In order to better interpret failure features of the failure of soil in front of tunnel face, a new threedimensional failure mechanism is proposed to analyze the limit support pressure of the tunnel face in multilayered cohesivefrictional 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.
Nowadays, tunnel constructions in urban shallow soft ground are more frequently being carried out using closed shields, which are basically divided into compressedair shields, slurry shields, and earth pressure balanced shields. By supporting the excavation face and preventing the seepage flow to the face, closed shields control the surface settlement and limit the risk of tunnel face failure through the continuous support of the face during excavation. However, lack of sufficient face support leads to the instability of tunnel face. In extreme cases, the collapse propagates up to the ground surface creating a surface depression. Researchers have developed experimental, numerical, and analytical approaches to investigate the tunnel face stability and to determine the limit support pressure of the tunnel face in cohesivefrictional soils.
The stability of tunnel face in cohesivefrictional soils has been analyzed by using experimental tests (laboratory centrifuge tests [
From the results obtained from experimental tests and numerical simulations, it is shown that the failure of soil in front of tunnel face shows two main features, that is, shear failure band in the lower part and pressure arch effect in the upper part. Referring to the remarks claimed by Sloan [
Based on the limit analysis methods, Zhang et al. [
The tunnel face stability to be analyzed in this paper is idealized as shown in Figure
The improved failure mechanism.
Referring to the concept proposed by Zhang et al. [
The intersections of two truncated cones, tunnel face, and horizontal plane crossing the top of the tunnel face are two ellipses and a circle and are called
The area of the contact elliptical surface
The intersection of the second truncated cone with the horizontal plane across the top of the tunnel face is a circle
In addition, the lateral surfaces and volumes of the two truncated cones are as follows:
For cohesivefrictional soils, the results obtained from experimental tests and numerical simulations show that the failure of soil in front of tunnel face demonstrates two main features, that is, shear failure band in the lower part and pressure arch effect in the upper part. The existing researches [
Distributed force calculated by Terzaghi earth pressure theory.
Assuming that the cover layer above the tunnel is homogeneous and the soil in cover layer satisfies the MohrCoulomb failure criteria, the vertical equilibrium of a microthin layer
Equation (
Since the ground above the tunnel is heterogeneous and consists of
Then the final result of vertical stress distribution acting on the two truncated cones is obtained as follows:
The two truncated rigid cones are translated with velocities with different directions, which are collinear with the cones’ axes and are at an angle
To satisfy the stability conditions of the tunnel face according to the upper bound theorem, the following relation is considered:
By equating the total rate of external work to the total rate of internal energy dissipation, as shown in (
In (
To validate the results obtained from the limit analysis developed in this paper, comparisons between the results of this work and existing approaches (Broere [
Three sets of analyses were carried out by referring to the researches recently reported by Tang et al. [
Soil parameters of layers.
Sets’ number  Layers’ name  Layers’ number 





1  Single crossed layer  Variable  (0) 






Single cover layer  Constant  (1) 






2  Single crossed layer  Constant  (0) 



Single cover layer  Variable  (1) 









3  Single crossed layer  Constant  (0) 



Two cover layers  Variable  (1) 




(2) 



The first set of analyses described the cases of a single cover layer with constant strength parameters (
Influence of
Influence of
In Figure
Figure
The second set of analyses presented a reverse situation, which described the cases of a single cover layer with different strength parameters (
Influence of
Influence of
Figure
In Figure
Since this section was a reverse situation with the last section, it is necessary to compare Figures
The third set of analyses described the cases of two cover layers with constant strength parameters (
Influence of
In order to better interpret the failure features, a new threedimensional failure mechanism is proposed to analyze the limit support pressure of the tunnel face in multilayered cohesivefrictional soils based on limit analysis methods. 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. The distributed force could be calculated by using Terzaghi earth pressure theory. Moreover, the comparisons between the results of the present study and those of existing approaches were provided. The main conclusions are presented as follows.
(1) Results show that influence rules obtained from different models are similar. More importantly, our mechanism provides limit pressures that are almost equal to the results form Senent and Jimenez [
(2) For the strength parameters variations of soil in the crossed soil or in the cover soil, the results show that
(3) No matter strength parameters variations of soil in the crossed soil or in the cover soil, it has also been found that the friction angle affected the support pressure effectively compared to the cohesion.
(4) The results indicated that strength parameters’ variation in crossed layer plays bigger role in limit support pressures than in cover layers with the same variable range of strength parameters.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors acknowledge the financial support provided by the Fundamental Research Funds for the Central Universities of China (Grant no. 2015YJS128).