EXPLORATION OF SCOUR CHARACTERISTICS AROUND SPUR DIKE IN A STRAIGHT WIDE CHANNEL

Transcription

1 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 EXPLORATION OF SCOUR CHARACTERISTICS AROUND SPUR DIKE IN A STRAIGHT WIDE CHANNEL Elsaiad A.A. and Elnikhely E.A. *2 Professor of hydraulics, Water and Water Str. Eng. Dep., Faculty of Engineering, Zagazig University, Zagazig, Egypt, aelsaiad23@yahoo.com Lecturer 2, Water and Water Str. Eng. Dep., Faculty of Engineering, Zagazig University, Zagazig, Egypt, *Corresponding author emanaly_99@yahoo.com ABSTRACT Investigation of scour and determination of hole of scoring around spur dike are among the most important issues for channel protections. Laboratory experiments were carried out in a straight rectangular flume with a non-submerged spur dike. The effect of spur dike angled at 9 ο, 55 ο, 4 ο and 25 ο was studied. Experiments were also conducted for different spur dike nose angle with various Froude number. The experimental results of the model indicated that the relative maximum depth of scour is highly dependent on the spur dike inclination angle with channel wall and the nose angle of spur dike. The relative maximum scour depth decreased by 55% for decreasing the inclination angle of spur dike from 9 ο to 25 ο and by about 45% for decreasing the nose angle from 9 ο to 4 ο. The greatest hole dimensions of scour was associated with 9 ο nose angle of spur dike. Furthermore, the 9 degree spur dike was modeled using SSIIM numerical model. The numerical model was based on the finite-volume method to solve the non-transient Navier-Stocks equations and a bed load conservation equation. The numerical results were compared with the experimental results to verify the numerical model. Moreover, Empirical equations are obtained by using linear regression analysis for estimating the maximum value of relative scour depth. The predicted results agreed with the experimental results. Keywords: Experimental, Spur dike, Scour, Froude number, SSIIM. Received 6 March 26.Accepted 6, May 26 INTRODUCTION A spur dike can be defined as an elongated structure having one end on bank and the other end projecting into the current. Spur dikes have been widely used to redirect the flow in channels and protect eroding stream banks. The problem of scour around any obstruction placed in an alluvial channel is of great importance to hydraulic engineers, because an accurate estimation of local scour beside these structures is very important for safe and economic design of their foundations. Gill (972) by changing the radius of curve, the flow depth and the diameter of particles in the direct and bent channels, showed that the distance between dikes depends on the radius of the curve. Zaghloal (983) conducted experimental investigations to study the effects of upstream flow conditions, sediment characteristics, and spur-dike's geometry on the maximum scour depth and scour pattern around a spur-dike. Suzuki et al. (987) conducted experiments on characteristics of the movable channel bed around a series of spur dikes and found that the bed form around a non-submerged spur dike has a significant impact on the relative distance between the spur dikes and their lengths. Kuhnle et al. (22) investigated the local scour associated with angled spur dikes to downstream channel side wall. The model of spur dikes with two contraction ratios and three angles 45, 9 and 35 were tested to predict the depth and volume of the scour hole associated with a spur dike. Nagy (24) studied maximum depth of local scour near emerged vertical wall spur dike. An equation for estimating the maximum scour depth ratio was derived. Ezzeldin et al. (27) investigated local scour around spur dikes installed as a training structure on straight channel. Equations to estimate scour depth and scour hole length upstream and downstream the spur dike were proposed. Ghodsian and Vaghefi (29) presented the results of an experimental study on scour and flow fields around a T-shaped spur dike in a 9 o bend and found that 3

