# Assessment of the Impact of Sand Mining on Bottom Morphology in the Mekong River in An Giang Province, Vietnam, Using a Hydro-Morphological Model with GPU Computing

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## Abstract

**:**

## 1. Introduction

^{2}in size and about 4800 km in length. The main portion of the Mekong River flows through six countries including China, Myanmar, Thailand, Laos, Cambodia, and Vietnam. [11]. The lower Mekong morphology is created by bedrock-controlled and alluvial reaches [12]. There are many causes of continuous and severe erosion in the area, such as excessive sand mining and sediment imbalances leading to erosion [13,14]. The annual extraction, according to the estimation of Bravard et al. (2013), is 34 Mm

^{3}(approximately 54 MT/year for an aggregate density of 1.6 t/m

^{3}), featuring mostly (90%) sand and, to a smaller degree, gravel (8%) and pebbles (1%). This utilization is focused on mining in Cambodia (21 MT/year), Vietnam (8 MT/year), Thailand (5 MT/year), and Laos (1 MT/year) [15]. It has been estimated that sand mining has removed 200 Mm

^{3}of bedload since 1998. Hackney’s research indicated that sand in the Mekong riverbed is minimal and that sand transport to the delta is under threat from increased bed sediment extraction [16]. The total sand flux entering the Mekong delta (6.17 MT/year ± 2.01 MT/year) is far less than the current sand extraction rates (50 MT/year). As a result, it takes only 10 to 18 years to scour the riverbed sufficiently at these current rates to change the riverbed and sediment transport [17].

- (1)
- First, the computational times on a single-core CPU machine are too slow to meet the simulation’s on-demand requirements. We thus parallelize our solver using massively multi-core GPUs to accelerate the computing speed, which is evaluated with a strong-scaling factor.
- (2)
- Second, we assess the changes in bottom morphology in the Mekong River in An Giang province under sand mining.

## 2. Materials and Methods

#### 2.1. Study Area

^{3}/s, with a predictable 20-fold seasonal fluctuation from the dry season (November–June) to the wet season (July–October) [12,20].

^{3}, and its mining area is 91 ha [49]. From 2014 until the present, the Vinh Hoa mine has operated (According to License No. 04/GP-UBND 23 April 2013) with an annual output of 200,000 m

^{3}and a mining area of 27.9 ha.

#### 2.2. Numerical Model

#### 2.2.1. Reynolds Equation in the Ox and Oy Directions

#### 2.2.2. Suspended Sediment Transport Equation

_{b}> τ

_{e}, S = E (Erosion rate):

_{b}< τ

_{d}, S = D (Deposition rate):

_{e}≥ τ

_{b}≥ τ

_{d}:

#### 2.2.3. Bed Load Continuity Equation with Sand Mining Component:

_{sm}is the sand mine source and the standing sand mining rate (m/s).

_{sm}is not involved in the suspended sediment transport equation. Sand mining will stop when the bottom elevation reaches the government’s permitted mining level, where q

_{b}= (q

_{bx}, q

_{by}).

#### 2.3. Graphics Processing Unit (GPU)

## 3. Setting up the Model

#### 3.1. Study Area Mesh

_{sm}(i, j) (as Figure 3), in which S

_{sm}(i, j) is the sand mining rate at i, j cells (the locations of these sand mines are described in Figure 1). The sand mining rate at the i, j cell corresponding to scenarios (SC1, SC2A, SC2B, SC3, SC4A, SC4B), the annual output, the square of Tan An, and the Vinh Hoa sand mines, is outlined in Table 1.

#### 3.2. Initial and Boundary Conditions

#### 3.2.1. Initial Conditions

_{0}= 0, the hydraulic module is tied to a static state (Figure 2), and the sediment transport module is set to an initial constant basal concentration. Where the problem is calculated from a time t = t

_{1}, the initial condition will be the velocity fields u, ν (x, y), and concentration C (x, y) at time t

_{1}across the computational domain.

#### 3.2.2. Boundary Conditions

#### The Open Boundary

_{o}.

#### Solid Wall Boundary

_{n}= 0

## 4. Results and Discussion

#### 4.1. Calibration and Validation

#### 4.1.1. Hydraulic Model

^{2}) were used to measure the model performance [57,58,59].

^{2}values were 0.98 and 0.99. According to Moriasi’s research [59], these values indicate that the hydraulic model performance achieved outstanding values. Thus, it is believed that the hydrodynamic model is well-calibrated and that the predicted results are close to actual water movements.

