Applying 2D numerical model to calculate the scour at the Cua Dai bridge, Quang Nam province

• Abstract:  When the Cua Dai bridge is built across the Thu Bon River, it causes a narrowing of the flow leading to scour, which seriously threatens the pier and endangers the structure. In order to limit the influence of scour the bridge, it is necessary to ensure that the scour under the bridge is within the allowable range. At the same time, it is necessary to take measures to limit and overcome the causes of scour. Therefore, the study and prediction of locations that are likely to cause scour are of great significance in choosing effective and versatile prevention solutions for works on this river section. Most of the scour formulas for bridge use the 1D average velocity to calculate; The calculated results are much different from the real distribution of flow velocity in the river. Therefore, the results of scour calculation often have big deviations from reality, especially when the river cross-section has no flats or curved rivers... The article focuses on researching scour at the bridge pier based on the two-dimensional horizontal velocity in front of the pier by using RIVER 2D model, built from the mathematical model of two horizontal flows and solved by the finite element method. The results of the paper show that the scour depth of pier by the one-dimensional (1D) average velocity gives much larger than when applying the two-dimensional horizontal velocity to calculate the scour.

Keywords: Scour, 2D average velocity; RIVER 2D model, scour depth

2. Methods of calculating bridge pier scour

2.1 Calculation of pier scour by the method of using 1D average velocity.

General scour.

O.V.Andreev (1955) [7] proposed a method to calculate the maximum general scour under the bridge (lower limit of scour) based on the analysis of the movement of alluvium particles in the mainstream and the river beach below the bridge. In the river beach part under the bridge, scour only starts when the velocity of water flowing under the bridge is greater than the allowed non-scour velocity (v_ox) of the geological soil layer forming the river beach (v_bc>v_ox) and the scour will stop when the flow rate decreases to the allowed non-scour rate. In the mainstream, the flow rate is always greater than the allowable rate of non- scour of the riverbed’s geological layer and therefore the topsoil layer of the riverbed is always in a state of motion, but the river is not deeply eroded because there is a balance of alluvium along the river. Thus, the flow rate under the bridge is greater than the allowable rate without erosion, which is not the cause of scour in the mainstream and the deformation of the river under the bridge can only be explained by the imbalance of alluvium along the river. The overall scour under the bridge is calculated according to the principle of balance of sediment limit for the mainstream and the flow part with alluvium transport of O.V.Andreev (1955) [7]. The flow depth after scouring is determined according to equation (1) .

Where:

+ Q₁=Q_ch, Q₂=Q'_ch: Water flow before and after bridge construction at the mainstream.

+ h_ch, h'_ch : Water depth at mainstream before (natural time) and after scouring.

h_ch = ▼h_hm – ▼h_tbs

▼h_hm: Elevation of flow rate at natural time (taken according to design frequency)

▼h_tbs: average elevation of the riverbed

+ B_ch, B'_ch: Mainstream width before and after bridge construction.

B_ch = L₀ = 1657.34m.

B'_ch = L = 1401.5 m.

Calculation results of general scour depth according to table 1 Table 1. Table of results for calculating the general scour depth of piers located on the main stream according to the 1D average velocity method.

