SEDIMENT SCOUR AT PIERS WITH COMPLEX GEOMETRIES

Transcription

1 SEDIMENT SCOUR AT PIERS WITH COMPLEX GEOMETRIES D. MAX SHEPPARD Civil an Coastal Engineering Department, University of Floria, 365 Weil Hall Gainesville, Floria 3611, US TOM L. GLASSER Ocean Engineering Associates, Inc., 531 NW 41 st St., Blg. D. Gainesville, Floria 3606, US This paper presents proceures for computing local scour epths at complex piers uner clear-water an live-be flow conitions. The proceure is vali for complex piers having a column, pile cap (footer), an pile group, or any combination of these components. The proceure is base on the concept that, for the purpose of computing local scour epth, a complex pier can be replace by a circular pile. The iameter of the circular pile (referre to as the effective iameter of the complex pier) is such that the pile will experience the same equilibrium scour epth as the complex pier uner the same flow an seiment conitions. The effective iameter is compute using relationships that are functions of the shapes, locations an orientations of the pier components an the seiment properties an flow conitions. These relationships were evelope using the results of laboratory tests conucte by D. Max Sheppar (University of Floria), Sterling Jones (Feeral Highway Aministration), an Steven Coleman (University of Aucklan). 1 Introuction Most large brige piers are complex in shape an consist of several clearly efinable components. While these shapes are sensible an cost effective from a structural stanpoint, they present a challenge for those responsible for estimating esign seiment scour epths at these structures. This paper presents a revise methoology for estimating scour epths at a class of structures compose of up to three components. The ata use in the evelopment of this methoology is from laboratory tests conucte by D. Max Sheppar at the University of Floria, J. Sterling Jones at FHWA, an Stephen Coleman at the University of Aucklan. Aitionally, the experiments liste in this paper have extene the applicability of the revise proceure to partially an fully burie complex piers, an valiate the proceure for use in live be flows Methoology Due to space limitations the methoology presente here is brief an with little or no explanations. The reaer is referre to the Floria Scour Manual (004) (FDOT website in late 004) for a more etaile iscussion an example problems. This section presents the methoology for estimating equilibrium local scour epths at brige piers with complex pier geometries. These methos apply to brige piers compose of up to three 1

2 components referre to here as the column, pile cap, an pile group as shown in Fig. 1. The methos presente in this chapter are base on the assumption that a complex pier can be represente (for the purposes of scour epth estimation) by a single circular pile with an effective iameter enote by D. The magnitue of the effective iameter is such that the scour epth at a circular pile with this iameter is the same as the scour epth at the complex pier for the same seiment an flow conitions. The problem of computing equilibrium scour epth at the complex pier is therefore reuce to one of etermining the value of D for that pier an applying the single pile equations evelope by Sheppar (004) to this pile for the seiment an flow conitions of interest. The single pile equations are liste below in Eqs.(1)-(5) for completeness. In the clear-water scour range ( 0.47 V V 1 ): c = se y0 D V.5 f 1 f ln D D D50 Vc (1) In the live-be scour range up to the live-be peak ( 1< V Vc Vlp V c ) se y0 V Vc 1 D Vlp Vc V Vc = f 1..5 f + D D Vlp Vc 1 D50 Vlp Vc 1 () an in the live-be scour range above the live-be peak (V/ V c > V lp / V c ) where D y =. f D se 0 1 (3) 0.4 y0 y0 f1 tanh = D D (4) f D = D D D D D 10.6 D D ( 50 ) ( 50 ). (5) The methoology is base on the following assumptions: (1) The structure can be ivie into up to three components. () For scour computation purposes, each component can be replace by a single, surface penetrating, circular pile with an effective iameter (D ) that epens on the shape, size an location of the component an its orientation relative to the

