基于变分法原理的浅埋隧道围岩压力上限研究

浅埋段隧道上覆岩土厚度随埋深发生变化,且受地形条件影响,有必要考虑埋深对隧道支护结构设计的影响。为得到变化埋深条件下洞口浅埋段的围岩压力分布和影响长度,基于Hoek-Brown 破坏准则,采用极限分析上限理论,得到浅埋段隧道上方塌落体的构成曲线,并基于变分法原理获得浅埋段隧道极限支护力(反力为围岩压力)沿隧道轴向的变化规律曲线。通过分析,得到以下结论: 1)围岩压力随上覆土厚度增加而呈曲线增加; 2)依据围岩压力随距离(埋深)的变化关系可以得到浅埋段的有效影响范围,超过影响范围的围岩压力几乎不随埋深变化,可以视为深埋段; 3)围岩压力和浅埋段临界范围不仅与岩土材料参数有关,也受到隧道断面宽度和地表坡度的影响。

Study on Upper Limit of Surrounding Rock Pressure of Shallow Tunnel Based on Variational Principle

The influence of burial depth on the design of shallow tunnel is of great significance. In order to obtain the urrounding rock pressure distribution and influence length of shallow-buried section of tunnel portal under the condition of varying burial depths, the composition curve of the collapse body above the shallow buried section of tunnel is obtained based on Hoek Brown failure criterion and the upper limit theory of limit analysis, and the variation rule curves of the limit support force (the reaction force is surrounding rock pressure) along the axial direction of tunnel is obtained based on the variational principle. The analytical conclusions are drawn as follows: (1) The surrounding rock pressure increases in a curve with the increase of overburden thickness. (2) The effective influence range of the shallow-buried section can be obtained according to the relationship between the surrounding rock pressure and the distance (burial depth); and the surrounding rock pressure beyond the influence range hardly changes with the burial depth, which can be regarded as the deep-buried section. (3) The surrounding rock pressure and the critical range of the shallow-buried section are not only related to the geological conditions, but also related to the tunnel cross-section width and surface lope.