# Model and Experimental Studies of the Seepage Failure of Damaged Geotextile at the Joint between Tubes in a Geotextile Tube Dam

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Critical Gradient Theoretical Model

#### 2.1. Vertical Stress Calculation

_{0}in the cylindrical coordinate system. The overburden load caused by the weight of the upper-layer geotextile tubes is distributed around the hole. Assuming that this load is uniformly distributed with a value of q, the micro-concentration force on the micro area P, which is a distance of r from the center point O of the hole, is:

_{0}. Moreover, Equation (3) can be written as:

#### 2.2. Force Analysis of Seepage Failure

_{1}, t

_{2}, h

_{1}, and h

_{2}, respectively. Hence, the hydraulic gradient of the two sand layers J

_{1}and J

_{2}(${J}_{2}>{J}_{1}$) can be written as follows:

_{1}and J

_{2}are the critical hydraulic gradients of the upper and lower sand parts, respectively.

_{0}= 0, seepage failure of the sand in the geotextile tube would not occur and Equation (12) is not applicable. When r

_{0}is very large, geotextiles no longer have a protective effect on sand. The shearing resistance of sand in the tube is equal to that of sand without a tube.

_{t}is the Terzaghi theoretical critical gradient, and α and β are the overburden load and hole effect coefficients, respectively.

## 3. Sand Erosion Tests by Upward Seepage Flow

#### 3.1. Test Apparatus and Materials

_{90}< d

_{85}) and permeability criterion (O

_{90}> d

_{15}) are both satisfied.

#### 3.2. Testing Program and Procedures

- Before the sand seepage erosion tests, the steady-flow chamber, sand chamber, stainless-steel perforated plate, and filter cloth were assembled successively, as shown in Figure 5. To ensure the homogeneity of the sand sample, the sand was compacted layer by layer with a thickness of 4 cm per layer. Each layer was compacted with a metal rod several times to the target relative density. This process was repeated until the sand was filled to the top of the sand chamber. During sand filling, pore-water sensors were placed at predetermined positions.
- The geotextile with the hole and the acrylic cylinder of the overflow chamber were placed successively after the surface of the sand sample was flattened. Then, the hard stainless-steel mesh and the load-bearing platform were installed. In the end, the overflow chamber was secured by bolting the cover plate and flange.
- In the process of specimen saturation, the required overburden load was first applied through the loading device. Second, water from the external tank was slowly introduced into the specimen through the steady-flow chamber. To avoid sand particle disturbance, the saturation process must be slow. Then, the sand was soaked for 12 h under a static head to ensure a high degree of saturation.
- Starting with zero differential head, the water tank was first raised by 3 cm (hydraulic gradient = 0.15). During this period, the pore-water pressure and the seepage rate were recorded using a measuring cylinder under the overflow pipe every 2 min, and the corresponding hydraulic conductivity was calculated. If there is no change in the water pressure and seepage rate for two consecutive times and no notable seepage channel is observed, then the sand sample is considered to be stable. After another 20 min under this hydraulic gradient, the hydraulic gradient was increased by raising the tank another 3 cm. This process was repeated until hydraulic conductivity changed by more than 20%. For the remainder of the test, the differential head was increased in small increments of 1 cm (hydraulic gradient = 0.05). The test progressed until the sand sample completely failed.

## 4. Test Results and Analysis

#### Seepage Failure Progression

^{2}) of each curve are also placed in the picture The coefficient of determination (R

^{2}) indicates that the theoretical model is in good agreement with the experimental results.

## 5. Discussion

#### 5.1. Effect of the Overburden Load

#### 5.2. Effect of the Hole

_{1}in the theoretical model decreases, the increase in overburden load further increases the critical gradient difference between the upper and lower sand body parts. Combined with Equations (8) and (12), it can be found that, with the increase in overburden load, the overall anti-seepage strength of the sand sample is more affected by the compacted sand body of the lower part.

_{1}nor the critical gradient J

_{1}of the upper sand part can be reduced to zero with the increase in overburden load. That is, the specific conditions of the theoretical model (Equation (8)) can always be satisfied.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) field photo and (

**b**) simplified diagram, geotextile tubes collapse and joint seams between tubes.

**Figure 3.**Distribution contours of the additional vertical stress relative to ${\sigma}_{z}$ near the damaged hole.

**Figure 7.**Seepage rate versus water head difference. (

**a**) seepage rate under different hole radii and (

**b**) seepage rate under different loads.

**Figure 9.**Images of the four seepage erosion stages (q = 0 kPa, r

_{0}= 1.0 cm). (

**a**) Seepage stability stage (SS), (

**b**) sand particle wash-out stage (SP), (

**c**) preferential flow formation and development stage (PF), and (

**d**)complete failure stage (CF).

Geotextile Type | M_{a} | T_{gt} | k_{n} | n | O_{90} | T_{s} | ε_{u} | T_{c} |
---|---|---|---|---|---|---|---|---|

Woven polypropylene | 170 | 0.68 | 6.7 × 10^{−3} | 85 | 0.12 | 75 × 75 | 17.8 × 17.8 | 3.4 |

_{a}= mass per unit area (g/m2); T

_{gt}= thickness (mm); k

_{n}= hydraulic conductivity normal to the geotextile plane (cm/s) (ASTM D4491); n = porosity (%); O

_{90}= characteristic opening size (mm) (ASTM D4751); T

_{s}= tensile strength (kN/m) (ASTM D4595); ε

_{u}= ultimate elongation at maximum load (%) (ASTM D4595); and T

_{c}= static puncture strength (kN).

Soil Type | Cu | Cc | Gs | k | e0 | φ | J_{t} |
---|---|---|---|---|---|---|---|

Quartz sand | 2.6 | 1.1 | 2.65 | 3.5 × 10^{−3} | 42.8 | 30° | 1.155 |

_{t}= Terzaghi theoretical critical gradient.

Load (kPa) | 0 | 5 | 10 | 20 | 30 | |
---|---|---|---|---|---|---|

Radius (cm) | ||||||

0.5 | 3.52 | 4.64 | 5.12 | 5.36 | 5.52 | |

1 | 3.12 | 4.16 | 4.8 | 5.28 | 5.44 | |

1.5 | 2.96 | 3.92 | 4.64 | 5.2 | 5.36 | |

2 | 2.88 | 3.76 | 4.56 | 5.2 | 5.36 |

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**MDPI and ACS Style**

Mao, W.; Wang, T.; Shu, Y. Model and Experimental Studies of the Seepage Failure of Damaged Geotextile at the Joint between Tubes in a Geotextile Tube Dam. *Water* **2022**, *14*, 3934.
https://doi.org/10.3390/w14233934

**AMA Style**

Mao W, Wang T, Shu Y. Model and Experimental Studies of the Seepage Failure of Damaged Geotextile at the Joint between Tubes in a Geotextile Tube Dam. *Water*. 2022; 14(23):3934.
https://doi.org/10.3390/w14233934

**Chicago/Turabian Style**

Mao, Wenlong, Tianwen Wang, and Yiming Shu. 2022. "Model and Experimental Studies of the Seepage Failure of Damaged Geotextile at the Joint between Tubes in a Geotextile Tube Dam" *Water* 14, no. 23: 3934.
https://doi.org/10.3390/w14233934