山体斜坡附近有压隧洞最小覆盖厚度的解析解

Analytical Solution to Minimum Overburden of Pressure Tunnel under Mountain Slope

以重力作用下三角形山体的初始应力场解析解为基础,求出初始应力场的最小主应力值表达式,再根据有压隧洞的内水压力应小于拟开挖隧洞处的初始应力场最小主应力准则,给出了确定山体斜坡附近有压水工隧洞的位置、最小覆盖厚度及最小坡高的解析表达式。计算结果表明:一般情形下,最小覆盖厚度不但取决于山体的坡角,而且与隧洞所处的坡高有关;只有当山体的2个坡角相等且为45°或山体的2个坡面相互垂直时,隧洞的最小覆盖厚度才与坡高无关。山体的2个坡角都为45°时,隧洞的最小覆盖厚度是水头高度的0.5656倍,这与修正的挪威准则给出的结果相同。

The expression of minimum principal stress in triangular mountain under gravity is given by using the analytical solution based on the initial stress in a mountain body. Then, on the basis of the criterion that the internal water pressure should be less than the initial minimum principal stress in a pressure tunnel, the analytical expressions for calculating the minimum slope height, minimum overburden and suitable location of the pressure tunnel are proposed. In general cases, the correspondingly calculated results show that the minimum overburden depends on not only the slope angle but also the slope height. The minimum overburden of the tunnel is independent of the slope height only in the following two cases： one is that both slope angles are equal, the other is that the two slopes are perpendicular to each other. In the first case, the minimum overburden equals 0. 565 6 times of water head of the tunnel, which is consistent with the modified Norway rule.