SCOUR AROUND CIRCULAR PIERS FOUNDED IN CLAY-SAND-GRAVEL SEDIMENT MIXTURES

Abstract

Pier and abutment undermining due to scouring and riverbed erosion has been generally recognized as the main cause of bridge failure. Therefore, realistic estimation of maximum depth of scour around bridge piers is required for safe and economic design of bridge foundations. The accurate estimation of depth of scour, below the streambed around bridge elements is very important since that determines the depth of bridge elements such as pier, abutment, guide bank, spur, groynes, etc. The depth of scour below the bed level around bridge piers in erodible bed streams can vary significantly depending upon flow, pier and sediment characteristics. The process of scour around piers founded in cohesionless uniform and non-uniform sediments are reasonably well understood at present. However, the land surfaces and river bed materials frequently consist of mixture of cohesive as well as cohesionless sediments like mixtures of sand, gravel and clay etc. A few investigators have studied the process of scour around piers founded in cohesive sediments [Briaud et al. (1999), Ting et al. (2001) Ansari et al. (2002) and Debnath and Chaudhuri (2010)]. But no data was available as yet on scour around piers founded in cohesive sediments formed by clay-gravel and clay-sand-gravel mixtures. Several investigations have been conducted in past to study flow characteristics around piers and abutments founded in cohesionless sediments [Melville and Raudikivi, (1997); Graf and Istiarto, (2002); Dey and Raiker, (2007); Kumar (2007)] mainly in upstream of pier founded in cohesionless sediments. But no study was done so far on flow and turbulence field and quadrant analysis within a scour hole in wake zone of a pier founded in clay-gravel and clay-sand-gravel sediment mixtures. The present investigation was taken up to fill the above mentioned gaps in knowledge. EXPERIMENTAL SETUP AND PROCEDURE A major experimental program was undertaken to study the process of pier scour in claygravel and clay-sand-gravel mixtures and to quantify the flow and turbulence fields in the scoured wake zone of pier founded in such sediment mixtures. The experiments were i conducted in a tilting flume 16 m long, 0.75 mwide and 0.5 mdeep. The channel had a test section of 6.0 m length, 0.75 mwidth and 0.16 mdepth starting at a distance of 7.5 m from channel entrance. Observations were made at various slopes of flume ranging from 7.56 xlO" to5.4xl0"3. Locally available clay excavated from a depth of 1.0 mbelow the ground was used as cohesive material. Theclay material had a median size equal to 0.052 mm, sand had a median size of 0.18 mm and o-g of 1.18, while gravel had a median size of 3.1 mm and Og of 1.23. The relative density of sand and gravel was 2.65. The other engineering properties of clay material were: liquid limit = 27.75%, plastic limit = 21.59%, plasticity index = 6.16%, maximum dry density = 19.03 kN/m3, optimum moisture content OMC = 12%, cohesion at optimum moisture content, Cu =25A3 kN/m2, angle of internal friction at optimum moisture content, </)c =29.32° and relative density =2.65. The clay was classified as CL i.e. clay with low plasticity. Cohesive sediments were prepared by mixing clay material with fine gravel and with fine sand-fine gravel mixtures (each in equal proportion) in proportion varying from 20% to 60%. The tests were conducted under maximum possible range of antecedent moisture content so as to represent their different stages as anticipated in field conditions. Therefore cohesive sediments were tested for determination of depth of scour around pier at several moisture consistencies ranging from soft soil with negligible cohesion (having less value of unconfined compressive strength, UCS) to hard soil with a high value of cohesion (high value of UCS). 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) by using standard core cutter method. The value of dry density was computed by 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. In all 33 experimental runs were conducted for clay-gravel mixtures and 27 experimental runs were conducted for clay-sandgravel mixtures. A total of 6 experimental runs were also conducted for cohesionless sediment of gravel and gravel-sand mixtures for reference. The instantaneous three-dimensional velocity and turbulence characteristics in scoured bed in wake zone and front of the pier were measured by an acoustic Doppler velocimeter (ADV). The time-averaged velocity components in cylindrical coordinate system (r, 8, z directions) are represented by (u, v, w) whose corresponding fluctuations are (u ,v ,w ). The positive directions of u, v and w are stream-wise, outward and upward, respectively. In order to present the distance of different ADV measuring locations with respect to pier periphery the radial distance is given by r0 = r - 0.56, where r is the distance from centre of the pier to the point of location of measurement by an ADV, b is the diameter of pier. It means that r0 = 0 represents the pier boundary. VISUAL ANALYSIS OF THE SCOUR PROCESS The process of scour, shape and geometry of the scour hole in cohesive sediment mixtures