Pier and Contraction Scour in Cohesive Soils (2004)

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14 CHAPTER 3 EROSION FUNCTION APPARATUS (EFA) 3.1 CONCEPT The EFA shown in Figures 3.1 and 3.2 (Briaud et al. 1999, 2001, as well as http://www.humboldtmfg.com/pdf2/ hm4000ds.pdf and http://tti.tamu.edu/geotech/scour) was conceived in 1991, designed in 1992, and built in 1993. A sample of soil, fine-grained or not, is taken in the field using an ASTM standard Shelby tube with a 76.2-mm outside diameter (ASTM D1587). One end of the Shelby tube full of soil is placed through a circular opening in the bottom of a rectangular cross-section conduit. A snug fit and an O-ring establish a leak-proof connection. The cross section of the rectangular conduit is 101.6 mm by 50.8 mm. The conduit is 1.22-m long and has a flow straightener at one end. The water is driven through the conduit by a pump. A valve regulates the flow and a flow meter is used to measure the flow rate. The range of mean flow velocities is 0.1 m/s to 6 m/s. The end of the Shelby tube is held flush with the bottom of the rectan- gular conduit. A piston at the bottom end of the sampling tube pushes the soil until it protrudes 1 mm into the rectan- gular conduit at the other end. This 1-mm protrusion of soil is eroded by the water flowing over it. 3.2 EFA TEST PROCEDURE The procedure for the EFA test is as follows: 1. Place the sample in the EFA, fill the conduit with water, and wait 1 hour. 2. Set the velocity to 0.3 m/s. 3. Push the soil 1 mm into the flow. 4. Record how much time it takes for the 1 mm of soil to erode (visual inspection through Plexiglas window). 5. When the 1 mm of soil is eroded or after 1 hour of flow, whichever comes first, increase the velocity to 0.6 m/s and bring the soil back to a 1-mm protrusion. 6. Repeat Step 4. 7. Then repeat Steps 5 and 6 for velocities equal to 1 m/s, 1.5 m/s, 2 m/s, 3 m/s, 4.5 m/s, and 6 m/s. 3.3 EFA TEST DATA REDUCTION The test result consists of the erosion rate z˙– versus shear stress τ curve (Figure 3.1). For each flow velocity v, the ero- sion rate z˙– (mm/hr) is simply obtained by dividing the length of sample eroded by the time required to do so. Where h is the length of soil sample eroded in a time t. The length h is 1 mm and the time t is the time required for the sample to be eroded flush with the bottom of the pipe (visual inspection through a Plexiglas window). After several attempts at measuring the shear stress τ in the apparatus it was found that the best way to obtain τ was by using the Moody Chart (Moody, 1944) for pipe flows. Where τ is the shear stress on the wall of the pipe; f is the friction factor obtained from the Moody Chart (Figure 3.3); ρ is the mass density of water (1,000 kg/m3); and v is the mean flow velocity in the pipe. The friction factor f is a func- tion of the pipe Reynolds Number Re and the pipe roughness
/D. The Reynolds Number is vD/v where D is the pipe diam- eter and v is the kinematic viscosity of water (10−6m2/s at 20°C). Since the pipe in the EFA has a rectangular cross sec- tion, D is taken as the hydraulic diameter D = 4A/P where A is the cross-sectional flow area, P is the wetted perimeter, and the factor 4 is used to ensure that the hydraulic diameter is equal to the diameter for a circular pipe. For a rectangular cross-section pipe: Where a and b are the dimensions of the sides of the rec- tangle. The relative roughness
/D is the ratio of the average height of the roughness elements on the pipe surface over the pipe diameter D. The average height of the roughness ele- ments
is taken equal to 0.5D50 where D50 is the mean grain size for the soil. The factor 0.5 is used because it is assumed that the top half of the particle protrudes into the flow while the bottom half is buried in the soil mass. D ab a b= +( )2 3 3( . ) τ ρ= 1 8 3 22f v ( . ) ˙ ( . )z h t = 3 1

15 Figure 3.1. Schematic diagram and result of the Erosion Function Apparatus (EFA). (b)(a) 3.4 EFA PRECISION AND TYPICAL RESULTS If the erosion rate is slow (less that 10 mm/hr), the error on z˙– is estimated at 0.5 mm/hr. If the erosion rate is fast (more than 100 mm/hr), the error on z˙– is estimated at 2 mm/hr. Therefore, the relative error on z˙– is estimated to be less than 10%. Comparison between the τc results for the sand and the gravel tested in this study and shown on Figure 2.2 with Shields data indicates a difference of about 10%. Therefore, it is estimated that both z˙– and τ are measured with a relative error of about 10%. The z˙– versus τ curve is the result of a series of tests, each of which is performed at a constant velocity. A typical series of eight velocity tests lasts one work day. Figure 2.1 and Fig- ure 3.4 show examples of EFA test results. Figure 3.2. Photographs of the EFA: (a) general view, (b) close-up of the test section.

Figure 3.3. Moody Chart (reprinted with permission from Munson et al., 1990). 16 Figure 3.4. Erosion function for a soil sample taken near Pier 27E of the existing Woodrow Wilson Bridge (2.6 to 3.2 m depth): a) scour rate versus shear stress, b) scour rate versus velocity.