3 flow. In situations where the pile cap is burie or partially burie D also epens on the seiment properties an flow conitions. (3) The total D for the complex structure can be approximate by the sum of the effective iameters of the components making up the structure, that is 3 D = D + D + D col (6) where D = effective iameter of the complex structure, column, D = effective iameter of the pile cap an D group. D col = effective iameter of the = effective iameter of the pile Figure 1. Complex pier compose of column, pile cap an pile group. The proceure for computing the local scour epth for complex piers is further ivie into three categories as illustrate in Fig. : (1) Case 1 complex pier () Case complex pier (3) Case 3 complex pier The case 1 complex pier is fully expose to the flow prior to calculating the scour. The case complex pier has a partially burie pile cap, an the case 3 complex pier is completely burie. The proceure for computing the local scour epth at the three ifferent categories of complex piers is liste below in Sections Figure. Definition sketch showing three ifferent complex pier cases.

4 Case 1 complex pier local scour preiction proceure The proceure for computing local scour epth for Case 1 complex piers is outline in steps (1) through (). The proceure starts by analyzing the upper most component an proceeing to the lowest component. Fig. 3 illustrates a complex pier an the naming conventions use throughout the proceure for computing the local scour at complex piers for the three ifferent cases. Figure 3. Complex pier efinition sketch showing symbols use in the analysis. The proceure for computing effective iameter of the column, D col, is given in steps 1-7. (1) Calculate y 0(max) for the column using Eq. (7). y 0(max) 5b col for yo 5bcol = y o for yo < 5bcol () Determine if the column contributes to the complex structure effective iameter. If H y, the column will not contribute to the effective iameter (set col o(max) D col = 0an procee to step (8), otherwise go to step (3). (3) Compute the column shape factor, K s, with Eq. (8). 1 for circular columns 4 K s = π, (8) for square columns α where α is the flow skew angle. (4) Compute the column skew factor, K α, with Eq. (9). ( α ) + col ( α ) bcol cos l sin Kα = (9) b col (7)

5 5 (5) Compute the weighte average value of the pile cap extension, f, using Eq. (10). f = 3f 1+ f π for α 4 4, (10) 3f + f1 π for α > 4 4 where f 1 an f are the front an sie overhangs of pile cap. (6) Compute the pile cap extension coefficient, K f, using Eq. (11). f f K f = b b. (11) col col (7) Compute the effective iameter for the column, D col, with Eq. (1). Hcol Hcol Dcol = KsKαKfbcol y0(max) y0(max) (1) The proceure for computing the effective iameter of the pile cap, D steps (8)-(1). (8) Calculate y 0(max) for the pile cap with Eq. (13). y 0(max) T T.5 b yo.5 b y0 y0 = 0.4 T y o yo <.5 b y 0, is presente in (9) Determine if the pile cap contributes to the complex structure total effective iameter. If H yo(max), the pile cap will not contribute to the effective iameter (procee to step (13)), otherwise continue to step (10). (10) Compute the pile cap shape factor, K s, using Eq. (14). (13) K = s 1 for circular pile caps 4 π (14) for square pile caps α (11) Compute the pile cap skew factor, K α, with Eq. (15). ( α ) + ( α ) b cos l sin Kα = (15) b

6 6 (1) Compute the effective iameter of the pile cap, D, using Eq. (16) an noting that the values of H /yo(max) an T/yo(max) shoul not excee 1. 1 H T D = Ks Kα b exp exp y0(max) y 0 (max) (16) The proceure for computing the effective iameter of the pile group, D, is presente in steps (13)-(). The scour create by the upper components is ae to the height of the pile group, H, an water epth, y o. D + (13) Calculate the effective iameter of the column an pile cap, (col ), using Eq. (17). D D D (col+ ) = col + (14) Compute the scour ue to the column an pile cap, s(col+ ), using Eqs. (1) (5). (15) Compute H an y o using Eqs. (18) an (19). (17) H = H + s(col+ ) (18) y o = yo + s(col+ ) (19) (16) Compute the pile group shape factor, K s, using Eq. (0) an Eq. (1). K K s 10 K K K 9 b 9 s (pile) s (pile group) s = + s( pile) ( s (pile) s (pile group) ) K (0) K 1 for circular piles or pile group arrays π for square piles or pile group arrays α 4 s(pile or pile group) = (17) Compute the non-overlapping projecte with of the pile group, W p, using only the first rows an the first column. (18) Compute the pile spacing coefficient, K sp, for the pile group using Eq. (). (1) 4 w pi 1 Ksp = , () 3 Wp s w pi where w pi is the projecte with of a single pile. (19) Compute K m (accounts for the number of piles inline with the flow) for the pile group using Eq. (3). If the skew angle is greater then 5 egrees, K m =1.