2 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 the amount of scour at the upstream of spur dike is much more compared to the downstream of spur dike. Naji Abhari et al. (2) reviewed the numerical simulation of flow patterns in a 9 o bend using the SSIIM model and concluded that this model has the ability to calculate the flow pattern in a 9 o bend. T-shape spur dike in a 8 degree channel bend was studied by Masjedi et al. (2). Tests were conducted using one spur dike with mm length in position of 6 under four flow conditions to study the effects of various flow intensities. It was found that the depth of scour increased as time increased, Masjedi et al. (2). Masjedi and Foroushani (22) studied the effect of different shape of single spur dike in river bend on local scour. It was found that, the least erosion of the around in the near bank resion was associated with the spur dikes with oblong shape. For different sets of dikes arrangements, the local scour magnitude for permeable dikes was reduced significantly compared to that of impermeable ones, Osman and Saeed (22). The time evolution of scour around spur dike for several duration was investigated by Shafaie et al. (28). An equation shown the relation between scour depth and time of scour was derived. The turbulence intensity distribution around spur dikes with different structures under the same flow condition was studied by Zhang et al. (22). It can be calculated that the turbulence intensity in the arc-like spur dike and fan-like are relatively weaker than that of the hook-like spur dike, and the strongest turbulence intensity occurs around the trapezoidal spur dike. Downstream of the spur dike, the concentration fluctuation became intensive with the increase of spur dike angle, Chen and Jiang (2). Flow and scour patterns resulted from the installation of two T-shaped spur dikes were evaluated in a 9 ο bend under clear water conditions. The submerged and nonsubmerged spur dikes were modeled numerically at different locations in the bend. In the submerged mode, the maximum scour depth decreased to 22% compared to the non-submerged mode one, Vaghefi et al. (25). The turbulent flow in the local scour hole around a single non-submerged spur dyke was investigated with both experimental and numerical methods Zhang et al. (29). It was found that the simulation results are reasonably consistent with those of the experimental measurements. Karami et al. (22) investigated scour phenomenon around a series of impermeable, nonsubmerged spur dikes with both experimental and numerical methods. A comparison between experimental and numerical results was carried out to verify the CFD model. Li et al. (23) used FLOW-3D software to simulate the three-dimensional flow and local scour around a non-submerged spur dike. Ali et al. (22) studied the time development of the scour hole around the spur dike plates. It was observed that, with increasing time development the greatest hole of the scour was associated with 75 degree spur dike. Vaghefi et al. (24) used a numerical study around a T-shaped spur dike in a 9 ο bend, it was concluded that by increasing the submersion of the spur dike, the flow changes into up flow behind the wing. Vaghefi et al. (24) studied the effect of submergence ratio of a T-shaped spur dike on the water surface profile in a 9 ο bend, using the SSIIM model. They concluded that the SSIIM numerical could accurately simulate the flow pattern and scour in a 9 ο bend. Lodhi et al. (26) investigated the influence of cohesion on scour depth around submerged spur dike founded in the mixtures of cohesive sediment consisting of clay gravel and clay sand gravel. The process, geometry and scour depth around submerged spur dike in cohesive sediments were significantly affected by clay percentage and unconfined compressive strength of cohesive sediment mixtures. The principle objective of this study is to carry out experimental tests to investigate the local scour phenomenon and the relation between the dimensions of the scour hole that takes place beside the spur dike, and between the flow parameters, the angle of inclination, and the spur dike nose angle. The 9 ο spur dike was modeled numerically using SSIIM model. Regression analysis was used to predict some formulas between the relative maximum scour depth against other parameters involved in the phenomena. 2 EXPERIMENTAL SETUP Layout of experimental set up is illustrated in Fig. (). Experiments were conducted in a straight rectangular flume of.4 m wide,.2 m deep and 4. m length, as shown in Fig. () and Fig. (2a). The laboratory flume was made from a self-colored, glass reinforced plastic mounding. The discharges were measured using a pre-calibrated orifice meter fixed in the main flow line. The tailgate was fixed at the end of the experimental part of the flume; it was used to adjust the tail water depth at the downstream side. The water 3

