## Li Gong* , Zhonghui Wang* , Yaxian Li* , Chunling Jin* and Jing Wang*## |

Elasticity modulus (Mpa) | Poisson ratio | [TeX:] $$\left(\mathrm{kg} / \mathrm{m}^{3}\right)$$ | Compression strength (Mpa) | Tensile strength (Mpa) | Compressive strength (Mpa) |
---|---|---|---|---|---|

2.7×1010 | 0.3 | 2,500 | - | - | - |

8×108 | 0.3 | 910 | 2.5 | 0.504 | 0.84 |

The automatic single contact (ASSC) was chosen as the contact type. Output control was conducted after assuming initial conditions of initial velocity, contact type and boundary condition, and then the K file was got. In the input calculation, the dynamics was used to analyze command stream file which is called K file in ANSYS, Fig. 3 shows part of K file. In the calculation, 3D SOLID164 solid element was adopted in the drift ice and tunnel model which are linear elastic material. The unit division adopted mesh mapping generation method as unit division. We consider the tunnel lining surface as the dominative surface and drift ice contact surface as the subsidiary surface. The parameters are shown in Table 1, where the parameters of ice were from the relation between the ice elastic modulus and ice in the references [11,12].

The impact between the drift ice and tunnel is a complex collision problem between ice structures with many instability factors such as dynamic coupling, fluid-solid coupling, and so on. The main influence factors are velocity, plane size, thickness, shape, tensile strength, compressive strength, elastic modulus, flexibility of structure, friction, impact angle, and so on. This study mainly researches the impact force of drift ice on diversion tunnel surface in different velocity, different drift ice plane size, different drift ice thickness, and so on. In the calculation, other factors were ignored to reduce complexity. The tunnel finite element model is shown in Fig. 4

The impact forces of drift ice crashing tunnel are different with different drift ice velocity. Set 2 m as water depth and 2 × 0.5 × 2 [TeX:] $$\mathrm{m}^{3}$$ as drift ice size, and calculate the drift ice impact force when the drift ice velocities are 0.5, 0.8, 1.0, 1.5, 1.8, 2.0, 2.3, 2.5, 2.8, 3.0 m/s, respectively. Within the damage permissible limits, the calculation results of the drift ice impact force are shown in Fig. 5.

Different velocities produce different stress and impact force when the drift ice crashing the tunnel, the flow velocity-maximum stress relationship graph and flow velocity-maximum impact force relationship graph are shown in Fig. 6.

In order to research the influence of drift ice plane size on impact force, set 2 m as water depth, v = 5 m/s as drift ice velocity, 0.5 m as ice thickness. When the drift ice plane sizes are 0.5×0.5×2 m3, 1.0×0.5×2 m3, 1.5×0.5×2 [TeX:] $$\mathrm{m}^{3}$$, 2×0.5×2 [TeX:] $$\mathrm{m}^{3}$$, 2.5×0.5×2 m3, which are 1, 2, 3, 4, 5 times of 0.5×0.5 [TeX:] $$\mathrm{m}^{2}$$, respectively. Within the damage permissible limits, the calculation results of the drift ice impact force are shown in Fig. 7.

Different drift ice plane sizes produce different stresses and impact forces when drift ice crashing tunnel, the drift ice plane size-maximum stress relationship graph is shown in Fig. 8 and drift ice plane size-maximum impact force relationship is shown in Fig. 9.

Figs. 8 and 9 show that the collision stress relation curve is accordance with the collision impact force relation curve. When the drift ice has small plane size, the collision stress increases with the drift ice plane size, presenting linear relationship.

The drift ice thicknesses change, the impact force of drift ice crashing tunnel changes accordingly. When other parameters are fixed, and the drift ice thicknesses are 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 m, respectively. Within the damage permissible limits, the calculation results of the drift ice impact force are shown in Fig. 10.

In different drift ice thicknesses, the relationship between maximum stress and thickness is shown in Fig. 11.