_{2}(0.003) corresponding to h

^{2}(25 m) was found to make the roughness coefficient in the study area more suitable. Hence, the roughness value is changed from 0.005 to 0.03 when the bed level ranges from 0.1 to 25 m and from 0.003 to 0.06 when the bed level ranges from 25 to 41 m.

^{2}values were 0.99 for both these features.

#### 4.1.2. Sediment Transport Model

^{2}values. The graphical results during calibration and validation at Tan Chau station are shown in Figure 8.

**.**

#### 4.2. Improved Computing Speed When Combining GPUs

#### 4.3. The Hydraulic Simulation of the Tien River Segment in Mekong Delta

#### 4.4. Results of Bottom Changes and Analysis

- SC1: From 1999 to 2002 was the time before the sand mines started operating.
- SC2A: From 2002 to 2006 was the time that Tan An sand mine was in operation.
- SC3: From 2006 to 2014, there was no sand quarry in the study area.
- SC4A: From 2014 to 2019, the Vinh Hoa sand mine is in operation.

- SC2B: From 2002 to 2006, there was no sand mining at Tan An sand mine.
- SC4B: From 2014 to 2019, there was no sand mining at Vinh Hoa sand mine.

#### 4.4.1. From 1999 to 2002 (SC1)

#### 4.4.2. From 2002 to 2006 (SC2A and SC2B)

#### 4.4.3. From 2006 to 2014 (SC3)

#### 4.4.4. From 2014 to 2019 (SC4A and SC4B)

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclatures

u | Depth-averaged horizontal velocity components in x-direction (m/s) |

ν | Depth-averaged horizontal velocity components in y-direction (m/s) |

ς | Fluctuation of the water surface, compared to a “zero” level (m) |

h | Static depth from the still water surface to the bed (m) |

K | Friction bed coefficient |

A | Eddy horizontal viscosity coefficient (m^{2}/s) |

g | Acceleration gravity (m/s^{2}) |

C | Depth-averaged concentration of the suspended load (m^{3}/m^{3}) |

K_{x} | Dispersion coefficient in the Ox direction (m^{2}/s) |

K_{y} | Dispersion coefficient in the Oy direction (m^{2}/s) |

H | Average depth used in the model (H=h+ ς) (m) |

γ_{v} | Velocity coefficient for the depth; calculated from ${\gamma}_{v}=\frac{(1-Z)\left[1-{\left(\frac{a}{H}\right)}^{0.2}\right]}{(1.2-Z)\left[1-{\left(\frac{a}{H}\right)}^{1-Z}\right]}$ |

Z | Suspension number defined after Van Rijn (1993), $Z=\frac{{\omega}_{s}}{\chi ({u}_{*}+2{\omega}_{s})}$ |

χ | Von Karman constant = 0.4 |

u | Bed shear velocity, ${u}_{*}=\sqrt{\frac{g}{C{h}^{2}}({u}^{2}+{v}^{2})}$ |

Ch | Chezy coefficient, $Ch=18\mathrm{log}\left(12\frac{H}{{K}_{s}}\right)$ |

K_{s} | Bed roughness, K_{s} = 3D_{90} |

D_{90} | Diameter of particle that is equal to or less than 90% of the mass of the particles present |

S | Standing for erosion and deposition rates (m/s). |

M | Sediment size-dependent coefficient after Van Rijn (1993): 0,00001 (kg/m^{2}/s) |

C_{b} | Concentration of bedload, (m^{3}/m^{3}) |

ω_{sm} | Particle fall velocity in a mixture of water and sediment (m/s), ${\omega}_{sm}={(1-C)}^{4}{\omega}_{s}$ |

ω_{s} | Particle fall velocity, ${\omega}_{s}=\frac{\left(\frac{{\rho}_{s}}{\rho}\u20131\right)g{d}^{2}}{18v}$ |

D | Mean diameter of the particle (m) |

ν | Kinematic viscosity coefficient (m^{2}/s) |

τ_{e} | Critical bed shear stress for erosion at the bottom (N/m^{2}) |

τ_{d} | Critical bed shear stress for deposition at the bottom (N/m^{2}) |

τ_{b} | Bed shear stress (N/m^{2}), ${\tau}_{b}=\frac{1}{8}\begin{array}{cc}\rho {f}_{w}{V}_{}^{2}& \begin{array}{cc}& \end{array}\end{array}$ |

f_{w} | Friction coefficient of Darcy – Weisbach, calculated from the Chezy formula; ${f}_{w}={\frac{8g{n}_{r}{}^{2}}{{H}^{1/3}}}_{}^{}$ |

