Maximum Abutment Scour Depth in Cohesive Soils

Most conventional methods to predict the depth of abutment scour were developed with flume test results using cohesionless soils, and those methods have been used to the abutment scour depth prediction in cohesive soils. Generally floodplains where most abutments are located are composed of less erodible soils such as cohesive soils. Therefore those methods usually predict overly conservative scour depths. For the cost effective designs, a series of flume tests were carried out using Porcelain clay. Based on dimensional analysis and the test results, a new method to predict the bridge abutment scour depths is proposed. The new method built on the difference between the local Froude number and the critical Froude number. Because abutment scour occurs only when the local velocity is higher than the critical velocity which is the maximum velocity the channel bed material can withstand. INTRODUCTION Floodplains where most bridge abutments exist are typically composed of cohesive soils such as silts and clays. The soil properties of cohesive soils on erosion resistance are much complicated than those of cohesionless soils. Cohesion less soils resist erosion by buoyant weight and the soil particle friction , while cohesive soils do it by electromagnetic and electrostatic interparticle forces (Briaud et al. 1999b). The critical shear stress, which is the maximum shear stress soil particles can resist from the flow, of uniformly distributed cohesionless soils linearly decreases with particle size decrease . On the contrary, the critical shear stress of cohesive soils cannot be defined by the particle size (Briaud et al. 2001). Moreover, the erosion rate of cohesive soils can be 1,000 times slower than that of coehsionless soils, and a few days may generate only a small fraction of the maximum scour depth (Briaud et al. 2004) . Hence, both the critical velocity and the scour rate should be considered in the prediction of scour depth in cohesive material for more accurate and economic bridge design and maintenance, and these requirements stimulated to the development of the SRICOS-EFA (Scour Rate In Cohesive Soils Erosion Function Apparatus) method. The SRICOS-EF A method was initially developed to predict the depth around single circular pier in cohesive soil (Briaud et al. 1999b). It was further developed to predict complex pier scour and contraction scour (Briaud et al. 2004). Moreover,


INTRODUCTION
Floodplains where most bridge abutments exist are typically composed of cohesive soils such as silts and clays. The soil properties of cohesive soils on erosion resistance are much complicated than those of cohesionless soils. Cohesion less soils resist erosion by buoyant weight and the soil particle friction , while cohesive soils do it by electromagnetic and electrostatic interparticle forces (Briaud et al. 1999b). The critical shear stress, which is the maximum shear stress soil particles can resist from the flow, of uniformly distributed cohesionless soils linearly decreases with particle size decrease . On the contrary, the critical shear stress of cohesive soils cannot be defined by the particle size (Briaud et al. 2001). Moreover, the erosion rate of cohesive soils can be 1,000 times slower than that of coehsionless soils, and a few days may generate only a small fraction of the maximum scour depth (Briaud et al. 2004). Hence, both the critical velocity and the scour rate should be considered in the prediction of scour depth in cohesive material for more accurate and economic bridge design and maintenance, and these requirements stimulated to the development of the SRICOS-EFA (Scour Rate In Cohesive Soils -Erosion Function Apparatus) method.
The SRICOS-EF A method was initially developed to predict the depth around single circular pier in cohesive soil (Briaud et al. 1999b). It was further developed to predict complex pier scour and contraction scour (Briaud et al. 2004). Moreover, 132 more complicated but realistic geological and hydrological conditions were considered (Briaud et al. 1999a).
In the present study a method to predict the maximum abutment scour depth in cohesive soils is introduced to extend the use of the SRICOS-EFA method to the scour depth prediction around the toe of abutment. The method was developed using the results of a series of large flume tests for ab utment scour in cohesive soi Is .

PREVIOUS STUDIES ON MAXIMUM ABUTMENT SCOUR DEPTH
Since most prediction methods to predict abutment scour depths are developed flume test results using cohesion less soils, many equations include soil particle sizes to define the critical shear stress or erodibility.

Froehlich 's studv
Froehli ch (1989) collected abutment scour test results taken by other researchers in rectangular channels in different laboratories from 1953 to 1985, and performed data regression using a total of 164 clear-water and 170 live-bed abutment scour measurements in sand. He proposed both the live-bed and the clear-water abutment scour equation as follows: Clear-water scour: where u g =(D S4 ID'6t 5 is the geometric standard deviation of the bed material, and D 1 6, Dso, and D S4 are the particle size for 16, 50 and 84 percentile of weight, respectively, Fr, = (V; 1 g . y,) is Froude number based on approach water depth and approach velocity, K, is the correction factor for abutment shape that has a value of 1.0, 0.82 and 0.55 for vertical wall, wing-wall, and spill-through abutment, respectively.

SRICOS-EF A METHOD
The principle of the SRlCOS-EF A method is summarized here to provide a necessary background. The SRlCOS-EF A method is highly dependent on the maximum scour depth and the shear stress between the flow and soil interface. The methodology of maximum scour depth is developed by flume test results, and the maximum shear stress on the channel bed is developed by three-dimensional numerical simulations. The procedure of SRlCOS method is consisted with following steps.
(1) Obtain standard 76 .2 mm diameter Shelby tube samples as close to the bridge support as possible.
(2) Conduct EF A test (Briaud et al. 1999a) of the samples to obtain the critical shear stress (Tc) and the erodibility curve of erosion rate versus shear stress (i vs. T).
(4) Obtain the initial scour rate (z;) corresponding to ""ox. Yf where t is time (hour), andys is the maximum scour depth.