Fig. 12 shows that when other parameters are fixed, the impact force increases with the drift ice thickness when the thickness is less than 0.9m, and the stress value has a little change when the thickness is larger than 0.9m. When the drift ice thickness is small, the impact force increases with the thickness, presenting approximate linear relationship.

Above all, the tunnel lining surface would have different degrees of distortions when drift ice crashing tunnel lining in different drift ice velocity, different drift ice plane size, different drift ice thickness and so on. The distortions have little influence on the tunnel stability. But the tunnel lining surface breaks, and the tunnel lining surface would fall off by long time water erosion. It would destroy structure strength and stability. In the practical engineering, it would pay attention to this harm and adopt suitable protection measures.

This study conducts indoor model test to research the impact mechanism of ice on tunnel in thawing period. In the indoor model test, the impact force of drift ice on diversion tunnel were tested on different drift ice plane size, different drift ice thickness, different drift ice velocity and so on. The model test state schematic diagram is shown in Fig. 13. Fig. 14 is the pump which used to pump water to other devices.

In this test, the main devices are a 2 m×1 m×1 m water tank which is used to store the water circulating in the system and a water pump which is the dominant body drives water from water tank to water channel, rises water level and operates circularly. They are shown in Fig. 15.

Test steps

The test has 15 steps:

Step 1: Fill the water tank with water.

Step 2: Open the main power and make water in the water tank rush into water channel by water pump.

Step 3: Put the ice blocks of 7 cm×3.5 cm×7 cm in water channel.

Step 4: Adjust flow velocity by rotary screw.

Step 5: The flow velocity is 0.5 m/s measured by flow meter.

Step 6: Measure the depth by water level probe and let the water depth be 7.2 cm.

Step 7: Stick 10 plexiglass strain gauges on the water line location of each side of tunnel model surface.

Step 8: Make the transient strain tester be close.

Step 9: Connect the strain gauges with transient strain tester by test wires and correspond each strain gauge with the joint in the transient strain tester.

Step 10: Turn on the transient strain tester and adjust to manual mode.

Step 11: Read the strain value which is the reading of the transient strain tester in sequence, along with the ice striking the tunnel surface.

Step 12: Record data, and process them.

Step 13: Change the conditions that set the flow velocity is 0.8, 1.0, 1.2, 1.5, 1.8, 2.0, 2.3, 2.5, 2.8, and 3.0 m/s, then repeat Step 4 to Step 12.

Step 14: Change the conditions that set the flow velocity is 1 m/s and set the ice blocks size to 7 cm×1 cm×7 cm, 7 cm×1.8 cm×7 cm, 7 cm×2.9 cm×7 cm, 7 cm×3.5 cm×7 cm, 7 cm×4.3cm×7 cm, 7 cm×5.5 cm×7 cm, respectively, then repeat Step 4 to Step 12.

Step 15: Change the conditions that set the flow velocity is 1 m/s and set the ice blocks size to 3.5 cm×1.8 cm×7 cm, 5.5 cm×1.8 cm×7 cm, 7 cm×1.8 cm×7 cm, 9 cm×1.8 cm×7 cm, respectively, then repeat Step 4 to Step 12.

The drift ice velocity changes, the impact force and stress value on the tunnel surfaces changes accordingly, showing in Table 2.

Table 2.

Flow rate [TeX:] $$\boldsymbol{v}$$ (m/s) | Model strain [TeX:] $$\varepsilon_{m}$$(E-05 KN) | Model stress [TeX:] $$\sigma_{m}$$(kPa) | Prototype stress [TeX:] $$\sigma_{p}$$(MPa) | Prototype impact force [TeX:] $$F_{m}$$(E+03 KN) |
---|---|---|---|---|

