SCOUR AROUND SPUR DIKES AND BRIDGE PIERS FOUNDED IN COHESIVE SEDIMENT MIXTURES

Abstract

One of the major considerations in the design and construction of a bridge is the scour around its foundation. Many of the bridge failures have been attributed to the scour or the undermining of hydraulic structures (i.e. piers, abutments and spur dikes etc.). Hence, for safe and economic design of hydraulic structures, it becomes essential to estimate the scour depth around such structures with greater accuracy. The accurate estimation of scour depth around bridge piers and spur dikes below the stream bed is important since, that determines the depth of such structures. Several formulae and mathematical models developed for the estimation of the scour depth are still primarily based on theoretical approaches and laboratory tests because of variable field data. Accurate field measurements are difficult to obtain due to the severe three dimensional flow pattern that occur at bridges during flooding, high cost of instrumentation and the costs of getting skilled personnel at bridge sites during period of peak flow. Unrealistic estimation of scour depth may lead to either over expenses in the construction or failure of the structure. Several studies are available on the scour around spur dikes and abutments in cohesionless sediment mixtures, but very few works have been carried out with cohesive sediments. Estimation of scour depth around spur dikes has attracted considerable research interest. Different prediction methods were presented by Garde et al. (1961), Melville (1992, 1997), Lim (1997), Cardoso and Bettess (1999), Melville and Chiew (1999), Ahmad and Rajaratnam (2000), Kothyari and Ranga Raju (2001), Sarma and Roy (2001), Thompson (2002) and Oliveto and Hager (2002, 2005) etc. The studies of scour around partially submerged spur dike and abutments in cohesionless sediments were conducted by Ettema and Muste (2004), Dey and Barbhuiya (2004, 2005), Giri and Shimizu (2004, 2005), Ezzeldin et al. (2007), Kothyari et al. (2007), Nasrollahi et al. (2008), Fazli et al. (2008), Zhang and Nakagawa (2008), Ghodsian and Vaghefi (2009), Vaghefi et al. (2009), Giri (2010), Uddin and Hossain (2011), and Masjedi and Foroushani (2012), Rashedipoor et al. (2012) and Zhang et al. (2012) etc. The experiments with submerged dikes for the prediction of scour depth were carried out by Kuhnle et al. (1999, 2002), Elawady et al. (2001) and Rodrigue-Gervais et al. (2011) etc. ii No studies have been conducted on scour depth around spur dikes (partially submerged and submerged) founded in cohesive sediment mixtures. Only few studies have been conducted on the scour around bridge abutments embedded in cohesive sediment mixtures consisting of clay and sand viz; Monilas and Reiad (1999), Oh et al. (2007), Chen (2008), Abou-seida et al. (2012) and Debnath et al. (2014). Kand (1993), Ansari (1999), Molinas et al. (1999), Briaud et al. (1999, 2001), Ram Babu et al. (2002), Kho (2004), Brandimate et al. (2006), Debnath and Chaudhuri (2010a, 2010b) and Chaudhuri and Debnath (2013) studied the scour depth around bridge piers embedded in the mixtures of cohesive sediments containing clay, sand and silt. Kumar (2011) and Kothyari et al. (2014) studied scour in the wake region of bridge pier embedded in mixtures of cohesive sediment composed of clay-gravel and clay-sandgravel mixtures. Very limited investigations have been carried out on scour around spur dikes and bridge piers founded in cohesive sediments with gravel present in it. Thus, there is a need for in-depth study on the effect of presence of cohesive material (clay) in addition to gravel and sand on the process of scour around pier and spur dikes founded in cohesive sediments. The present investigation was taken up to fill the above mentioned gaps in knowledge. EXPERIMENTAL SETUP AND PROCEDURE Extensive experiments were undertaken to study the process of scour around spur dikes (partially submerged and submerged) and pier founded in clay- gravel and claysand- gravel mixtures and to quantify the flow and turbulence fields around the spur dikes founded in cohesive sediment mixtures. The experiments were conducted in a fixed bed masonry flume of 25.0m length, 1.0m width and 0.60m depth, which is located at the Hydraulic Engineering Laboratory of Civil Engineering