EXPERIMENTS
A concrete flume with dimension of 45 .7 m in length, 3.7 m in width and 3.4 m in depth was used to conduct the abutment scour tests. A sediment pit, which has dimensions of 7.5 m in length, 3.7 m in width and 1.5 m in depth, is located around the middle of the flume. The pit was filled with the Porcelain clay, and the geotechnical properties of the clay are given in Table 1 Two types of channel were used for flume tests: one is a rectangular channel, and the other is a compound channel. The channel cross sections are shown in Figure  I. Three types of abutment made of plywood were used in the flume tests: the first one is the wing wall shape, the second one is the spill-through shape with a 2(H): I (V) slope, and the third one is the spill-through shape with a 3(H): 1 (V) slope.
A point gauge was used to measure the water depth and the maximum scour depth, and a bed profiler was used to scan the channel bottom topography. The velocity was measured at the 60% of water depth from the free surface by two side looking 3-D ADVs (Acoustic Doppler Velocimeters).

TEST RESULTS
Eighteen flume tests were conducted by varying the abutment shape, approach embankment length, abutment alignment, channel shape, water depth and flow velocity. During each test the channel bottom was scanned as many times as possible, and the maximum scour depth in each measurement (Ys (.4 blllit)) was recorded because scour develops very slowly in cohesive soil. This is different with scour development in cohesionless soil. Velocity was measured at the beginning, approximately 100 hours after the test started, and before end of the test.  Figure 3. The maximum average velocity was found to be close to the wall which is away from and downstream of the abutment (dashed circle in Figure  2(a», while the highest turbulence intensity was around the toe of the abutment at slightly downstream (dashed circle in Figure 2(b» . These patterns are coincident with locations at which the deepest contraction scour and the abutment scour were measured during every measurement (Figure 3). The scour depth was recorded as a function of time as Ys(Aburj{t). At the end of each test, the scour depth was still developing although the test time is longer than 300 hours (Figure 3 and Figure 4). It is therefore not feasible to obtain the maximum scour depth directly through the test. A hyperbolic model was thus used to obtain the maximum abutment scour depths (Figure 4). During experiments, it was found that the maximum scour depth, in the same test conditions except abutment shape, of the 2(H): 1 (V) spill through abutment is 70% of that of the wing-wall abutment. This ratio is close to the abutment shape correction factor between the spill-through abutment and the wing-wall abutment in Melville (1992). However, contrary results were found in the abutment alignment effect to previous studies (Froehlich 1989;Melville 1992;Richardson and Davis 1995). The maximum scour depth for the abutment skewed upstream is less than that for the abutment normally aligned to the flow . The contrary may be due to the use of different types of abutment. The spill-through abutment which induces a relatively smooth flow around the toe of the abutment was used in this study, whereas vertical abutments were used in the previous studies. This is evidenced in TI. The maximum TJ for the abutment with e = 120 0 was approximately 10% less than that for the abutment with e = 90 0 • Note that the turbulence pattern is identical to the abutment scour pattem.
As shown in Figure 2 and Figure 3, the local velocity is the most important parameter on abutment scour. However, it cannot be easily calculated. In addition, flume tests cannot account for all possible conditions in the field. For the calculation of the local velocity around the abutment, the approximation in Maryland SHA Bridge Scour Program (ABSCOUR) was adopted. The method to convert the hydraulic data to the local velocity is as follows: where Q lbl is the discharge on the floodplain at the approach section immediately upstream of the abutment, ~ is total flow area at the contracted section, Af2 is the flow area on the floodplain at the contracted section, and L f is the width of floodplain at the approach section, and Yml is the water depth of main channel at the approach section.

DIMENSIONAL ANALYSIS
The variables affecting abutment scour can be expressed in equation (6) and rewritten in dimensionless form in equation (7) below.
where Sh is the abutment shape, e is the alignment angle of abutment, J.1 is the VJc r c / P

J.1
Abutment scour occurs when the local flow velocity is higher than the critical velocity, and continues until the local velocity equals to the critical velocity. Thus the abutment scour equation may be expressed in the form of Froude number difference as follows: (8) where KL is the correction factor for the abutment location, KG is the correction factor for the channel geometry, K Re is the correction factor for the Reynolds number effect, and al , PI and XI are constant.
In equation (8), the three constants (ai , PI and XI ) and four correction factors (KI,K 1 ,K L and KG) were obtained after data regression using flume test results. They are as follows: In equation (9), the correction factors for the Reynolds number effect was not obtained using the 18 flume test results because the range of Reynolds numbers in the tests are too narrow. As expected, equation (9) fits well to the flume test results of the present study while mostly under estimates when compared with smaller scale laboratory test and over estimates when compared with field data. The main cause of the discrepancy is the Reynolds number effect. The range of Reynolds number in several studies, including the present study, is given in Table 2.  Froehlich (1989) Stunn ( Figure 5 shows the effect of Reynolds number on the maximum abutment scour depth. In order to quantify the effect, laboratory data in Table 2 from Froehlich (1989) and Strum (2004) were plotted. Note that the database from Benedict et al. (2006) was not used because the accuracy of the field data is likely to be much lower than that of the laboratory test. According to the curve fitting shown in Figure 5, the effect of Reynolds number can be expressed as ;:

CONCLUSION
A series of flume test were conducted for the abutment scour in cohesive soils. A method to predict the maximum abutment scour depth is proposed using the flume test results. The method is based on the difference between the local Froude number and the critical Froude number. Four correction factors, abutment shape, alignment, channel geometry, and abutment location, were included. The scale effect is also considered.