轴对称解对隧道衬砌水压力计算的适用性研究

文章根据渗流理论推导了隧道衬砌水压力的轴对称解,并利用数值分析方法研究了轴对称解对不同形状隧道断面与浅埋隧道的适用性.研究结果表明:轴对称解适用于非圆形隧道断面衬砌水压力的估算；隧道断面形状对衬砌水压力折减系数的影响较小,可以忽略不计,其影响大小主要由衬砌与围岩的渗透系数比值决定.对于浅埋低水头隧道,用轴对称解计算的毛洞流量Qm与数值解比较,其误差较大,最大误差为36.5％；但用来计算衬砌水压力p1以及衬砌后水流量Q1时,误差相对较小,最大误差为6.3％,特别是利用轴对称解得出的衬砌水压力值与利用数值解得出的衬砌水压力特征值最大误差仅为3.4％.

A Study of the Applicability of an Axisymmetric Solution for Calculating the Water Pressure on a Tunnel Lining

Based on seepage theory,water pressure formulas for tunnel linings under the conditions of axial symmetry were deduced.Then,through numerical analysis,the applicability of an axisymmetric solution for non-circular cross section tunnels-including circular section,square section,passenger-dedicated railway tunnel section and horseshoe section tunnels-and shallow tunnels was analyzed.The research results are presented as follows: Firstly,the cross section shape of a tunnel has little influence on the water pressure exerted upon the lining and can be ignored.Secondly,the main factor determining the reduction factor of water pressure on linings is the relative permeability of the lining to the rock mass.Thirdly,for shallow tunnels with low water heads,the non-lining water inflow calculated using the axisymmetric solution has a large margin of error compared to the real value of water inflow,with a maximum error of 36.5%.It is,however,consistent with numerical solutions,and the maximum error is only 6.3% for the calculations of the lining water inflow and the water pressure exerted on the lining.