Department, Indian Institute of Technology, Roorkee, India. Experiments were conducted on two longitudinal slopes of the flume bed viz; 0.003 and 0.005. The slope of the flume was changed to 0.005 by pasting the cementing material from upstream to downstream of the flume. The flume had a test section of 4.0m length, 1.0m width and 0.60m depth, starting 12m downstream of the flume entrance. iii Locally available clay excavated from a depth of 1.0m below the ground was used as cohesive material. The clay properties were determined as per Indian Standard Code (IS-1498, 1970; IS-2720-29, 1975 and IS-2720-10, 1991). The median size of clay was 0.0014mm as observed by laser particle size analyzer. The geometric standard deviation ( g d84 d16 )   for the same was 2.16. The median size of sand and gravel obtained by sieve analysis were observed to be 0.24mm and 2.7mm respectively, and geometric standard deviation for the same was 1.41 and 1.21 respectively. The relative density of sand and gravel was 2.65. The engineering properties of clay material were: liquid limit (LL) = 43%, plastic limit (PL) = 22% and plasticity index (PI) = 21%, optimum moisture content (OMC) = 19%, maximum dry density  d max  = 16.43 kN/m3, cohesion at OMC = 49.23 kN/m2, angle of friction at OMC ( ( ) c  = 30.7o and relative density 2.65. The mineralogical properties of clay were determined by X-ray diffraction (XRD) test. It was observed the clay were composed of approximately 77.5% Illite, 18% Kaolinite, and 4.5% Montmorillonite. Cohesive sediments were prepared by mixing clay material with fine gravel and fine sand-fine gravel mixtures (each in equal proportion) in proportions varying from 10% to 50%. The channel bed of cohesive sediments was prepared as per Kothyari and Jain (2008). The unconfined compressive strength of the sediments was determined using laboratory based unconfined compression test apparatus as per IS - 2720-Part X (1991). The bulk unit weight of sediment was computed as per IS-2720-Part XXIX (1975) using standard core cutter method. The value of dry density was computed using the observed value of bulk density and antecedent moisture content. The void ratio was derived from computed value of dry density of cohesive sediments. Spur dikes with transverse length of 6.10cm, 8.90cm and 11.52cm were used as partially submerged spur dike. However, spur dike with 11.52cm transverse length was used for the submerged dike experiments. In all the experiments, single spur dike was installed at 90o angle to the direction of flow. Piers with outer diameter 11.52cm and 8.9cm were used for the study conducted in cohesive sediment mixtures. The spur dike or pier was installed 14m downstream of the flume entrance. The instantaneous three dimensional velocities and turbulence characteristics around the partially submerged and submerged spur dikes were measured by a down iv looking 16MHz Vectrino+ Acoustics Doppler Velocimeter (ADV) in the three spatial direction x, y and z at a sampling rate of 25Hz. In the data analysis, positive x- axis was along the flow direction, the positive y- axis was across the left of flow and positive zaxis was vertically upward. Intersection point of spur dike, inner face of wall and the original bed is considered as the origin (0, 0, 0) for the grid measurement. MATHEMATICAL MODELLING FOR TEMPORAL VARIATION OF DEPTH OF SCOUR A mathematical model for the computation of scour depth in cohesive sediments was developed by using Kothyari et al. (2007) method for the computation of depth of scour in cohesionless sediments as the basis. Analysis of data on temporal variation of scour depth around spur dikes and piers revealed that dc / d is inversely proportional to clay percentage ( ) c P , unconfined compressive strength(UCS ) , dimensionless cohesion ( ) * C and dimensionless angle of internal friction ( ) *  for both sediment mixtures. After making a number of trials using all relevant dimensionless parameters, it was found that the following functional relationships for maximum depth of scour could be derived for variation of dc / d with change in values of (Pc ) , (1 * / *)  C  and (1 UCS* ) .                   * * * f (P ), 1 C* , (1 UCS ),t d d c c  Here, dc is depth of scour in cohesive sediment mixtures, d is depth of scour in cohesionless sediment, c P is clay percentage, UCS* is dimensionless unconfined compressive strength, C* is dimensionless cohesion and *  is dimensionless angle of internal friction.   