7 7 ( ) m α < 5,an m 5 Km = 1.19 α < 5,an m>5 1 α 5 where m is the number of piles along the axis of the pier. (0) Compute y 0(max) for the pile group using Eq. (4)., (3) y 0(max) y for y W K K =.5 W K K for y W K K 0 0 p sp m p sp m 0 p sp m (1) Compute the pile group height coefficient, K h, using Eq. (5). note: 0 Kh 1an that K h = 0.86 tanh 1.8 H 0 1. y 0(max) H y 0(max) () Compute the effective iameter for the pile group, D, using Eq. (6). (4) (5) D = K K K K Wp (6) s sp m h The effective iameter for the complex pier is calculate by summing up the iniviual effective iameters using Eq. (6). The total scour for the complex pier is etermine by substituting the D for the complex pier into Eqs. (1)-(5) Case Complex Pier Local Scour Preiction Proceure This section outlines the proceure for computing local scour epths for Case complex piers as illustrate in Fig (). (1) Calculate the effective iameter of the column [following steps (1) through (7) in Sec The proceure for computing the effective iameter of the pile cap, D, is presente below in steps ()-(14). The effective iameter calculation for the Case complex pier requires an iterative scheme to etermine how much of the pile cap is expose. The subscript i refers to the number of iterations (e.g. i = 1 for the first iteration, for the secon, etc.). () Calculate the scour ue to the column, s(col) using the effective iameter of the column calculate in step (1). (3) Compute the pile cap shape factor, K s, using Eq.(14) in Sec (4) Compute the pile cap skew factor, K α, using Eq. (15) in Sec (5) Compute H an T using Eqs.(7) an (8), an noting that T is always positive an H 0for Case complex piers.

8 8 H ' = ol) (7) s(c ' T T H (6) Calculate y 0(max) for the pile cap using Eq. (9). y 0(max) = + (8) ' ' T T.0 b y ' o.0 b ' y0 H y0 H + + = 0.4 (9) ' ' T y0 + H yo <.0 b ' y0 + H (7) Compute the pile cap effective iameter using Eq.(30), noting that the values of H /y an T/y can not excee 1. o(max) o(max) 1 ' ' H T D = Ks Kα b exp exp y0 (max) y 0(max) (30) D + (8) Compute the effective iameter for the column an pile cap combination, (col ), using Eq. (17). (9) Compute the scour epth for the column an pile cap combination, using Eqs. (1)-(5). (10) Compute H an T using Eqs. (31)-(3). s () i H s(i) H H = s(i) s(i) H (31) T y s(i) H T = T+ H y s(i) H (11) Check for convergence using Eq.(33). If i = 1 procee to step (5) above If i > 1 1) Compute ) If > s (i) s(i-1) s (i-1) 0.05 procee to step (1) below 0.05 procee to step (5) above (1) Determine if the pile group has been expose using Eq. (34). (3) (33)

