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In this paper, we mainly prove some congruences involving Apéry-like numbers S n = ∑ k = 0 n ( n k ) ( 2 k k ) ( 2 n − 2 k n − k ) : Let p>3 be a prime. Then S p ≡ S 1 + (− 1) (p − 1) / 2 8 p 2 E p − 3 (mod p 3) , S 2 p ≡ S 2 + (− 1) (p − 1) / 2 128 p 2 E p − 3 (mod p 3) , S 2 p − 1 ≡ (− 1) (p − 1) / 2 32 2 (p − 1) S 1 + 20 p 2 E p − 3 (mod p 3) , S 3 p ≡ S 3 + (− 1) (p − 1) / 2 1440 p 2 E p − 3 (mod p 3). where E n stands for the nth Euler number. [ABSTRACT FROM AUTHOR]

Owing to the limitation of inner space of the shield machine, it is difficult to arrange the monitoring elements within a certain distance behind the excavation face. As a result, the deformation of the segments may not be detected in time. For underwater shield tunnels, the consequences of the lack of deformation data of the supporting structure are more serious. In this paper, the FLAC3D and the regression analysis method are used to obtain the lagging deformation data that cannot be monitored. Eight influencing factors of segments deformation and the two deformation indexes are selected to establish a BP neural network model for predicting the lagging deformation of the underwater shield tunnel. The feasibility of the prediction method is verified through engineering application. Among the three prediction methods used, namely regression analysis, neural network model, and numerical simulation, the neural network model has the highest prediction accuracy and the fastest calculation speed. Totally, the findings of this study can act as a reference for deformation prediction in similar underwater shield tunneling engineerings. [ABSTRACT FROM AUTHOR]

The foundation of subsea tunnel construction is that the expected benefit of the tunnel is greater than the construction cost. The location of subsea tunnels is the most fundamental factor determining the size of both tunnel revenue and cost. At present, the evaluation model for the site selection of subsea tunnels is mainly based on specific engineering projects, and the universal evaluation model for the subsea tunnels site selection is deficient. In this paper, nine parameters including lithology, geologic structure, rock strength, environmental conditions, economic benefit, construction cost, Minimum leakage method, Coal cutting experience under water method, and Norway experience method are selected as evaluation indexes for the site selection of subsea tunnels. The weight of each index is determined by weight back analysis. An evaluation model for subsea tunnel site selection is established based on weight back analysis method and efficacy coefficient method, and evaluation criteria are divided into four grades: excellent, good, medium, and bad. The evaluation model of subsea tunnel site selection is applied to the Qingdao Jiaozhou Bay subsea tunnel, the Xiamen Xiangan subsea tunnel, and the Seikan subsea tunnel. Results show that the site selection of the Qingdao Jiaozhou Bay subsea tunnel is grade II, the site selection of the Xiamen Xiangan subsea tunnel is grade III and the site selection of the Seikan subsea tunnel is grade IV. This new selection process provides a new method for subsea tunnel site selection and evaluation and also provides some reference for site selection of other types of structures. [ABSTRACT FROM AUTHOR]

In this paper, we mainly prove some congruences involving Apéry-like numbers S n = ∑ k = 0 n ( n k ) ( 2 k k ) ( 2 n − 2 k n − k ) : Let p>3 be a prime. Then S p ≡ S 1 + (− 1) (p − 1) / 2 8 p 2 E p − 3 (mod p 3) , S 2 p ≡ S 2 + (− 1) (p − 1) / 2 128 p 2 E p − 3 (mod p 3) , S 2 p − 1 ≡ (− 1) (p − 1) / 2 32 2 (p − 1) S 1 + 20 p 2 E p − 3 (mod p 3) , S 3 p ≡ S 3 + (− 1) (p − 1) / 2 1440 p 2 E p − 3 (mod p 3). where E n stands for the nth Euler number. [ABSTRACT FROM AUTHOR]