t  t Uo da * = time parameter. The variation of scour depth with * * C  did not show significant influence on scour depth in any cases. Multiple nonlinear regression analysis was used to find out relationship for scour depth around spur dikes (partially submerged and submerged) and pier using all pertinent dimensionless parameters. v Temporal Variation of Depth of Scour around Partially Submerged Spur Dike For depth of scour at nose of partially submerged spur dike in clay-gravel and clay-sand-gravel mixtures un un cun F d d  Where, un F = parameter that represents cohesion of clay-gravel and clay-sand-gravel mixtures at nose of the partially submerged spur dike and is expressed as (5Pc ) 1 (1 0.001 * ) 2 ( * ) 3  a a a Fun  ao  UCS t Where, 0.00144 ; 1.82; 0.705 ; 0.335 1 2 3 a  a   a   a  o for 10%  20% c P (Adjusted R2= 0.798) and 1.25 10 ; 1 4.75; 2 0.25; 3 0.786 ao   6 a   a   a  for 30%  50% c P (Adjusted R2= 0.837) For depth of scour at the wake of the partially submerged spur dike in clay-gravel and clay-sand-gravel mixtures uw uw cuw F d d  Where, uw F = parameter that represents cohesion of clay-gravel and clay-sand-gravel mixtures at the wake of the partially submerged spur dike and is expressed as c (5Pc ) 1 (1 0.01 * ) 2 ( * ) 3  c c c Fuw  o  UCS t Where, 0.00195; 1.525; 0.1067; 0.324 1 2 3 co  c   c   c  for 10%  20% c P (Adjusted R2= 0.785) and 2.96 10 ; 3.633; 0.306; 0.638 1 2 3 c   5 c   c   c  o for 30%  50% c P (Adjusted R2= 0.792) The temporal variation of computed depth of scour around partially submerged dike was also compared with the corresponding observations and mostly a satisfactory comparison was noticed. vi Temporal Variation of Depth of Scour around Submerged Spur Dike In the case of scour depth at nose of the submerged spur dike founded in mixtures of clay-gravel and clay-sand-gravel sn sn csn F d d  Where, Fsn = parameter that represents cohesion of clay-gravel and clay-sand-gravel mixtures at nose of the spur dike and is expressed as b (5P ) 1 (1 0.01 ) 2 ( ) 3  c * * b b b sn o F   UCS t Where, 0.0032; 1 1.365; 2 0.444; 3 0.298 bo  b   b   b  for 10%  20% c P (Adjusted R2= 0.85) and 5.7 10 ; 1 5.535 ; 2 0.43; 3 0.895 bo   7 b   b   b  for 30%  50% c P (Adjusted R2= 0.95) In the case of scour depth at wake of the submerged spur dike founded in mixtures of clay-gravel and clay-sand-gravel sw sw csw F d d  Where, Fsw= parameter that represents cohesion of clay-gravel and clay-sand-gravel mixtures at wake of the spur dike and is expressed as d (5Pc ) 1 (1 0.01 * ) 2 ( * ) 3  d d d Fsw  o  UCS t Where, 0.0028; 1 1.024; 2 0.4355; 3 0.331 do  d   d   d  for 10%  20% c P (Adjusted R2= 0.76) and 6.1 10 ; 1 4.33; 2 0.281; 3 0.876 do   7 d   d   d  for 30%  50% c P (Adjusted R2= 0.90) The temporal variation of computed depth of scour around partially submerged dike was also compared with the corresponding observations and mostly a satisfactory comparison was noticed. vii Temporal Variation of Depth of Scour around Pier For depth of scour at the sides of the pier in clay-gravel and clay-sand-gravel mixtures ps p cps F d d  Where, Fps = parameter that represents cohesion of clay-gravel and clay-sand-gravel mixtures at the sides of the pier and is expressed as m (Pc ) 1 (1 * ) 2 ( * ) 3  m m m Fps  o UCS t Where, 0.00024; 1 1.226; 2 0.0914; 3 0.3385 mo  m   m   m  for 10%  20% c P (Adjusted R2= 0.844) and 9.68 10 ; 1 2.653; 2 0.3785; 3 0.656 mo   7 m   m   m  for 30%  50% c P (Adjusted R2= 0.813) For depth of scour at the wake of the pier in clay-gravel and clay-sand-gravel mixtures pw p cpw F d d  Where, Fpw = parameter that represents cohesion of clay-gravel and clay-sand-gravel mixtures at the wake of pier and is expressed as n (Pc ) 1 (1 * ) 2 ( * ) 3  n n n Fpw  o UCS t Where, 5.9 10 ; 1 1.678; 2 0.346; 3 0.342 no   5 n   n   n  for 10%  20% c P (Adjusted R2= 0.853) and 2.41 10 ; 1 2.42; 2 0.253; 3 0.747 no   8 n   n   n  for 30%  50% c P (Adjusted R2= 0.808) viii The comparisons between computed and observed depth of scour at pier sides based on Da , a  , Rd and d  indicate that however, differences exists between corresponding computed and observed values, the accuracy of predictions of depth of scour for cohesive sediments is similar to