0.5 | 0.635793 | 21 | 0.6 | 0.6 |

0.8 | 0.794741 | 27 | 0.75 | 0.75 |

1 | 1.483520 | 50 | 1.4 | 1.4 |

1.3 | 1.769620 | 60 | 1.67 | 1.67 |

1.5 | 1.939170 | 65 | 1.83 | 1.83 |

1.8 | 2.543170 | 86 | 2.4 | 2.4 |

2 | 2.331240 | 79 | 2.2 | 2.2 |

2.3 | 2.755100 | 93 | 2.6 | 2.6 |

2.5 | 2.861070 | 96 | 2.7 | 2.7 |

2.8 | 3.178960 | 107 | 3 | 3 |

3 | 3.390890 | 114 | 3.2 | 3.2 |

3.5 | 4.026690 | 136 | 3.8 | 3.8 |

By analyzing large number of test data, it is found that the test results are close to the finite element simulation results. Fig. 16(a) shows that the impact force variations are approximately the same in the software simulation results, test observation calculation results and the results of y = 10x. Therefore, the finite element calculation method is feasible. The impact force of drift ice increases with the flow velocity, appearing linear distribution.

The drift ice sizes are different, the impact force and stress on tunnel surfaces are different. The values are shown in Table 3.

The comparison of test values and model simulation values are shown in Fig. 16(b). The test values are close to model simulation calculation values. The impact force increases with the drift ice size.

Table 3.

Plan size | Model strain [TeX:] $$\varepsilon_{m}$$(E-05 KN) | Model stress [TeX:] $$\sigma_{m}$$(kPa) | Prototype stress [TeX:] $$\sigma_{p}$$(MPa) | Prototype impact force [TeX:] $$F_{m}$$(E+03 KN) |
---|---|---|---|---|

0.5×0.5×2 | 0.833333 | 25 | 0.7 | 0.7 |

1.0×0.5×2 | 5.250000 | 158 | 4.41 | 4.41 |

1.5×0.5×2 | 6.726190 | 202 | 5.65 | 5.65 |

2.0×0.5×2 | 6.642860 | 199 | 5.58 | 5.58 |

2.5×0.5×2 | 7.464290 | 224 | 6.27 | 6.27 |

By the tests, the drift ice thickness is different, the impact force and stress on the tunnel surfaces are different. The values are shown in Table 4.

The comparisons of test observation results and model calculation results are shown in Fig. 16(c). Fig. 16(c) shows that the impact force variations are approximately the same in the software simulation results, test observation calculation results and the results of y = 6.7x + 0.2. Therefore, the finite element calculation method is feasible. Within a certain range, the impact force of drift ice increases with the drift ice thickness, appearing linear distribution.

Table 4.

Thickness (m) | Model strain [TeX:] $$\varepsilon_{m}$$(E-05 KN) | Model stress [TeX:] $$\sigma_{m}$$(kPa) | Prototype stress [TeX:] $$\sigma_{p}$$(MPa) | Prototype impact force [TeX:] $$F_{m}$$(E+03 KN) |
---|---|---|---|---|

0.3 | 2.64914 | 89 | 2500 | 1.5 |

0.4 | 3.57633 | 121 | 3375 | 2.7 |

0.5 | 3.6876 | 124 | 3480 | 3.48 |

0.6 | 3.53218 | 119 | 3333 | 4 |

0.7 | 4.01155 | 135 | 3786 | 5.3 |

0.8 | 3.57633 | 121 | 3375 | 5.4 |

0.9 | 3.94427 | 133 | 3722 | 6.7 |

1.0 | 3.86774 | 130 | 3650 | 7.3 |

The comparison results of software simulation and test observation show that their trends are almost the same. The impact force of drift ice on tunnel lining increases with the drift ice thickness, appearing linear distribution, which verifies the reliability of the following simulation results.

The researches show that there are damages of drift ice impact force on tunnel lining in the thawing period in cold and dry region. By long time water scouring, the tunnel lining surfaces are broken and falling off which breaks the strength and stability of the structure. With the increasing of the size, thickness and the flow velocity of the drift ice, the impact force is different.

In different ice velocity, different size, different thickness of the drift ice, the tunnel lining surfaces would be destroyed and deformed when the drift ice crashing the lining. When the drift ice thickness is less than 0.9m, the impact force increases with the drift ice thickness, and the relationship between drift ice size and maximum stress appears linear relationship. When the drift ice thickness is larger than 0.9m, the impact force changes a little.