9 9 If s(col+) H procee to step (13) s(col+) > H procee to step (14) (34) (13) The pile group is not uncovere an hence the pile group effective iameter is zero. The complex pier s total effective iameter is compute with Eq. (6) noting that D = 0. (14) Compute D following steps (13) - () for case 1 piers (Sec ). The effective iameter for case complex piers is the sum of the component effective iameters [Eq.(6)]. The equilibrium scour epth is then compute using D in Eqs. (1)- (5) Case 3 Complex Pier Local Scour Preiction Proceure. This section etails the proceure for computing local scour epths for Case 3 complex piers as shown in Fig. (). The proceure for computing local scour epths for Case 3 complex piers is outline below in steps (1) through (14). Compute the effective iameter of the column. (1) Calculate K s an K α for the column following steps (3) an (4) in Sec () Compute an effective iameter for the column using Eq. (35). D = K K b col s α col (35) (3) Compute the scour epth for the column, s(col) as if it were an infinitely eep single pile using Eqs. (1)-(5). Compare this scour epth with the height of the column using Eq. (36). If s(col) H col D = D col an D = D = 0 s(col) > H col pile cap expose, procee to step (4) (36) (4) Compute f an K f using Eqs. (5) an (6) in Sec (5) Compute the attenuate column effective iameter,, using Eq. (37). H = + D col(f) col Dcol(f) Kf KsKα b col s(col) (6) Compute the minimum effective iameter of the column that will prouce a scour epth to the base of the column,. is compute by setting s co D col(min) = H l in Eqs. (1)-(5) an solving for D. D col(min) (7) Compute the effective iameter of the column using Eq. (38). (37)

10 10 D col D if D D = D if D < D col(f) col(f) col(min) col(min) col(f) col(min) (38) The proceure for computing the pile cap effective iameter, D steps (8) (15), is presente below in (8) Perform steps () (4) in Sec (9) Compute the burie pile cap attenuation coefficient, K b, using Eq.(39). col col Kb = a + b s(col) s(col) H H + c, (39) where a = 0.1(f/b ) , b = 0.08(f/b ) (f/b ) an c = -0.5(f/b ) (10) Perform steps (5) an (6) in Sec (11) Compute the pile cap effective iameter using Eq.(40), noting that the values of H /y or T/y can not excee 1. o(max) o(max) 1 ' ' H T D = Ks KαK b bp c exp exp y0 (max) y 0(max) (1) Perform steps (8) (10) in Sec (13) Check for convergence using Eq. (41). If i = 1 procee to step (10) above If i > 1 1) Compute ) If > s (i) s(i-1) s (i-1) 0.05 procee to step (14) below 0.05 procee to step (10) above (14) Determine if the pile group has been expose using Eq.(4). (40) (41) If s(col+) H procee to step (16) s(col+) > H procee to step (17) (4) (15) The pile group is not uncovere an hence the pile group effective iameter is zero. The complex pier s total effective iameter is compute with Eq. (6) noting that D = 0. The proceure for computing the pile group effective iameter, D in steps (17)-(0)., is presente below

11 11 (16) Perform steps (13) - (1) in Sec (17) Compute the burie pile group attenuation coefficient, K b using Eq. (43). K b H = + 1 (43) s(col + ) H note: 1 0 an 0 Kb 1 s(col + ) (18) Compute the effective iameter for the pile group, D, using Eq. (44). D = K K K K K W (44) s sp m h b p The effective iameter of the complex pier is compute by summing the effective iameters of the components using Eq. (6). The total scour for the complex pier is compute using D in Eqs. (1)-(5). Preicte versus Measure Scour Depths Preictions using the methos in HEC-18 version 4 an the methos outline in this paper for the conitions in three ifferent laboratory ata sets were mae an compare with the measurements. The piers use in Sheppar s an Coleman s experiments were compose of a column, pile cap an pile group. The piers in Jones experiments consiste of a column an pile cap (footer). Sheppar s experiments were performe in the live-be scour range while Coleman s an Jones experiments were in the clear-water scour range. Figs. 4-6 compare the preicte an measure scour epths for the three sets. The average error an stanar eviation for the two preiction methos are given in Table 1 by ata set. Table 1. The average error an stanar eviation for the two preiction methos. Revise Methoology Existing HEC-18 Methoology Data Stanar Stanar Average error Average error Deviation Deviation Coleman 0% 16% 1% 54% Jones 3% 17% 13% 14% Sheppar 13% 1% 78% 3%

