Unsteady Flow and River Bed Stratification Mutual Impact on Scour at the Abutments

DOI: 10.31534/engmod.2020.1-2.ri.04m Original scientific paper Received: 8.04.2020. ENGINEERING MODELLING 33 (2020) 1-2, 49-57 49 Unsteady Flow and River Bed Stratification Mutual Impact on Scour at the Abutments B. Gjunsburgs(1), J. Parilkova(2) (1) Riga Technical University, Department of Water Engineering and Technology, Kipsala Str. 6A, LV-1048, Riga, LATVIA e-mail: [email protected] (2) Brno University of Technology, Department of Water Structures, Veveri 95, 60200, Brno, CZECH REPUBLIC SUMMARY The floods of different probability, sequence, frequency, duration, and the riverbed with different grain sizes, numbers, sequences, and thickness of the layers are one of the reasons for the bridge`s abutments failure because of scour. Although the problem is very topical, the mutual impact of multiple floods and stratified riverbed conditions on scour at the bridge abutments has not been studied. The method for computing scour development in time at bridge abutments was elaborated and confirmed by tests results. The method enables the computer to perform modelling of the mutual impact of unsteady flow and bed layering of scour processes. Computer modelling was made to expand scenarios for tests data in flume for unsteady flow for two steps of hydrograph with different dischargers and for the bed layers with varying grain sizes, numbers, sequence, and thickness. This approach makes it possible to estimate in advance mutual impact, with different scenarios, floods and geological data on the depth of scour at vertical wall abutment, at the design stage or during the maintenance period of the bridge crossing. KEY WORDS: flow; ,unsteady flow; bed stratification; scour; bridges; modelling. 1. INTRODUCTION The mutual impact of floods and layering of the riverbed is one of the reasons for the bridge abutments failure because of scouring. To forecast worst scenarios of possible loads on the bridge inflow, floods of different probability, sequence, duration, and frequency should be considered and the river bed layers with different grain sizes, numbers, sequences, and thickness impact on the scour evaluation should be estimated. Analysis of the possible scenarios of the local scour development near abutments with time can be performed at the design or the maintenance stages of the bridge crossing and, as a result, protection measures can be taken in time. Scours near bridge piers, abutments, spur dikes, guide bank and intakes have been widely studied by researchers: Kothyari and Ranga Raju (2001) [1], Olivetto and Hager (2002) [2], Radice et al. (2002) [3], Malavasi, et al. (2004) [4], Dey and Barbhuiya (2005) [5], Grimaldi et al. B. Gjunsburgs, J. Parilkova: Unsteady Flow and River Bed Stratification Mutual Impact on Scour at the Abutments 50 ENGINEERING MODELLING 33 (2020) 1-2, 49-57 (2006) [6], Cardoso and Fael (2010) [7], Ghani et al. (2011) [8], Guo (2014) [9], Sheppard et al. (2014) [10], Evangelista et al. (2017) [11], Link et al. (2017) [12] and the others. As the analysis of the literature shows, at the present time, there are no methods or formulas to calculate the depth of scour at mutual impact floods and complex geological river bed conditions. The differential equation for equilibrium bed-sediment movement under clear water conditions, at unsteady flow or at uniform and stratified bed at the vertical wall abutments was used to create the model for the depth of scouring calculation. Based on the model the computer program ARobo was performed. The calculation method for scour development