those of Jain and Kothyari (2009 a and 2010) for bed load and suspended load transport in case of cohesive sediment mixtures and Yang et al. (1996); Almedeij and Diplas, (2003) relationships for sediment transport of the cohesionless sediments. Here, Da is average discrepancy ratio based on the average value of the logarithm ratio between computed and observed results, a  is standard deviation based on the average value of the logarithm ratio between computed and observed results, Rd is average discrepancy ratio based on the difference of computed and observed value and d  is standard deviation of the computed results based on difference. FLOW CHARACTERISTICS AROUND THE PARTIALLY SUBMERGED AND SUBMERGED SPUR DIKES The flow characteristics around the partially submerged and submerged spur dike in the clay-gravel were analyzed in the form of mean velocity, turbulence intensity, Reynolds stresses and turbulent kinetic energy. Quadrant analysis was also carried out to quantify the contribution of outward interaction, ejection, inward interaction and sweep events out of whole data for a particular z hvalue. At locations (5, 5), (5,10), (10,5) and (10,10) in the flow field of partially submerged and submerged spur dikes, very small values of longitudinal velocity component u (negative) were obtained whereas, larger values of u were obtained within the flow field bounded by the region x = 5 to 20cm and y = 15 to 25cm. At the point (5, 15) the value of u varied from 1.24 to 1.48 times the approaching flow velocity for partially submerged dike and 1.07 to 1.38 times the approaching flow velocity for submerged dike (velocity profile were measured from bed surface to water surface). The maximum value of longitudinal component of turbulence intensity occured near the original bed level ( z /h = 0.3 to -0.3) just behind the partially submerged spur dike within the region x = 5 to 20cm and y = 5 to 10cm. Whereas, in the case of submerged spur dike, maximum value of longitudinal component of turbulence intensity ix was observed to occur near the original bed level ( z /h = 0.5 to -0.25) just behind the submerged spur dike within the region x = 5 to 20cm and y = 5 to 10cm. The maximum value of Reynolds stress component u'w' was observed to occur in the wake zone of partially submerged and submerged spur dikes. The value of Reynolds stresses component u'w' is larger for partially submerged spur dike than that for submerged spur dike whereas, the Reynolds stress component v'w' did not show significant value around the spur dikes (partially submerged and submerged). The maximum value of turbulent kinetic energy was observed to occur in the wake zone (bounded by the region x = 5 to 20cm and y = 5 to 10cm) of partially submerged and submerged dike. Outside the scour hole, the values of the turbulent kinetic energy were larger for submerged spur dike than those for partially submerged dike while, within the scour hole the values of turbulence kinetic energy were larger for partially submerged dike than those observed for submerged spur dike. Quadrant analysis of ADV data showed that the values of outward and inward interaction were higher within the scour hole in partially submerged spur dike as compared to the values of ejection and sweep events, while outside of the scour hole the values of ejection and sweep events were higher as compared to the values of outward and inward interaction events. It was also observed that value of outward and inward interactions increases toward the lower most regions within the scour hole in case of partially submerged dike. In case of submerged spur dike, the values of outward and inward interaction events were higher at the downstream of the submerged dike (x = 5, 10 and 20cm) than its upstream (x = -15 and -5cm) at an azimuthal plane of y = 5 and 10cm. The trend observed for ejection and sweep events around the submerged spur dike was also similar to that observed around partially submerged spur dike. At outside of the scour hole, small values of ejection and sweep events were measured at the downstream of the submerged dike (x = 10 and 20cm) than its upstream (x = -15 and -5cm) at an azimuthal plane of y = 5 and 10cm. While, within the scour hole at (5, 5) and (5, 10) the ejection and sweep events have maximum value at lower most level and decreases near initial bed level.