ρ | Mass density of water, (kg/m^{3}) |

ρ_{s} | Density of particles, (kg/m^{3}) |

n_{r} | Roughness coefficient |

ε_{p} | Void ratio of sediment |

D_{*} | Dimensionless particle parameter ${D}_{\ast}={d}_{m}{\left[\frac{g\left(\frac{{\rho}_{s}}{\rho}-1\right)}{{\nu}^{2}}\right]}^{\frac{1}{3}}$ |

T | Dimensionless bed shear stress: $T=\left[\frac{{u}_{*}^{2}-{u}_{*,cr}^{2}}{{u}_{*,cr}^{2}}\right]$ |

u_{*,cr} | Critical depth-averaged flow velocity based on Shields (m/s), ${u}_{*,cr}=0.25{(\frac{{\rho}_{\mathrm{s}}}{\rho}-1)}^{\frac{8}{15}}{d}^{\frac{9}{15}}{g}^{\frac{8}{15}}{\nu}^{-\frac{1}{15}}$ |

q_{b} | Bedload ${q}_{b}=0.053\left(\right(\frac{{\rho}_{s}}{\rho}-{1\left)g\right)}^{0.5}{d}_{m}^{1.5}{T}^{2.1}{D}_{\ast}^{-0.3}\frac{(u,v)}{\sqrt{{u}^{2}+{v}^{2}}}$ |

h_{i} | Bottom depth at the calculation node (m) |

Δx | The distance between two nodes (m) |

n_{p} | Perpendicular to the shoreline |

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**Figure 1.**The study area (Source: Tan Chau bathymetry (

**a**) collected on October 1999 from the Department of Investment and Construction Project of Tan Chau town area, An Giang, Vietnam; Tan Chau bathymetry (

**b**) collected on October 2014 from The Southern Institute Of Water Resources Research; Mekong delta map (

**c**) is referenced from Kuenzer et al. [50].

**Figure 4.**Input discharge Q(t) in 1999 (

**a**) and 2018 (

**b**); input water level ς(t) in 1999 (

**c**) and 2018 (

**d**); and the input total suspended solids (TSS) C(t) in 1999 (

**e**) and 2018 (

**f**).

**Figure 5.**Calibration results at Tan Chau station from 11 July 2002 to 30 October 2002 for water level ς (m) (

**a**) and discharge Q (m

^{3}/s) (

**b**).

**Figure 7.**Observations and simulations at Tan Chau station from 10:00 6 June 2018 to 10:00 13 June 2018 for the water level ς (m) (

**a**) and discharge Q (m

^{3}/s) (

**b**).

**Figure 8.**Observations and simulations at Tan Chau station for calibration TSS (g/l) (

**a**) and validation TSS (g/l) (

**b**).

**Figure 9.**A visual comparison of the vector fields on the CPU (rendered using Surfer) (

**a**) and on the graphics processing units (GPU) (rendered using Python) (

**b**) after 15 h of simulation using 20 m-grid data.

**Figure 10.**A visual comparison of the vector fields on the CPU (rendered using Surfer) (

**a**) and on the GPU (rendered using Python) (

**b**) after 15 h of simulation using 10 m-grid data.

**Figure 12.**The initial bathymetry of the study area (

**a**) and the velocity field of the peaking flood at 21:00 on 29 September 2002 (

**b**).

**Figure 13.**Simulation of the bed changes over 3 years from 1999 to 2002: (

**a**,

**b**) figures describing the results of simulations for 1999 and 2002, respectively; (

**c**) the bed change simulation during the period; and (

**d**) the comparison graphs of simulations at cross-section 1.1.

**Figure 14.**Simulation of the bed changes over 4 years from 2002 to 2006: (

**a**,

**c**) the results of simulations for 2002 and 2006, respectively; (

**b**) the case with no sand simulation for 2006; (

**d**) riverbed measurements in 2006; (

**e**,

**g**) bed change simulations during the period with sand mining and no sand mining, respectively; (

**f**) comparison graphs of simulations and measurements at cross-section 1.1.

**Figure 15.**Simulation of the bed changes over the period of 8 years from 2006 to 2014: (

**a**,

**b**) results of the simulations for 2006 and 2014, respectively; (

**c**) riverbed measurements for 2014; (

**d**) bed change simulations during the period; (

**e**) a comparison graph of simulations and measurements at cross-section 1.1.

**Figure 16.**Simulation of the bed changes over 5 years from 2014 to 2019: (

**a**,

**c**) results of the simulations in 2014 and 2019, respectively; (

**b**) the case of no sand simulations in 2019; (

**d**) riverbed measurements in 2019; (

**e**,

**h**) bed change simulations during the period with no sand mining and sand mining, respectively; (

**f**,

**g**) comparison graphs of simulations and measurements at cross-sections 1.1 and 2.2, respectively.

Sand Mine | Annual Output (m ^{3}/year) | Square (m ^{2}) | Average Exploitation Rate (m/s)-S_{sm}(i, j) | |||||
---|---|---|---|---|---|---|---|---|

