Upper-bound solutions for face stability of circular tunnels in undrained clays

Abstract

The aim of this paper is to determine the critical supporting pressure on the circular face of an advancing tunnel in undrained clay in which undrained strength increases linearly with depth. Based on the kinematic approach of limit analysis, a continuous velocity field with a toric envelope is adopted to yield upper bounds of the face pressure for both collapse and blow-out. Combining with a closed-form expression describing the overall velocity field, an optimisation procedure is carried out to find the lowest upper-bound solutions. The calculated results are presented in terms of a dimensionless coefficient N (called the stability number) and then stability charts for use are produced. Alternatively, an approximation formula is given to estimate easily the collapse and blow-out pressure in practice.

Undrained Stability Analysis of Shallow Tunnel and Sinkhole in Soft Clay: The Cavity Contraction Method

“…It is shown that the theoretical results derived by Equation (18) agree well with numerical results when H/D ≤ 3 but underestimate the tunnel stability when H/D = 5. It means the tunnel may not collapse when the plastic zone expands to the ground surface because of the arching effect, and some errors may also be induced from the simplified definition of k, as shown in Equation (19).…”

“…, L/D ≥ 0.5 (19) and we chose this relationship mainly because there is only this equation available in the literature without losing simplification. Under the above assumptions, the 3D tunnel stability (L/D ≥ 0.5) can then be assessed by substituting Equation ( 19) into Equation (18).…”

“…Davis, et al [1] assessed the stability of shallow tunnels using the lower and upper bound theory under plane strain conditions. Afterwards, many attempts have been made to derive the upper bound (UB) solutions for 2D/3D tunnel stability, with various kinematically admissible velocity fields [11][12][13]16,18,19]. Sloan [20,21] developed the finite element limit analysis (FELA) method by linear programming, which made it possible to conduct geotechnical stability analysis without predefining a failure mode.…”

Progressive and asymmetric active and passive mechanisms of shallow tunnels under the effect of seismic forces

“…When a shallow tunnel is surrounded by weak rocks, insufficient supporting pressure or improper support will lead to collapse (active failure), while excessive supporting pressure will result in a blowout (passive failure) [1] . Current studies on the stability of shallow tunnels have made satisfactory progress, especially on the evaluation of the face stability [2][3][4][5] . Davis et al [3] evaluated the stability of shallow tunnels in a newly created failure mode by means of the upper and lower limit theorems of limit analysis.…”

Practical Approach to Predicting theK0Behavior of In Situ Sandy Gravel

“…e at-rest earth pressure coefficient K 0 is defined as the ratio of the effective horizontal stress versus vertical stress. It is a basic mechanic parameter of the soils in many practical engineering works such as slope [1] and tunnel [2] but is relatively difficult to determine. e mechanical properties of soil essentially depend upon the stress state, and therefore, accurate measurement of the initial stress state plays an important role in analyzing and designing the earthworks.…”