in unsteady flow (Gjunsburgs et al. 2013) [13] or at the stratified bed (Gjunsburgs et al. 2012, 2019) [14,15] was confirmed by test results. The method allows the computer to perform modelling of the mutual impact of unsteady flow and bed layering of scour processes. Modelling was made to expand scenarios for test data in flume for unsteady flow and bed stratification layers with changing grain sizes, numbers, sequences, and thickness on scour at vertical wall bridge abutments. The model and the ARobo program allow analysis performing and finding the worst possible scenarios for scour evaluation near bridge abutments at the natural flow conditions. 2. EXPERIMENTAL SET-UP The tests were carried out in a flume L=3.5 m wide and Lf=21 m long. Cross-section of the flume with different flow opening is presented in Figure 1. Experimental data obtained in flumes in the open flow conditions are presented in Table 1. The flow distribution between the channel and floodplain was studied under open flow conditions. The rigid bed tests were performed to investigate flow modification near bridge structure and sand-bed tests were made to study the scour development with time under different flow parameters and at uniform or stratified river bed model.  Fig. 1 Cross section of the flume with different flow opening Lbi Table 1 Test data for the open flow conditions L L L L b1 b2 b3 b4 h =12cm ch =7cm f floodplain channel 300 50 80 120 200 350 L cm hf cm Vap cm/s Q l/s Fr Rec Ref L1 350 7 6.4 16.6 0.078 7500 4390 L2 350 7 8.5 22.7 0.103 10010 6060 L3 350 7 10.0 23.60 0.124 12280 7190 L7 350 13 7.5 35.48 0.066 13700 9740 L8 350 13 8.7 41.38 0.075 16010 11395 L9 350 13 9.9 47.10 0.087 14300 14300 B. Gjunsburgs, J. Parilkova: Unsteady Flow and River Bed Stratification Mutual Impact on Scour at the Abutments ENGINEERING MODELLING 33 (2020) 1-2, 49-57 51 The tests were made: 1. for unsteady flow and uniform bed and 2. for steady flow and stratified bed conditions. For unsteady flow tests, the openings of the bridge model were (50, 80, 120, and 200) cm. The flow contraction rate Q/Qb (where Q is the flow discharge and Qb is the discharge in the opening under open-flow conditions) varied respectively from 1.56 to 5.69. Tests with stratified bad were made with different grain sizes 0.24 mm and 0.67 mm, with a standard deviation and the thickness of the bed layers equal to (4, 7, or 10) cm for each grain size. The opening of the bridge model was 80 cm. For both types of the tests: the floodplain width was Lf= 320cm and the depth hf was 7 cm or 13 cm. The channel width was Lc=30 cm and depth hc was 12 cm or 18 cm, the approach flow velocity Vap changing from 6.4 to 10.0 cm/s, the flow dischargers varying from 16.6 to 47.1 l/s, with the Froude number in the open-flow conditions from 0.078 to 0.1243, densimetric Froude numbers – from 0.62 to 1.65, the slope of the flume was equal to 0.0012. The scour evaluation was studied within one 7 hour step-time interval and within two 7 hour step-time search. The condition FrR = Frf was fulfilled, where FrR and Frf are the Froude numbers for the low-land river and the flume, respectively. Computer modelling was made to study the mutual impact of unsteady flow and stratified bed model on scour, and to expand scenarios for tests data in flume for unsteady flow for two timesteps of hydrograph with dischargers: 1. 16.7/35.5 l/sec; 2. 22.7/41.4 l/sec; 3. 