3 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 depths were measured by means of point gauges. The model sand is non uniform (uniformity coefficient =D 6 /D =.52<6.) with D 5 =.78mm, and geometric mean standard deviation =D 85 /D 5 =.54. The model of spur dike was built from wood with length L= cm, height h= 5 cm, and.5 cm thickness. The water surface levels were measured along the center line of the flume at the upstream and downstream of the spur dike model. Water surface levels and scour dimensions were measured around the spur dike by using an ordinary point gauge (of. mm accuracy) which was mounted on a carriage. The experimental program is summarized as in tables (), it is including two stages. Stage I explores the effect of spur dike alignment angle. This stage includes four different angles θ =9 ο, 55 ο, 4 ο and 25 ο, while the nose angle was fixed α=9 ο see Fig. (). Stage II explores the second group of models were aligned perpendicular, i.e. θ=9 ο, and the nose was sloped with angles α=9 ο, 7 ο, 55 ο and 4 ο, as shown in Fig. (2b). The total number of Experiments is 9. Figure. Schematic diagram of the experimental model (a) (b) Figure 2. a) The flume used. b) The tested models α=9 ο, 7 ο, 55 ο and 4 ο Table. Scheme of experimental work stages. Model 2 Description θ =9 ο, 55 ο, 4 ο and 25 ο for α=9 ο θ =9 ο for α=9 ο, 7 ο,55 ο, and 4 ο 3 DIMENSIONAL ANALYSIS A dimensional analysis is used to correlate the different variables affecting the local scour at spur dike. The different variables affecting the local scour at spur dikes (h s ) are expressed as: h s y = f, L us y, L ds y, w, θ, α y () 32

4 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 which: h s L us y y = the relative maximum scour depth; is the kinetic energy factor = F n 2 ; F n = Froude number; = the relative length of scour upstream the spur dike; L ds = the relative length of scour downstream the y = the relative width of scour hole; y = the water depth ; θ = the angle of spur dike junction with spur dike; w y channel side; and α = angle of spur dike nose. 3 THE NUMERICAL MODEL SSIIM is an abbreviation for simulation of sediment movements in water intakes with multiblock option empirical equations. The SSIIM program solves the Navier-Stokes equations with the k ε on a three dimensional and general non-orthogonal grids. These equations are discredited with a control volume approach. An implicit solver is used, producing the velocity field in geometry. The velocities are used when solving the convection-diffusion equations for different sediment sizes. The Navier-Stokes equations for noncompressible and constant density flow can be modeled as: U i t + U j U i x j = ρ x j pδ ij ρu i u j (2) where, U i = the local velocity, x j = space dimension, p = pressre, δ ij = kronecker delta, ρ = fluid density and u i = the average velocity. The first term on the left side of the Equation (2) indicates the time variations, the second term is the convective term. The first term on the right-hand side is the pressure term and the second term on the right side of the equation is the Reynolds stress. This equation is solved using finite discontinuing volume method. A control-volume approach is used for discretization of the equations. The Reynolds stress is evaluated using turbulence model k ε. u i u j = υ T u i x j + u j x i kδ ij (3) The first term on the right hand side of the Equation (3) is the diffusive term in The Navier-Stokes equations.the influence of rough boundaries on fluid dynamics is modeled through the inclusion of the wall law as given as follows: U U = K ln 3z K s (4) where, ks equals to the roughness height, which calculated using Van Rijns (987), K is von Karmen constant, U is the mean velocity, U is the shear velocity and z is the height above the bed. 4 MODEL GEOMETRY AND PROPERTIES A structured grid mesh on the x-y-z plane was generated. An uneven distribution of grid lines in both horizontal and vertical directions was chosen in order to keep the total number of cells in an acceptable range and to get valuable results in the area. The spur dike was generated by specifying its ordinates, and then the grid interpolated using the elliptic grid generation method. However, the spur dike was generated by blocking the area of spur dike, Fig.(3) shows the grid mesh generation around spur dike. 33

5 hs/y hs/y Experimental International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 5 MODEL VERIFICATION Figure 3. Mesh generation around spur dike Figure (4) shows experimental results of maximum scour depth as a ratio of the tail water depth, (h s /y) Experimental, versus the numerical values, (h s /y) SSIIM, predicted by the 3D numerical model for the case of spur dike angled at 9 o. It is noticeable that there were well agreement between the experimental and numerical values of maximum scour depth with an average correlation coefficient of 97%. Figure (5) shows also a comparison between the present experimental results and the experimental results of Ezzeldin et al (27). It is observed that very close values of scour depth were obtained hs/y (SSIIM data) Figure 4. Simulated versus experimental for (h s /y) for 9 o spur dike Figure 5. Agreement of Ezzeldin et al (27) results with the experimental measurements for 9 o spur dike Recent data )27Ezzeldin et al ( 34

