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The phenomena of progressive failures are very common and important in geotechnical engineering. In this paper, a reliable prediction model is proposed to interpret the progressive failure phenomenon of roof collapse in deep tunnels using the functional catastrophe theory. The progressive collapse mechanisms and collapsing block shapes of deep circular tunnels under conditions of plane strain are investigated. The analytical solutions for the shape curves of the collapsing blocks of circular tunnels are derived based on the nonlinear power-law failure criterion considering variable dilatancy angle and detaching velocity. Moreover, criterions with variable dilatancy angle on progressive failure occurrence for deep tunnels are obtained. Then, the analytical predictions obtained in this paper are compared with experimental testing results, which indicate that the impacts of variable detaching velocity on the shape curves of the several continuous collapsing blocks should be considered to obtain more consistent prediction results with the corresponding experimental testing results. [ABSTRACT FROM AUTHOR]

In order to better interpret failure features of the failure of soil in front of tunnel face, a new three-dimensional failure mechanism is proposed to analyze the limit support pressure of the tunnel face in multilayered cohesive-frictional soils. The new failure mechanism is composed of two truncated cones that represent the shear failure band and a distributed force acting on the truncated cones that represents the pressure arch effect. By introducing the concept of Terzaghi earth pressure theory, approximation of limit support pressures is calculated using the limit analysis methods. Then the limit support pressures obtained from the new failure mechanism and the existing approaches are compared, which show that the results obtained from the new mechanism in this paper provide relatively satisfactory results. [ABSTRACT FROM AUTHOR]

This paper investigates the collapse mechanisms and possible collapsing block shapes of shallow unlined tunnels under conditions of plane strain. The analysis is performed following the framework from a branch of catastrophe theory, functional catastrophe theory. First, the basic principles of functional catastrophe theory are introduced. Then, an analytical solution for the shape curve of the collapsing block of a shallow unlined tunnel is derived using functional catastrophe theory based on the nonlinear Hoek-Brown failure criterion. The effects of the rock mass parameters of the proposed method on the shape and weight of the collapsing block are examined. Moreover, a critical cover depth expression to classify deep and shallow tunnels is proposed. The analytical results are consistent with those obtained by numerical simulation using the particle flow code, demonstrating the validity of the proposed analytical method. The obtained formulas can be used to predict the height and width of the collapsing block of a shallow unlined tunnel and to provide a direct estimate of the overburden on the tunnel lining. The obtained formulas can be easily used by tunnel engineers and researchers due to their simplicity. [ABSTRACT FROM AUTHOR]

• Investigates the progressive failure phenomenon of the shallow tunnel roof by virtue of the functional catastrophe theory. • The failure mechanism proposed can not only predict the 'underground' collapse but also the 'spalling' collapse. • The comparisons of the results between analytical predictions are validated. Collapse mechanism for the tunnel or underground cavern is important for the support system design. This paper investigates the progressive failure phenomenon of the shallow tunnel roof under the condition of plane strain by virtue of the functional catastrophe theory. Firstly, considering the plastic strain energy as an index for the state of the studied system, the analytical solutions for the profile curves of the collapsing blocks from the shallow tunnel roof including the 'underground' collapse and 'spalling' collapse are deduced on the basis of the nonlinear power-law failure criterion. Moreover, the criterions are derived to estimate whether the progressive failure phenomena including the 'underground' collapses and 'spalling' collapses for shallow tunnel roof would occurr or not. Then, the analytical prediction obtained from this paper for the shallow tunnels is compared with the existing analytical prediction for the deep tunnels. Finally, the comparisons of the results between analytical prediction obtained from this paper and two existing model tests are conducted to demonstrate the validity of the proposed analytical methodology. [ABSTRACT FROM AUTHOR]