27.6/47.1 l/sec, contraction rate 3.66 – 4.05, floodplain depth 7 cm and 13 cm, layers with grain sizes (0.24, 0.67 and 1.00) mm, up to 3 layers with changing sequence of the grain sizes and thickness of the bed layers, with the opening of the bridge model equal to 80 cm. 3. MODEL The method for calculating the scour development with time at the abutments, guide banks, intakes during the multiple floods, or at stratified bed was elaborated and confirmed with experimental data (Gjunsburgs et al. 2004, 2012, 2013, 2019) [14,13,15]. There are many scenarios for multiple floods of different probability, sequence, duration, frequency, and the layers of the river bed as uniform layers with different grain sizes, sequence, nonuniform layers, cohesive layers follow or before noncohesive layers, number of layers. Computer program ARobo allows studying, analysing scenarios with the use of additional data for different hydraulic conditions, contraction rates, Froude number of the open flow, densimetric Froude numbers, depths of the flow, backwater, as well as parameters which reflect the river bed conditions: grain size diameter d50, critical velocity βVo or grain bed shear stress, sediment non-uniformity parameter σ, specific weight γ, bed layering, numbers, sequences and thickness of the layers with grain sizes di. According to the method, the hydrograph was divided into time steps, and each step was subdivided into time intervals. Calculations were performed for two steps of the hydrograph, to estimate the influence of the flow unsteadiness. The parameter As in proposed model (Gjunsburgs et al. 2012, 2013) [14,13] changes during the scour evolution because water depth, local velocity and critical velocity changes with time and as well as the river bed layering grain size diameter, so that: B. Gjunsburgs, 52 ENGI N where: With an in increasing increasing when the l o where Vl i s water on t reduction n velocity c h different g r 4. RES U The depth gradual re results ar e different g r Figure 2 p flow and o n hours and hydraulic p J. Parilkova: Uns t N EERING MODEL L s 0 . A= crease of th e because di s because of s o cal velocit y k s the local v e t he floodpla n ear the ab u h anges in ti r ain size di o U LTS of scour is duction in t e presented r ain sizes, n u resen t s calc n e bed laye r is increasin g p arameters. Fig. 2 Dept h t eady Flow and R L ING 33 (2020) 1 - l k βV 002 1 gV ⎛ ⎜− ⎜ ⎜ ⎝ β V e scour dep t s charge inc r s cour depth y becomes e q l s f V h k 12h ⎛⎞ + ⎜⎟ ⎜⎟ ⎝⎠ e locity, Vo – t in, di – the u tment. The m m e at vary i n the depth rapidly inc t ime at a st e for extend e u mbers, seq u u lated and t r . The depth g more rapi d h of scour dev e R iver Bed Stratifi c - 2, 49-57 1 s 0 f h V 12h ⎛⎞ + ⎜⎟ ⎜⎟ ⎝⎠ ot 0 lt l β Vk β V VV = t h, the local v r eases (as s hs and vary q ual to the c r i β 3.6 d = ⋅⋅ ⎞ ⎟ ⎟ ⎠ t he critical v grain size d m odel allo w i ng number s of scour at t h reasing at t e ady flow a n e d laborato r u ences, and t t est data fo r of scour is i n d ly (Figure 1 ) e lopment in t i c ation Mutual Im p ( 1 .25 0.5 f gh d ⎞ ⎟ ⎟ ⎟ ⎠ 1. s f h 12h ⎛⎞ + ⎜⎟ ⎜⎟ ⎝⎠ v elocit y Vlt i s s equence Vl ing with di i r itical on Vlt = 0.25 0.25 i f h⎛ ⋅⎜ ⎜ ⎝ v elocity, hs – d iameter, β w s estima t in g s , sequence , h e abutmen t he beginni n n d one bed r y data for t t hickness of r scour dept h n creasing at ) at the seco i me at unstea d p act on Scour at t ) 0.25 1 h d 12 h ⎛ + ⎜ ⎜ ⎝ 2 5 . s decreasin g increases), n bed layer s = βVot: 0.2 s f h 12h ⎞ +⎟ ⎟ ⎠ the depth o f – the coeffi c g mutual im p and thick n t s. g of the sc o layer. Furt h t wo steps o the bed lay e h evaluatio n the first int e nd time inte d y flow in one t he Abutments 0.25 s f h h ⎞ ⎟ ⎟ ⎠ , g due to the the critical s (Eq. 2). Sc o 2 5 , f scour, hf – c ient of