A semi-analytical solution to steady-state groundwater inflow into a circular tunnel considering anisotropic permeability

2021 ◽  
Vol 116 ◽  
pp. 104115
Author(s):  
Lin Li ◽  
Haohua Chen ◽  
Jingpei Li ◽  
De'an Sun
1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.


2008 ◽  
Vol 18 (1) ◽  
pp. 23-36 ◽  
Author(s):  
A.I. Shawky ◽  
M.S. El-Paoumy

The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained. .


2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zequn Hong ◽  
Xiangdong Hu

In order to solve the problem of sealing water and bearing capacity of a connected aisle in an underwater shield tunnel, a double-circle horizontal freezing method was adopted for ground reinforcement in the connected aisle of Maliuzhou Tunnel, which is China’s first shield tunnel with superlarge diameter built in a composite stratum. This paper proposed a new double-row-pipe freezing model for the calculation of frozen wall thickness based on analytical solution to steady-state temperature field. Besides, field measurement and transient numerical studies of the active freezing period were also carried out to study the freeze-sealing effect. The results show that frozen wall thickness obtained by analytical solutions agrees well with numerical simulation results, which verifies the applicability of the newly proposed calculation method. Field analysis indicates that soil temperature gradually approaches a stable value which is far below the freezing point, and a reliable water-sealing curtain can be formed around the designed connected aisle. Maximum impact of soil excavation on the frozen wall is about 10°C, and reducing exposure time of excavation surface can effectively alleviate the weakening of frozen wall. To obtain comprehensive analysis for freezing wall thickness, a more reasonable arrangement of temperature-measuring holes is expected in future freezing engineering.


2019 ◽  
Vol 16 (6) ◽  
Author(s):  
Xiao-Fei Wang ◽  
Bin-Song Jiang ◽  
Qiang Zhang ◽  
Meng-Meng Lu ◽  
Miao Chen

2011 ◽  
Vol 261-263 ◽  
pp. 1862-1866
Author(s):  
Zheng Fang Dong ◽  
Yi Chao Yao ◽  
Jun Jie Wang

Firstly several seismic simplified methods commonly used for deep circular tunnel are evaluated and the difficulties in response displacement method are pointed out. Then the analytical solution of soil spring coefficient and soil response of deep circular tunnel is derived from using complex variable theory of planar elastic theory based on pseudo-static hypothesis. The analytical solution has been verified by comparing its predictions with results from an analysis in finite element method. It is concluded that the analytical solution can be regarded as one feasible reference for the simplification of response displacement method.


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