive soils erode at different rates. Indeed, if different clays erode at different rates, then the erosion function and therefore its could not be found within the budget and time of this proj- parameters should be functions of the soil properties. The ect. Instead, it was found much easier to develop an appa- likely explanation is that there is a relationship between ratus that could measure the erosion function on any sam- erodibility and soil properties but that this relationship is ple of cohesive soil. This device was called the Erosion quite complicated, involves advanced soil properties, and Function Apparatus, or EFA. c vs. w Si vs. w 35.00 10000.00 30.00 1000.00 25.00 R2 = 0.0928 Si(mm/hr x m2/N) 100.00 20.00 c (Pa) 15.00 10.00 R2 = 0.0245 10.00 1.00 5.00 0.00 0.10 0.00 20.00 40.00 60.00 80.00 100.00 0.00 20.00 40.00 60.00 80.00 100.00 W (%) W (%) Figure 2.3. Erosion properties as a function of water content.

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c vs. Su Si vs. Su 45.00 10000.00 40.00 35.00 1000.00 30.00 Si(mm/hr x m2/N) 100.00 25.00 c (Pa) R2 = 0.1093 20.00 10.00 15.00 10.00 1.00 5.00 0.00 0.10 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 Su(kPa) Su(kPa) Figure 2.4. Erosion properties as a function of undrained shear strength. c vs. PI Si vs.PI 45.00 200.00 40.00 180.00 35.00 Si(mm/hr x m2/N) 160.00 140.00 30.00 c (Pa) 120.00 25.00 100.00 20.00 80.00 15.00 60.00 10.00 40.00 R2 = 0.056 R2 = 0.0011 5.00 20.00 0.00 0.00 0.00 20.00 40.00 60.00 80.00 100.00 0.00 20.00 40.00 60.00 80.00 100.00 PI(%) PI(kPa) Figure 2.5. Erosion properties as a function of plasticity index. Figure 2.6. Erosion properties as a function of percent passing sieve #200.