formed by clay-gravel and clay-sand-gravel are significantly different as compared to that in cohesionless sediments. Scour holes of varying shapes and sizes were observed to develop in cohesive sediment mixtures. Location of maximum depth of pier scour in such sediment varied to based on the sediment characteristics. Whereas maximum depth of scour almost invariably occurs at upstream nose of pier in cohesionless sediments, it was noticed to occur at pier side and/or in the wake zone in case of cohesive sediments. The scoured zone in some sediment mixtures extended on downstream side of the pier in the form of a narrow but long strip. This result has implication in devising methods for control of scour in such cohesive sediments. MATHEMATICAL MODELLING FOR TEMPORAL VARIATION OF DEPTH OF SCOUR The mathematical model for the computation of depth of scour in cohesive sediments has been developed by using Kothyari et al. (2007) method for the computation of depth of scour in cohesionless sediments as the basis. in Temporal Variation of Maximum Depth of Scour at Side of Pier Analysis ofdata on temporal variation ofmaximum depth ofscour at side ofpier revealed that dscsldss is inversely proportional to (\+Pc), (1+ UCS.) and (I+ CJfa) for both sediment mixtures. After making a number of trials using all relevant dimensionless parameters, it was found that following functional relationships for maximum depth of scour could be derived for variation of dscs Idss with change in values of(1+PC), (1 +C, / fa) and (1+ UCS,). d„ ' ( 0 +^X v v \ +C' \ fa ,(\ + UCS.) Here dscs is depth of scour at side of pier in cohesive sediment, dss is depth of scour in cohesionless sediment, Pc is clay percentage, UCS* is dimensionless unconfined compressive strength, C, is dimensionless clay content and fa is dimensionless angle of internal friction. The main consideration used in above proposed model for scour computations is that when cohesion in sediment bed becomes zero, the proposed method transforms to the model of Kothyari et al. (2007) for scour in cohesionless sediments. Using all relevant dimensionless parameters, it was found that following relationships could be derived for describing the variation of dscs/dss as d.. F Where F =(1 +3.4/>c)C| (1 +0.0002C/GS,)°'[1 +0.0005(C, Ifa)* ] Withe, =0^.4, +3-. .2~ exp-0U'0U0W0WH** ;c2 = 0r>.3-> +, 3i .4aexp-0.00002/. in clay-gravel mixture for Pc = 20 to 40% IV c, =1.2 +2.7exp-°-0003'-;c2 =1.0 +3.2exp-0-00002'* in clay-gravel mixture for Pc = 50 to 60% c, =0.85 +3.2 exp-0000,5'-;c2 =0.75+3.4exp-0-0000,/* in clay-sand-gravel mixture for Pc = 20 to 40% c, =0.95+9.2 exp-0-0002'-;c2 =0.60 +3.9exp-0-000()"- in clay-sand-gravel mixture for Pc = 50 to 60% and dimensionless time, t =t— da Here F is parameter representing the cohesion of sediment bed, t, is dimensionless time, u, is shear velocity, da is arithmetic mean size of cohesive sediment. The comparisons between computed and observed depth of scour at pier sides based on Da, <Ja, Rd and ad 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\% average discrepancy ratio based on the average value of the logarithm ratio between computed and observed results, aa 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 ad is standard deviation of the computed results based on difference. Temporal Variation of Maximum Depth of Scour at Wake of the Pier Analysis of data on temporal variation of maximum depth of scour in the wake zone revealed that dscw/dss is directly proportional to dimensionless time t, and inversely proportional to (\+Pc) and (1+ UCS.). The following functional relationships could be derived for variation of dscw/dsswith change in values of t, , (1+PC), and (1+f/CSV). ^ =f[t.,(\+Pc),(l+UCS.)] And the following satisfactory relationships could be derived for describing the variation of dscw/dss with change in values of /„, (1+PC), and (\+UCS,) as for scour in clay-gravel mixture d F for scour in clay-sand-gravel mixture d 1 sew = «*« ^ where, parameter F„. , represents cohesion of sediment bed and is expressed as Fw ={t^1A)[(\+Pc)51\(\ +UCS.fM] and similarly Fw is expressed as FW2 =(t,-QA0)[(\+Pc)519][(l +UCS,)066] The temporal variation of computed depth of scour was also compared with the corresponding observations and mostly a satisfactory comparison was noticed. FLOW AND TURBULENCE FIELDS AROUND THE PIER Vertical Distribution of Stream-wise Velocity Relatively less variation in normalized velocity component u was observed in cohesionless sediment bed of gravel-sand in comparison to cohesive sediment bed consisting of clayvi gravel and clay-sand-gravel. The flow field in wake zone exhibits some trend as the value of u increases when we move from near to pier (r0 = 40 mm) to away from pier (r0 = 190mm) in the azimuthal plane 8 = 0 which represents downstream nose of the pier. The lowest value of normalized u among all the experimental runs was observed to be at the closest measuring point from pier periphery (i.e. at r0 = 40 mm) in the azimuthal plane 8 = 0° and for z/h > 0 in the wake zone. Here z is vertical distance and h is depth of approach flow. However the maximum value of normalized u above initial bed level (z/h > 0) among most of the