In the practical engineering, the two-phase movement between the ice and water is complex which exists multi-factor coupling effects among viscous force, drag force and other factors. The impaction between drift ice and tunnel lining is irregular. It needs further researches in the choice of the impact angle in the simulation.

He received B.S. degree in North China University of Water Resources and Electric Power in 2000, M.S. degree in Northwest A&F University in 2007, and a Ph.D. degree in Lanzhou Jiaotong University in 2014. Now he is a professor at the School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou, China.

- 1 K. L. Yang, "Review and frontier scientific issues of hydraulic control for long distance water diversion,"
*Journal of Hydraulic Engineering*, vol. 47, no. 3, pp. 424-435, 2016.doi:[[[10.13243/j.cnki.slxb.20150824]]] - 2 J. Wang, B. Zhang, P. Chen, T. Liu, "Experimental study of ice jam accumulation during freezing period,"
*Journal of Hydraulic Engineering*, vol. 47, no. 5, pp. 693-699, 2016.doi:[[[10.13243/j.cnki.slxb.20151048]]] - 3 S. Zhao, C. Li, C. Li, X. Shi, S. Zhao, "Processes of river ice and ice-jam formation in Shensifenzi Bend of the Yellow River,"
*Journal of Hydraulic Engineering*, vol. 48, no. 3, pp. 351-358, 2017.doi:[[[10.13243/j.cnki.slxb.20160721]]] - 4 K. Wang, P. Liu, S. Jin, N. Wang, Z. Yu, "Sea-ice growth and decay model of Bohai Sea based on thermodynamic process,"
*Advances in Water Science*, vol. 28, no. 1, pp. 116-123, 2017.doi:[[[10.14042/j.cnki.32.1309.2017.01.013]]] - 5 C. Shi, Y. Luo, Z. Hu, "Non-linear Burgers’ sea-ice model considering damage effects and its numerical application,"
*Engineering Mechanics*, vol. 35, no. 7, pp. 249-256, 2018.custom:[[[-]]] - 6 S. Jimenez, R. Duddu, J. Bassis, "An updated-Lagrangian damage mechanics formulation for modeling the creeping flow and fracture of ice sheets,"
*Computer Methods in Applied Mechanics and Engineering*, vol. 313, pp. 406-432, 2017.doi:[[[10.1016/j.cma.2016.09.034]]] - 7 A. Marchenko, D. Cole, "Three physical mechanisms of wave energy dissipation in solid ice," in
*Proceedings of the 24th International Conference on Port and Ocean Engineering under Arctic Conditions*, Busan, Korea, 2017;custom:[[[-]]] - 8 M. W. Shortt, P. R. Sammonds, "Experiments on the micromechanics of ice using scanning electron microscopy," in
*Proceedings of the 25th International Conference on Port and Ocean Engineering under Arctic Conditions*, Delft, Netherlands, 2019;custom:[[[-]]] - 9 C. Jin, M. Wu, L. Gong, "Risk prediction of ice-jam disaster in Ningxia-Inner Mongolia reaches of the Yellow River based on grey Markov-GMP-Verhulst model,"
*Journal of Natural Disasters*, vol. 28, no. 2, pp. 82-91, 2019.custom:[[[-]]] - 10 L. Gong, Y. Li, C. Jin, "Numerical simulation and verification on impact damage mechanical property of drift ice on diversion tunnel,"
*Transactions of the Chinese Society of Agricultural Engineering*, vol. 34, no. 13, pp. 144-151, 2018.doi:[[[10.11975/j.issn.1002-6819.2018.13.017]]] - 11 T. L. Yu, Z. G. Yuan, M. L. Huang, "Experimental study on mechanical behavior of river ice,"
*Journal of Liaoning Technical University (Natural Science)*, vol. 28, no. 6, pp. 937-940, 2009.custom:[[[-]]] - 12 F. Zhang, G. Li, "Simulation of flow ice impact on dam body based on LS-DYNA,"
*Water Conservancy Construction and Management. 0.9m0.9m*, vol. 33, no. 2, pp. 19-21, 2013.custom:[[[-]]]