cri t p act – disch a n ess of bed o uring proc e h er comput e o f hydrogra p e rs. n in time at a e rval, which e rval, becaus uniform laye r (1 ) s cour hs an d one βV0t i s o uring stop s (2 ) t he depth o f ical velocit y a rge, relativ e layers wit h e ss with th e e r modellin g p h and wit h a n unstead y is equal to 7 e of the ne w r ) d s s ) f y e h e g h y 7 w B. Gjunsburgs, J Figure 3 p r Q2 = 41.4 l / the thickn e increases m with fine g r Figure 4 s h flow with Q (1.00, 0.67, of the dept h at the seco critical vel o Fi g Impact of u scour for t h shown in F i . Parilkova: Unst e r esen t s the d / sec with th e e ss of the l a m ore rapidl y r ain size (Fi g Fig. 3 h ows relativ e Q 1=22.7 l/ s e c and 0.24) m m h of scour, t h o nd one bec a o city βVot in t g . 4 Relative v u nsteady flo h ree layers w i gure 5. As d e ady Flow and Ri v d epth of sc o e sequence o a yers 4.6 c m y at the seco n g ure 3). Depth of sco u e velocity c h c and Q2 = 4 m with the t h h e relative v e a use of the t he layer wit v elocity chang e w with dis c w ith di – (1. 0 ischarge inc r v er Bed Stratific a o ur evolutio n o f the layers m and 10 c m n d time int e u r evaluation a h anges in ti m 4 1.4 l/sec w i h ickness of t e locity Vlt/V o increase of h d3 = 0.24 m e s versus dept h c harges 16. 7 0 , 67, 0.24) m r eases the s c a tion Mutual Imp ENGIN E n a t an uns t with grain s m . The rate o e rval with Q 2 a t an unstead y m e because i th the seq u t he layers 4. o t increases i n the local v e m m (Eq. 2). t h of scour at u 7 /35.5 l/sec m m of each l c our depth i s act on Scour at t h E ERING MODELL t eady flow w s izes (1.00, 0 o f the scou r 2 = 41.4 l/ s e y flow in thre e of the scou r ence of the 6 cm and 1 0 n the first ti m e locity Vl a n u nsteady flow or 27.1/47. 1 l ayer with t h s increasing. h e Abutments I NG 33 (2020) 12 w ith Q1 = 22. 0 .6 7 , and 0.2 4 r ing depend s c and in the e layers r evolution a layers with cm r. With t m e interval a n d the redu c and three la y 1 l/sec on t h h ickness (4, 6 2 , 49-57 53 .7 l/sec and 4 ) mm with s on di and e third layer a t unsteady grain sizes t he increase a nd reduces c tion of the y ers h e depth of 6, 10) cm is B. Gjunsburgs, 54 ENGI N Fig. 5 Depth of s c cm, and in cm. For th e 0.67 mm, t h Fig. 6 Dep t a n With an i n increases ( and differ e J. Parilkova: Uns t N EERING MODEL L 5 Depth of sc c our in two l three layer s e same tim e h e depth of s t h of scour ev a n d in three la y n crease in t h ( Figure 7). C e nt thicknes s t eady Flow and R L ING 33 (2020) 1 - o ur developm l ayers with d s with di – ( 1 step is pre s s cour reduc e a luation in tw o y ers with d i – ( 1 h e thicknes s C omparison s of the fine s R iver Bed Stratifi c - 2, 49-57 m ent in two ti m d i – (1.00, 0. 2 1 .00, 0.67, 0 . s ented in Fi g e s. o layers with d 1.00, 0.67, 0. 2 s of the fin e is made for s end layer – c ation Mutual Im p m e steps with d 2 4) mm wit h . 24) mm an d g ure 6. Wit h d i – 1.00 mm, 0 2 4) mm and w i e sand laye r grain sizes (15, 5, 10) c m p act on Scour at t d ifferent disch a the thickne d with the t h h the additio n 0 .24 mm with i th thickness ( 1 r di – 0.24 m for each lay m (h1) or (5, t he Abutments a rges in three ss of the lay h ickness of 1 n of a third thickness 5 c m 10, 5, 10) cm ( m m, the de p y er (0.24, 0. 6 5, 10) cm. ( h layers ers 5 and 1 0 1 0, 5, and 1 0 layer of di = m , 10 cm (h s1 ) ( h s2 ) p th of scou r 67 , 1.00) m m h 2). 0 0 = r m B. Gjunsburgs, J Fig. 7 Dept h F Figure 8 p r the layers. S mm and (0. 