6 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 Figures (6) to (8) show the contour maps of scour holes for the case of spur dike angled at 9 o. It can be concluded that the hole geometry has the approximate form of an inverted frustum cone with its vertex representing the point of maximum depth of scour which is almost occurs near the groin tip. The base of scour hole is circular with its center on the extent of the spur longitudinal centerline. The horizontal velocity distribution over the mobile bed by distance.% of water depth for 9 o spur dike is shown in Fig.(9). It can be seen that, there is a large vortex around the spur dike due to the presence of spur dike, the velocity increased rapidly with the decrease of the channel wide. At downstream of the spur dike, the velocity recovers gradually; the water flow goes towards the side of the flume and forms a wake zone with low speed behind the dike. Figure 6. Scour hole contour map [θ= 9 o, F n =.247] Figure 7. Scour hole contour map [θ= 9 o, F n =.262] Figure 8. Scour hole contour map [θ= 9 o, F n =.322] 35

7 hs/hst International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 Figure 9. Horizontal velocity distribution over the mobile bed by distance.% of water depth for [θ= 9 o, F n =.322] 6 ANALYSIS A long experiment was conducted at the position of θ = 9 o, α=9 ο for a spur dike, to estimate the ultimate scour depth. Fig. shows the relation between h s /h st and T/T o where: h st : The ultimate scour depth, T: Time of scour, and T o : The ultimate scour time (5 min.). It is noticed that, the scour depth h s reaches to.95% h st at T/T o =.85, this means that the stability of scour depth occurs at time T= T o =2 min T/To Figure. The relation between T/T o and h s /h st 7.. Effect of Spur Dike Alignment Angle Spur dike may be positioned facing upstream (repelling groin), normal to flow (deflecting groin) or facing downstream (attracting groin). Each orientation to the flow affects the river current in a different way. The present study is limited on the cases of deflecting and attracting groins. The angle tested in this research was 9 ο, 55 ο, 4 ο and 25 ο. The relationships between and the different scour parameters including h s /y, L us /y, L ds /y and w/y are presented, for different spur dike alignment angles, see Figs. (a, b, c and d), respectively. Generally, it can be noticed that all scour parameters increases as increases. In addition, scour parameters h s /y and w/y are minified to the minimal limit in case of spur dike alignment angle, θ = 25 o. The relative scour depth h s /y decreases by about 55% for θ = 25 o compared to the case of θ = 9 o. This may be referred to that the angle affects on flow velocity where the velocity of flow changed to facing flow, angle 9 o repelling flow strongly than another and become smooth gradually as decreasing θ from 9 o to 25 o. It is 36

8 Lus/y hs/y International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 noticed that, the relative scour length L us /y decreasing by about 4% by decreasing the angle θ from 9 o to 4 o. It can be seen that for the case of θ = 25 o the upstream scour length disappears and the scour hole is totally exist in the downstream side of spur dike as shown in Fig. (b). In contrast, the relative scour length L ds /y decreasing by about 6% for the case of θ = 9 o (i.e. spur dike alignment doesn t show a significant effects on scour hole length downstream the spur dike), spur dike angled at 25 o gives the longer downstream scour hole length. The relative scour width w/y reduces by about 38% for θ = 25 o compared to θ = 9 o. From previous figures the case of θ = 25 o gives the best performance in bank protection Effect of Spur Dike Nose Angle Figs. (2a, 2b, 2c, 2d) show the relationships between and the different scour parameters including h s /y, L us /y, L ds /y and w/y for different spur dike nose angles of α=9 ο, 7 ο, 55 ο, and 4 ο. It is obvious that all scour parameters increase as increases. Spur dike nose angle of α=4 ο gives the minimum values of h s /y by about 45%, meaning that the nose angle α=4 ο is the best angle which causes minimum scour depth. It was investigated that, the relative scour length of hole in the upstream L us /y reached to its minimum value in case of α=4 ο, it reduces the relative upstream scour length L us /y, by about 5% compared to the case of α=9 ο. However, α=9 ο causes the maximum reduction of the relative scour length in the downstream L ds /y by about 3%. The maximum reduction of scour hole width w/y was found at α=4 ο by about 24%. It is noticed that the spur dike nose angle α has a significant effect on the different scour parameters (a) θ= 55θ= 4θ= 25θ= (b) 9θ= 55θ= 4θ=

