Pier and Contraction Scour in Cohesive Soils (2004)

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

11 Figure 2.1. Erodibility function for a clay and a sand. 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 * * unknown TABLE 2.1 Factors influencing the erodibility of cohesive soils Figure 2.2. Critical shear stress versus mean soil grain diameter. For such soils, the erosion rate beyond the critical shear stress is very rapid and one flood is long enough to reach the maximum scour depth. Therefore, there is a need to be able to predict the critical shear stress to know if there will be scour or no scour but there is little need to define the erosion τc m D mmN 2 50 2 1( ) = ( ) ( . ) function beyond that point because the erosion rate is not suf- ficiently slow to warrant a time-dependent analysis. In cohesive soils (silts and clays) and rocks, Equation 2.1 is not applicable (Figure 2.2) and the erosion rate is suffi- ciently slow that a time-dependent analysis is warranted. Therefore, it is necessary to obtain the complete erosion func- tion. An attempt was made to correlate those parameters, τc

could not be found within the budget and time of this proj- ect. Instead, it was found much easier to develop an appa- ratus that could measure the erosion function on any sam- ple of cohesive soil. This device was called the Erosion Function Apparatus, or EFA. 12 Woodrow Wilson Bridge (Washington) Tests 1 to 12 South Carolina Bridge Tests 13 to 16 Tests 17 to 26 National Geotechnical Experimentation Site (Texas) Arizona Bridge (NTSB) Test 27 Indonesia samples Tests 28 to 33 Porcelain clay (man-made) Tests 34 to 72 Bedias Creek Bridge (Texas) Tests 73 to 77 Sims Bayou (Texas) Tests 78 to 80 Brazos River Bridge (Texas) Test 81 Navasota River Bridge (Texas) Tests 82 and 83 San Marcos River Bridge (Texas) Tests 84 to 86 San Jacinto River Bridge (Texas) Tests 87 to 89 Trinity River Bridge (Texas) Tests 90 and 91 TABLE 2.2 Database of EFA tests τc vs. w τ c (P a) R2 = 0.0245 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 0.00 20.00 40.00 60.00 80.00 100.00 W (%) W (%) Si vs. w R2 = 0.0928 0.10 1.00 10.00 100.00 1000.00 10000.00 0.00 20.00 40.00 60.00 80.00 100.00 S i (m m/ hr x m 2 / N) Figure 2.3. Erosion properties as a function of water content. and Si, to common soil properties in the hope that simple equations could be developed for everyday use. The pro- cess consisted of measuring the erosion function and com- mon soil properties (i.e., water content, unit weight, plas- ticity index, percent passing sieve no. 200, undrained shear strength). This led to a database of 91 EFA tests (Table 2.2), which was used to perform regression analyses and obtain correlation equations (Figures 2.3 to 2.6). All attempts failed to reach a reasonable R2 value. The fact that in this project no relationship could be found between the critical shear stress or the initial slope of 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 parameters should be functions of the soil properties. The likely explanation is that there is a relationship between erodibility and soil properties but that this relationship is quite complicated, involves advanced soil properties, and

R2 = 0.1093 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 Su(kPa) c vs. Sτ u τ c (P a) 0.10 1.00 10.00 100.00 1000.00 10000.00 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 Su(kPa) Si vs. Su S i (m m/ hr x m 2 / N) R2 = 0.056 0.00 5.00 10.00 15.00 20.00 30.00 35.00 40.00 45.00 0.00 20.00 40.00 60.00 80.00 100.00 PI(%) τc vs. PI 25.00 τ c (P a) Si vs.PI R2 = 0.0011 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00 0.00 20.00 40.00 60.00 80.00 100.00 PI(kPa) S i (m m/ hr x m 2 / N) Figure 2.4. Erosion properties as a function of undrained shear strength. Figure 2.5. Erosion properties as a function of plasticity index. Figure 2.6. Erosion properties as a function of percent passing sieve #200.