2 coarse san d with di red u at the fine s 5. CON C The damag e bridge str u environme n river bed g hole, whic h dimension s failure. . Parilkova: Unst e h of scour co m F ig. 8 Depth of r esen t s the d S equence of 2 4, 0.67, 1.0 0 d on the top u ction, whe n s and layer a n C LUSION e of engine e u ctures – n tal and ec o g eology, flo w h under cl e s of the sco u e ady Flow and Ri v m parison for t h of scour evolu t d epth of sco u layers are g 0 ) mm and w layers incr e n the first tw o n d gives gre a e ring struct u abutments, o nomic loss e w contractio n e ar-water c o u r hole at t v er Bed Stratific a h ree layers a n equal 15 c t ion at unstea d u r evolutio n g rain size di a w ith the sa m e ases the ti m o layers are w a ter scour d e u res in river s guide ba n e s. The reas o n s, type an d o nditions is t he unexpec t a tion Mutual Imp ENGIN E n d two layers w c m or 5 cm d y flow and d if n at an unst e a meters: (0. 2 m e thickness m e of scour a washed out e pth (Figure s due to sco u n ks, dams, o ns are the d shape of t summing u t ed flush fl o act on Scour at t h E ERING MODELL w ith thickness if ferent seque n e ady flow a n 2 4, 1.00, 0.6 7 of the layer s a nd reduces the depth o f 7). u r (near int a etc.) leads mutual imp t he structur e u p from flo o od can lea d h e Abutments I NG 33 (2020) 12 for the first fi n n ce of the lay e d different s 7 ) mm; (1.00 s 4.6 cm and scour dept h f scour rapi d a kes, pumpi n to the c o ac t s of mul t e , and incre a o d to flood d to damag e 2 , 49-57 55 i ne sand one e r s equence of 0 , 0.67, 0.24) d 10 cm. The h . For layers d ly develops ng stations, o nsiderable t iple floods, asing scour d . Increased e or bridge B. Gjunsburgs, J. Parilkova: Unsteady Flow and River Bed Stratification Mutual Impact on Scour at the Abutments 56 ENGINEERING MODELLING 33 (2020) 1-2, 49-57 The models for calculation of scour development in an unsteady flow (Gjunsburgs et al. 2013) [13] or at stratified bed (Gjunsburgs et al. 2012, 2019) [14,15] were elaborated and confirmed by test results, which enabled to make computer modelling to study the mutual impact of an unsteady flow and bed layering on the depth of scour. Computer modelling was made to expand scenarios for test data in flume for an unsteady flow for two steps of hydrograph with dischargers: first 16.7/35.5 l/sec; second 22.7/41.4 l/sec; third 27.6/47.1 l/sec, and contraction rates 3.66 – 4.05, floodplain depths of 7 cm and 13 cm, layers with grain sizes 0.24, 0.67, and 1.00 mm, with up to 3 numbers, changing sequence and with the thickness 4 cm – 10 cm of the bed layers. As it is confirmed by calculation, the rate and value of scour depth depend on the mutual impact of an unsteady flow and river bed stratification (grain size d, numbers, sequences, and thickness of the layers). There are changes in scour depth evaluation with increased discharge and grain diameter in layers (Figure 3) and/or discharges (Figure 5), numbers (Figures 6 and 7), and sequence (Figure 8) of the layers. Relative velocity Vlt/Vot increases in time steps of hydrograph and in any sand layer (Figure 3), when the ratio of the velocities becomes equal, the scour evaluation stops. Model and ARobo program can detect worst possible scenarios in nature for scour evaluation at the abutments at an unsteady flow: for floods of different probability, sequence, duration or frequency and for river bed layering with different numbers, sequences and thickness of the layers with grain sizes di, at both the design and the maintenance stages of the bridge crossing. 6. REFERENCES [1] U. 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