9 hs/y w/y Lds/y International Water Technology Journal, IWTJ Vol. 6 No.2, June (c) 9θ= 55θ= θ= 25θ= (d) Figure. Relations between and the different scour parameters for different spur dike alignment angle θ and constant α=9 o. 9θ= 55θ= 4θ= 25θ= (a) α= 7α= 55α= 4α= 38

10 w/y Lds/y Lus/Y International Water Technology Journal, IWTJ Vol. 6 No.2, June (b) (c) (d) STATISTICAL REGRESSION Based on the experimental measurements, statistical equations were proposed to predict the relative scour depth. Depending on the regression tasks and statistical analysis and using the regression tool, the statistical equation () was built to predict the studied parameters. h s k.8456 y (5) 9α= 7α= 55α= 4α= 9α= 7α= 55α= 4α= 9α= 7α= 55α= 4α= Figure 2. Relations between and the different scour parameters for different spur dike nose angle α and constant θ = 9 o h s y k.7 (6) 39

11 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 where: k θ : alignment coefficient = θ/9. k α : nose angle coefficient = α/9. These equations are valid within the following ranges of the involved parameters: h s /y [.5-.3], [.3-.66], k θ [.5-.] and k α [.5-.]. Figs. (3a, 3b) shows the calculated values of the investigated parameters against the measured ones for eqns. 5 and 6, respectively. Generally, it can be observed that, there is an acceptable agreement between the measured data and the predicted ones. The results showed well agreement between the experimental and predicted values of h s /y (R 2 =.94,.86). The residuals of the previous equation are plotted versus the predicted values as shown in Figs. (4a, 4b). R 2 between residuals and predicted values are.6e -23 &7.25E -2. hs/y (measured) (a) hs/y (predicted) hs/y (measured) (b) hs/y (Predicted) Figure 3. Comparison between experimental results and statistical model Eqns. (5) & (6) results. 4

12 Residuals Residuals International Water Technology Journal, IWTJ Vol. 6 No.2, June (a)..5.5 Predicted.6.4 (b) Predicted 8 CONCLUSION Figure 4. Variations of residuals for different data sets with predicted data Eqns. (5) & (6) The results of several long duration scour laboratory experiments around spur dike are presented in this work to investigate the characteristics of scour hole around a single spur dike installed in a straight flume. The analysis of the results shows the following conclusions:- All of scour parameters increase with the increase of the kinetic flow factor with a linear trend. The spur dike oriented at angle 25 o showed a good performance in reducing the scour depth and in bank protection. Decreasing the spur dike alignment angle from 9 ο to 4 ο reduces the relative upstream scour length L us /y by about 4%. Spur dike angled at 25 o gives the longer downstream scour hole length. The relative scour dimensions decreases by decreasing the spur dike nose angle from 9 ο to 4 ο by ratios 45% for depth, 5% for upstream length, and 24% for width of scour hole. In addition, the simulated results show the ability of SSIIM for modeling the local scouring around spur dike with an average correlation coefficient of 98%. The results of the proposed statistical equations are compared to the experimental measurements and an acceptable agreement has been found 4