1999–2001 | 2002–2006 | 2007–2014 | 2014–2019 | |||||

SC1 | SC2A | SC2B | SC3 | SC4A | SC 4B | |||

Tan An | 200,000 | 910,000 | 0 | 5.09 × 10^{-6} | 0 | 0 | 0 | 0 |

Vinh Hoa | 200,000 | 279,000 | 0 | 0 | 0 | 0 | 1.66 × 10^{-5} | 0 |

Parameter | Value |
---|---|

Time step (Δt) | 2 s |

Mean diameter of particle (D) | 0.01 mm |

Diameter of particle 90% of the mass of particles present (D_{90}) | 0.04 mm |

Density of particles (ρ_{s}) | 2600 kg/m^{3} |

Kinematic viscosity coefficient (ν) | $1.01\times {10}^{-6}$ m^{2}/s |

Critical shear stress for deposition (τ_{d}) | 0.35 N/m^{2} |

Critical shear stress for erosion (τ_{e}) | 0.04 N/m^{2} |

**Table 3.**A direct comparison of running times on the CPU (a) and GPU (b) for 20 m- and 10 m-grid simulations.

20-m Grid | 10 m-Grid | |||||
---|---|---|---|---|---|---|

Hours of Simulation | Running Time on the CPU (s) | Running Time on the GPU (s) | Accelerating Factor | Running Time on the CPU (s) | Running Time on the GPU (s) | Accelerating Factor |

1 | 72.00 | 6 | 12 | 409.00 | 16 | 26 |

2 | 141.00 | 12 | 11.75 | 806.00 | 32 | 25 |

3 | 213.00 | 19 | 11.21052632 | 1,196.00 | 49 | 24 |

4 | 282.00 | 25 | 11.28 | 1,568.00 | 66 | 24 |

5 | 353.00 | 31 | 11.38709677 | 1,953.00 | 82 | 24 |

6 | 425.00 | 38 | 11.18421053 | 2,340.00 | 99 | 24 |

7 | 496.00 | 44 | 11.27272727 | 2,724.00 | 116 | 23 |

8 | 567.00 | 50 | 11.34 | 3,110.00 | 132 | 24 |

9 | 638.00 | 57 | 11.19298246 | 3,494.00 | 148 | 24 |

10 | 709.00 | 63 | 11.25396825 | 3,852.00 | 165 | 23 |

11 | 780.00 | 69 | 11.30434783 | 4,198.00 | 181 | 23 |

12 | 851.00 | 76 | 11.19736842 | 4,572.00 | 198 | 23 |

13 | 922.00 | 82 | 11.24390244 | 4,946.00 | 215 | 23 |

14 | 995.00 | 89 | 11.17977528 | 5,323.00 | 232 | 23 |

15 | 1,068.00 | 95 | 11.24210526 | 5,697.00 | 248 | 23 |

... | ... | ... | ... | ... | ... | ... |

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## Share and Cite

**MDPI and ACS Style**

Thi Kim, T.; Huong, N.T.M.; Huy, N.D.Q.; Tai, P.A.; Hong, S.; Quan, T.M.; Bay, N.T.; Jeong, W.-K.; Phung, N.K. Assessment of the Impact of Sand Mining on Bottom Morphology in the Mekong River in An Giang Province, Vietnam, Using a Hydro-Morphological Model with GPU Computing. *Water* **2020**, *12*, 2912.
https://doi.org/10.3390/w12102912

**AMA Style**

Thi Kim T, Huong NTM, Huy NDQ, Tai PA, Hong S, Quan TM, Bay NT, Jeong W-K, Phung NK. Assessment of the Impact of Sand Mining on Bottom Morphology in the Mekong River in An Giang Province, Vietnam, Using a Hydro-Morphological Model with GPU Computing. *Water*. 2020; 12(10):2912.
https://doi.org/10.3390/w12102912

**Chicago/Turabian Style**

Thi Kim, Tran, Nguyen Thi Mai Huong, Nguyen Dam Quoc Huy, Pham Anh Tai, Sumin Hong, Tran Minh Quan, Nguyen Thi Bay, Won-Ki Jeong, and Nguyen Ky Phung. 2020. "Assessment of the Impact of Sand Mining on Bottom Morphology in the Mekong River in An Giang Province, Vietnam, Using a Hydro-Morphological Model with GPU Computing" *Water* 12, no. 10: 2912.
https://doi.org/10.3390/w12102912