Research Article: Prediction of roof supporting pressure for shallow tunnels in layered soils incorporating the effect of pore water pressure

Date Published: June 13, 2019

Publisher: Public Library of Science

Author(s): Hong-tao Wang, Xiao-jing Li, Ping Liu, Xin Zhang, Lu-yao Liu, Hongbo Zhao.


In this study, we propose a method for predicting the supporting pressure required for shallow tunnels in layered soils, based on a curved roof collapse mechanism with multi-failure surfaces. In this method, the effect of the number and thickness of soil layers, pore water pressure, arbitrary roof profile, and ground additional load is considered simultaneously. A nonlinear power-law failure criterion is employed to describe the failure characteristics of the roof soils. The internal energy dissipation rate and the work rates produced by external forces are obtained based on the associated flow rule and plasticity potential theory. The analytical expressions of the required supporting pressure and roof collapse surfaces are obtained with the upper bound method. Furtherly, a shallow rectangular tunnel in two soil layers is selected for parametric investigation. The change laws of the required supporting pressure and collapse curves under varying parameters are obtained. Furthermore, the corresponding engineering recommendations are given, which may potentially provide references for the support design and construction of shallow tunnels in layered strata.

Partial Text

The tunnel, as an underground building, can not only effectively alleviate problems like road traffic congestion and land resource shortage, but also can bring enormous convenience to people’s travel and transportation. At present, with the rapid development of the world economy and technology, various types of tunnels are increasingly scaled up in engineering fields including transportation, water conservancy and hydropower, urban subway, and underground mining. The tunnels may be built in the rocks or soils based on the stratum geological conditions. For the tunnels in the soils, due to generally low strength of the soil masses, intense deformation and failure may occur in the surrounding rock after tunnel excavation. In particular, if the tunnels are buried in shallow soils or affected by adverse conditions such as groundwater seepage and ground additional loading, it is very easy to cause land subsidence and even a landslide, seriously threatening the safety of the lives and property of people.

Mohr-Coulomb failure criterion has been widely applied in geotechnical engineering due to its simplicity and effectiveness. In the expression of this criterion, the normal stress (σn) and shear stress (τn) at the failure surface are in linear relation in the Mohr plane σn-τn. However, previous studies [23–28] revealed that the soils present obvious nonlinear failure characteristics and the corresponding strength envelopes are approximately a convex curve. Based on this fact, the nonlinear failure criterion may be more suitable in analyzing the stability problems involving the deformation and failure of soils in engineering. Hence, we utilize a nonlinear power-law failure criterion [22, 25–26] to describe the failure characteristics of roof surrounding soil masses in this paper. The corresponding expression can be written as:
where c0 and σt are the initial cohesion and tensile strength of the soil mass respectively, m is the dimensionless nonlinear coefficient (related to the properties of the soil masses) and m≥1. Fig 1 shows the strength envelope curve. Particularly, σt and c0 are the intercepts of the curve with the x-axis and y-axis, the magnitude of m indicates the curvature of the envelope.




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