12 Measure Revise Methoology Current HEC-18 se (m) Experiment number Figure 4. Preicte versus Coleman s measure scour epth for a three component complex pier se (m) Measure Scour Revise Methoology Current HEC Experiment number Figure 5. Preicte versus Sheppar s measure scour epth for a three component complex pier uner live-be scour conitions.

13 13 se (m) Measure 0.15 Revise Methoology 0.1 Current HEC Experiment number Figure 6. Preicte versus Jones measure scour epths for complex piers with a column an pile cap. 3 Discussion The revise proceure outline in this paper has been extene to complex piers with partially or fully burie pile caps (footers). The proceure was evelope using both clear-water an live-be scour ata. The metho use by Sheppar to extrapolate measure scour epths to equilibrium values is conservative (i.e. the extrapolate equilibrium values are most likely larger than the actual values). The revise metho presente here appears to more accurately preict scour epths than the methos presente in the current version of HEC-18. The revise proceure is more accurate at preicting scour epths uring live-be flow conitions, an at preicting the scour for partially burie an fully burie pile caps. It is noteworthy that for the situations covere in Coleman s Experiments 5, 6, 7, 5 an 6 the current HEC-18 metho uner preicts the measure scour epth. All of these tests were with three component piers with burie or partially burie pile caps. References Coleman, S.(001), Personal communication by e- to D.M. Sheppar. Jones, J.S. (000). In personal communication by to D.M. Sheppar. Sheppar, D.M., an Jones, J.S. (1998) Scour at complex pier geometries. Compenium of scour papers from ASCE Water Resources Conferences, Es. E.V. Richarson an P.F. Lagasse, ASCE, New York. Sheppar, D. Max, an Sterling Jones. (000) Local Scour at Complex Piers, Proceeings for the 000 Joint Conference on Water Resources Engineering an Water Resources Planning an Management Conference, Minneapolis, MN, July 30-August, 000. Sheppar, D. Max an Rick Renna, (001), Floria Brige Scour Manual Publishe by Floria Department of Transportation, 605 Suwannee Street, Tallahassee, FL Sheppar, D. Max, Mufee Oeh an Tom Glasser (004), Large Scale Clearwater Local Pier Scour Experiments, J. Hyr. Engrg., ASCE, 114, No. 10,

14 14 Acknowlegments The authors thank Rick Renna, Shawn McLemore an Richar Long with the Floria Department of Transportation (FDOT) for supporting this research. Thanks to Bruce Melville an his staff, Jim Beckner an Raymon Hoffmann an University of Aucklan grauate stuents Sjoer van Ballegooy an Thomas Macougal Clunie for running the tests. Thanks also to Stephen Coleman (University of Aucklan) an Sterling Jones (U.S. Feeral Highway Aministration) for use of their ata. Notation b = circular pile iameter, b col = with of column, b = with of column, D = effective iameter of the complex pier, D col= effective iameter of the pier column, D co(f)l= effective iameter of the pier column attenuate by K f, D col(min) = smallest value for a case 3 column effective iameter D = effective iameter of the pier pile cap, D = effective iameter of the pier pile group, D 50 = meian seiment grain iameter, se = equilibrium scour epth, H col = height of column base from be, H = height of pile cap base from be, H = height of top of piles above be, K b = burie pile cap coefficient K b = burie pile group coefficient K h = submerge pile group coefficient, l col = length of column, l = length of pile cap f 1 = pile cap extension beyon the front of the column, f = pile cap extension beyon the sie of the column, V = epth average velocity, V c = seiment critical epth average velocity, V lp = live-be peak scour velocity (velocity where the be planes out), y 0 = approach water epth.