13 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 NOTATIONS F n :Froude number [-] h s : maximum scour depth [L] h st : The ultimate scour depth [L] L us :Scour hole length upstream the spur dike. [L] L ds :Scour hole length downstream the spur dike. [L] T : Time of scour [T] T o : The ultimate scour time [T] w : width of scour hole [L] y : water depth [L] θ : angle of spur dike junction with channel side [-] α : angle of spur dike nose [-] : Kinetic flow factor [-] REFERENCES Ali, R.; Alireza, J. & Rashid S. (22) Investigation on Scour Hole Around Spur Dike in a 8 Degree FlumeBend. World Applied Sciences Journal, 9(7), pp Chen, L.P. & Jiang, J.C. (2) Experiments and numerical simulations on transport of dissolved pollutants around spur dike. Journal of Water Science and Engineering, 3(3), pp Ezzeldin, M.M.; Saafan, T.A.; Rageh, O.S. & Nejm, L.M. (27) Local scour around spur dikes. th International Water Technology Conference, IWTC, Sharm El-Sheikh, Egypt, pp Ghodsian, M. & Vaghefi, M. (29) Experimental study on scour and flow field in a scour hole around a T-shape spur dike in a 9 degree bend. International Journal of Sediment Research, 24(2), pp Gill, M.A. (972) Erosion of sand beds around spur dikes. Journal Hydraulics Division, 98(9), pp Karami, H.; Basser, H.; Ardeshir, A. & Hosseini, S.H. (22) Verification of numerical study of scour around spur dikes using experimental data. Water and Environmental Journal, 28(), pp Kuhnle, R.A.; Alonso, C.V. & Douglas, S.F. (22) Local scour associated with angled spur dikes. Journal of hydraulic engineering, 28(2), pp Li, G.; Lang, L. & Ning, J. (23) 3D Numerical Simulation of Flow and Local Scour around a Spur Dike. IAHR World Congress, pp.-9. Lodhi, A.S.; Jain, R.K. & Sharma, P.K. (26) Influence of cohesion on scour around submerged dike founded in clay sand gravel mixtures. ISH Journal of hydraulic engineering, 22(), pp Masjedi, A.; Bejestan, M.S. & Moradi, A. (2) Experimental study on the time development of local scour at a spur dike in a 8 o flume bend. Journal of food, Agriculture & environment, 8(2), pp Masjedi, A.; Dehkordi, V.; Alinejadi, M. & Taeedi, A. (2) Experimental study on scour depth around a T-shape spur dike in a 8 degree bend. World Applied Sciences Journal, (), pp Masjedi, A. & Foroushani, E. (22) Reduction of local scour by shape of single spur dike in river bend. 9 th ISE, Vienna. Nagy, H.M. (24) Maximum depth of local scour near emerged vertical-wall spur dike. Alexandria Engineering Journal, Faculty of Engineering, Alexandria University, Egypt, 43(6), pp

14 International Water Technology Journal, IWTJ Vol. 6 No.2, June 26 Naji, A.M.; Ghodsian, M.; Vaghefi, M. & Panahpur, N. (2) Experimental and numerical simulation of flow in a 9 degree bend Flow. Measurement and Instrumentation, 2(3), pp Osman, M.A. & Saeed, H.N. (22) Local scour depth at the nose of permeable and impermeable spur dykes University of Khartoum Engineering Journal, 2(), pp.-9. Shafaie, A. & Ardeshir, A. (28) Length and orientation of minor spur in the sand bed. Proceedings of the 4 th IASME/WSEAS Int. Conference on water resources, hydraulics & hydrology, pp Suzuki, K.; Michiue, M. & Hinokidani, O. (987) Local bed form around a series of spur dikes in alluvial channel. In Proceedings of the 22 nd Congress, IAHR, Lausanne, Switzerland, pp Vaghefi, M.; Safarpoor, Y. & Hashemi, S.S.H. (24) Effect of T-shape spur dike submergence ratio on the water surface profile in 9 degree channel bend with SSIIM numerical model. International journal of advanced engineering and applied research, 7(4), pp. 6. Vaghefi, M.; Shakerdargah, M. & Akbari, M. (24) Numerical study on the effect of ratio among various of submersion on three-dimensional Velocity Components around T-shaped Spur Dike Located in a 9 degree bend. International Journal Scientific Engineering and Technology, 3(5), pp Vaghefi, M.; Safapoor, Y. & Hashemi, S.S. (25) Effects of distance between the T-shaped spur dikes on flow and scour patterns in 9 o bend using the SSIIM model. Ain Shams Engineering Journal, Zaghloul, N.A. (983) Local scour around spur-dikes. Journal of Hydrology, 6(-4), pp Zhang, H.; Nakagawa, H.; Kawaike, Y.B. & Baba, Y. (29) Experimental and simulation of turbulent flow in local scour around a spur dyke. International Journal of Sediment Research, 24(), pp Zhang, X.; Wang, P. & Yang, C. (22) Experimental Study on Flow Turbulence Distribution around a Spur Dike with Different Structure. International Conference on Modern Hydraulic Engineering, Science Direct, 28, pp