experimental runs was observed to be at r0 = 40mm in the azimuthal plane 8=90°. Turbulence Intensity The maximum value of longitudinal component of turbulence intensity 4uu is observed to occur near the original bed level (z/h = 0 to -0.6) in almost all the runs indicating the importance of turbulence intensity in sediment detachment for the process of scour to happen but relatively less turbulence intensity was observed in the case of cohesionless sediment bed. The maximum value of turbulence intensity was observed to exist at r0 = 40 mm in most of the experimental runs. Moving away from the pier the value of turbulence intensity seems to reduce to a great extent in most of the azimuthal planes. Above the original bed level (z/h > 0), fairly uniform distribution of turbulence intensity is observed at almost all the location in various azimuthal planes. The variation of normalized vertical component of turbulence intensity \w'w' across the flow depth almost follows the same trend as observed for longitudinal turbulence intensity. However, the magnitude of vertical component is much smaller than that of corresponding longitudinal component. Occurrence of maximum value of Vw u lu. and VwV Iu. at z/h ~ 0 clearly indicates that turbulence intensity is responsible for scour and suspension of sediment particle which is in conformity with the findings of previous investigators (Mazumdar and Ojha, 2007). vn Reynolds Stress The maximum value of normalized u'W component of Reynolds stresses is observed to occur in the scour hole (z/h < 0) in the azimuthal plane varying from 0 to 90 i.e. wake zone of pier. The remaining azimuthal planes (90° to 180°) indicated fairly uniform and much smaller value of Reynolds stresses. This indicates that turbulence is more prominent in the wake zone of the pier than in front of the pier. Larger scour in the wake zone in comparison to pier upstream in cohesive sediments as observed in present study is attributed to this reason. Also above the original bed level (z/h > 0) the Reynolds stresses do not show any significant value. The variation of vV component of Reynolds stress also shows the maximum value within the scour hole (z/h < 0). However its magnitude is fairly less than uw component. Also above the original bed level (z/h > 0) the vV component of Reynolds stresses do not show any significant value. Turbulent Kinetic Energy The maximum value of turbulent kinetic energy is observed to occur within the scour hole (i.e. for z/h < 0) predominantly at radial distance r0 = 40 mm in the various azimuthal planes in almost all the runs. This result indicates that maximum turbulence fluctuations occur in the flow within the scour hole near the pier. Further away from the scour hole i.e. when r0 > 40 mm, in various azimuthal planes, fairly uniform and much smaller value of turbulent kinetic energy is observed. In comparison to most of the experimental runs in cohesive sediment bed, the experimental run in cohesionless sediment bed recorded relatively more uniform distribution of turbulent kinetic energy (except in the azimuthal plane 8 = 0°). In a few runs, however the value of A; is observed above the original bed level (i.e. for z/h > 0) is noticeable. In some experimental runs the maximum value of turbulent kinetic energy is recorded near the scoured bed in azimuthal plane 8 = 150 to 180°. This may be attributed to reverse flow condition at these locations. In general relatively more uniform distribution of normalized turbulent kinetic energy is noticed for z/h > 0 in all the azimuthal planes (except 8 = 0°) in almost all the runs. viu QUADRANT ANALYSIS The highest value of occurrence probabilities S,,H was found for ejection in experimental run GC5.6 between z/h = -0.3 to -0.1 at all locations i.e., at r0= 40, 90, 140and 190 mm in the azimuthal plane 0°. Its value however reduces as one moves either towards scoured bed or water surface. Maximum value of occurrence probabilities 5,,// is recorded near about initial bed level in the case of sweep also in 8 = 0 plane. The outward and inward interactions have maximum value at lower most level and decreases near initial bed level. Their values further increase towards the water surface. In azimuthal plane of8 = 0° (experimental run GSC2.4), no specific trend of bursting events were recorded. However a well defined pattern of these events was exhibited in azimuthal plane of 8 = 30 . Outward and inward interaction recorded the lowest value of 5,// between z/h = -0.1 to -0.3 and they increased above and below of this range of z/h. This trend of variation in these two events was also similar in azimuthal plane of 8 = 60 and 90 except in 8 = 180 where, the minimum value of SiH were recorded in z/h = 0. A general trend of ejection and sweep in all the azimuthal planes of8 = 60°, 90° and 180° indicated that they had its maximum value of S(,h between z/h = -0.1 to -0.3 except in 8 = 180 where, the maximum value of SLh were recorded at z/h = 0. The variation of the value of SiyH in ejection and sweep along z/h were almost in complete agreement of each other in 8 = 180 plane. Above analysis indicates that out of the four bursting events ejection and sweep are the main events