Bridge Piers	Bottom elevation (m)	Surface elevation (m)	Water Depth before scour hch (m)	Water Depth after scour h'ch (m)	Rising water (m)	General depth scour (m)	Bottom elevation after local scour (m)
T3	-0.500	2.830	3.330	3.504	0.061	0.235	-0.735
T4	-1.250	2.830	4.080	4.293	0.061	0.274	-1.524
T5	-1.240	2.830	4.070	4.283	0.061	0.274	-1.514
T6	-1.210	2.830	4.040	4.251	0.061	0.272	-1.482
T7	-0.960	2.830	3.790	3.988	0.061	0.259	-1.219
T8	-1.420	2.830	4.250	4.472	0.061	0.283	-1.703
T9	-1.720	2.830	4.550	4.788	0.061	0.299	-2.019
T10	-1.900	2.830	4.730	4.977	0.061	0.308	-2.208
T11	-2.050	2.830	4.880	5.135	0.061	0.316	-2.366
T12	-2.540	2.830	5.370	5.651	0.061	0.342	-2.882
T13	-2.630	2.830	5.460	5.745	0.061	0.346	-2.976
T14	-3.400	2.830	6.230	6.556	0.061	0.387	-3.787
T15	-8.150	2.830	10.980	11.554	0.061	0.635	-8.785
T16	-11.600	2.830	14.430	15.184	0.061	0.815	-12.415
T17	1.260	2.830	1.570	1.652	0.061	0.143	1.117
T18	0.000	2.830	2.830	2.978	0.061	0.209	-0.209
T19	-0.050	2.830	2.880	3.031	0.061	0.212	-0.262
T20	0.040	2.830	2.790	2.936	0.061	0.207	-0.167
T21	-0.040	2.830	2.870	3.020	0.061	0.211	-0.251

Caculating local Scour (p = 1%)

Two authors N.X Truc and N.H. Khai (1982) [8] introduced the formula for determining the largest local scour value at the bridge pier. Based on the research results on the causes and development process of local scour on pier scour models in the hydraulic laboratory and the research results of foreign authors, a reasonable structural form of the local scour calculation formula has been selected. The formula (2) has the following simple form. When v³ v_ox (for mainstream piers). 

h_cb= 0,52.k_d.b^0,88.h^0,12.(V/V_ox)^1,16                                                                                  (2)

Where:

+ h_cb: maximum local scour depth at bridge pier, m 

+ k_d: factor taking into account the influence of cylinder shape, taken as  0,1k_ζ

+ k_ζ : Iaratslaxev's shape coefficient    

+ h: depth of water flow at bridge pier before local scour, m 

+ V: water velocity at bridge pier before local scour, m/s

+ V_ox  : allowable no- scour velocity of the soil layer at the location where scour development  

+ b: calculated width of the cylinder, m

The results of local scour calculation are obtained from Table 2

Table 2. Table of results of calculation of local scour depth of piers located on the main stream according to the average 1D velocity method.

Bridge Piers	Shape factor Kd	Width of pier b (m)	Depth of water flow h (m)	Velocity V (m/s)	No-scour velocity Vox (m/s)	Ratio V/Vox	Maximum local scour depth hcb (m)
T3	0.97	1.8	3.565	1.484	0.720	2.061	2.280
T4	0.97	1.8	4.354	1.484	0.790	1.878	2.097
T5	0.97	1.8	4.344	1.484	0.780	1.903	2.128
T6	0.97	1.8	4.312	1.484	0.770	1.927	2.158
T7	0.97	1.8	4.049	1.484	0.740	2.005	2.243
T8	0.97	1.8	4.533	1.484	0.805	1.843	2.062
T9	0.97	1.8	4.849	1.484	0.815	1.821	2.049
T10	0.97	1.8	5.038	1.484	0.820	1.810	2.044
T11	0.97	2	5.196	1.484	0.825	1.799	2.235
T12	0.97	4	5.712	1.484	0.835	1.777	4.103
T13	0.97	5	5.806	1.484	0.840	1.767	4.969
T14	0.97	5	6.617	1.484	0.860	1.726	4.911
T15	0.97	5	11.615	1.484	0.910	1.631	4.921
T16	0.97	5	15.245	1.484	0.950	1.562	4.837
T17	0.97	4	1.713	1.484	0.650	2.283	4.748
T18	0.97	2	3.039	1.484	0.705	2.105	2.515
T19	0.97	1.8	3.092	1.484	0.705	2.105	2.297
T20	0.97	1.8	2.997	1.484	0.690	2.151	2.346
T21	0.97	1.8	3.081	1.484	0.700	2.120	2.315