Experimental and analytical study of shield tunnel face in dense sand strata considering different longitudinal inclination

Highlights

• A new 1-g experimental equipment in evaluating tunnel face stability was designed.

• Tunnel face failure mode induced by longitudinal inclination angle was investigated.

• A series of novel theoretical models were proposed.

Abstract

Predicting the face support pressure and understanding the failure mode for shield tunnel with different longitudinal inclination, δ, in dense sand strata are crucial. Six laboratory model tests are conducted to explore the failure mechanism of tunnel face with δ = 15°, 0°, and −15°. It shows that the face support pressure declines sharply to the elastic limit value, and further decrease slowly to the minimum value for all δ conditions. When δ = 15° or 0°, the face support pressure rebounds slightly to a residual value. However, rebound is not prominent for δ = −15°. The influence of “soil arch” strength reduces when δ varies from −15°, 0°, to 15°. The final shape of the failure zone shows a “chimney” pattern, in which the area of the failure zone increases with δ. Similar failure patterns are obtained from the numerical simulations. Based on the measured contours of failure zones, novel theoretical models are proposed to calculate the limit face support pressure for three inclination conditions. The face support pressure, p_u, is predicted to be the highest for δ > 0°, following by the cases of δ = 0° and δ < 0°, and the change in p_u is higher between δ > 0° and δ = 0°.

Introduction

Subways are increasingly constructed in all big cities in China (Han et al., 2018, Jia et al., 2019, Jia et al., 2020, Zhao et al., 2019). Due to the complicated working conditions, shield driven tunneling is widely adopted in congested urban areas. Determining an appropriate range of face support pressure is vital to maintain the stability of shield face during tunneling in dense sand strata. In practice, a shield machine seldom drives through a completely horizontal plane; instead, the driven route often inclines in the longitudinal direction due to design optimization. Therefore, the failure mechanism near the tunnel face differs significantly due to the use of different longitudinal inclination angle, especially when a large angle is employed. It is necessary to investigate this problem and select appropriate methods to predict the face support pressure.

Previous researchers have paid sufficient attention to the investigation of failure mechanism near the tunnel face. Related studies can be mainly divided into three types: theoretical derivation, laboratory test, and numerical simulation. In terms of theoretical analyses, various models were established based on different hypotheses, which can be used to predict the required face support pressure. Two methods were used primarily, i.e., limit analysis method and limit equilibrium method. For limit analysis method, the upper bound solution was widely adopted to calculate the active limit face support pressure, such as the single-block model (Leca and Dormieux, 1990), the multi-blocks model (Ding et al., 2019, Huang et al., 2018, Soubra et al., 2008, Tang et al., 2014, Wan et al., 2019, Zhang et al., 2015, Zhao et al., 2017), and the rotational failure model (Dias et al., 2011, Mollon et al., 2011a, Mollon et al., 2011b, Pan and Dias, 2017, Zou et al., 2019). For limit equilibrium method, the silo-wedge model was modified by many scholars (Anagnostou, 2012, Anagnostou and Kovári, 1996, Broere, 2015, Chen et al., 2015, Chen et al., 2019a, Chen et al., 2019b, Hu et al., 2012, Ji et al., 2018). For example, Liu et al. (2019) proposed the dual-failure-mechanism model based on the principle of Murayama’s formula (Murayama et al., 1966). Furthermore, the relationship between displacement and lateral earth pressure was investigated, and a new analytical model was proposed (Ni et al., 2018a, Ni et al., 2018b). Chen et al., 2019a, Chen et al., 2019b explored the failure behavior of sandy soil by the Coupled Eulerian-Lagrangian method (CEL).

Numerical simulation is a good platform that can be adopted to investigate the failure mechanism of shield tunnel face efficiently. Finite element method (Vermeer et al., 2002, Zhang et al., 2017), finite difference method (Li et al., 2009, Senent and Jimenez, 2015, Zhang et al., 2015), and discrete element method (Chen et al., 2011, Zhang et al., 2011) were utilized extensively to discuss the tunnel face stability under different working conditions.

Laboratory model tests could directly show the evolution of failure zone in front of tunnel face. Two types of model tests were adopted in relevant investigations, in terms of centrifuge model tests (Chambon and Corté, 1994, Dziuban et al., 2018, Idinger et al., 2011) and 1-g model tests (Berthoz et al., 2012, Chen et al., 2013, Kirsch, 2010, Liu et al., 2018, Sun et al., 2018). Due to the high requirements of equipment, centrifuge model testing facility was only available in limited institutes. Kirsch (2010) systematically investigated the tunnel face stability by 1-g small scale tests, in which the failure mechanism near the tunnel face was observed through digital image correlation DIC technique, being similar to that obtained by centrifuge model tests. Chen et al. (2013) performed 1-g large scale tests to explore the evolution of “soil arch” in front of tunnel face in dry sand. Similarly, Liu et al. (2018) further discussed the effect of support plate’s backward velocity on the failure zone in dense sand. Lü et al. (2018) investigated the seepage effect on the evolution of failure zone in sand strata. Weng et al. (2020) conducted a series of centrifuge model tests to investigate the same problems by considering the effect of longitudinal inclination angle and steady-state seepage in soft clay. Ahmed and Iskander (2012) used transparent soil to track the failure process near the tunnel face.

In different studies with various analysis approaches, the research focus was mainly on the failure mechanism in front of tunnel face for a horizontally driving tunnel. Nevertheless, the shield machine often works with different longitudinal inclination angle in practice. The influence of longitudinal inclination angle of shield machine was rarely considered, especially in dense sand. This is because the longitudinal inclination angle was often considered to be small enough (i.e., the maximum value can generally be controlled at about 10°), such that ignoring its impact on the calculation of face support pressure could not lead to significant erroneous results. In addition, simplifying the analysis process with a horizontally driving tunnel is easy to derive analytical solutions, and the lack of related experimental data hinders the evaluation of complex derivations. Numerous existing research investigations on the mobilization of earth pressure in front of shield tunnel have limitations to analyze the behavior of inclined tunnel.

Understanding the characteristics of tunnel face failure patterns with different longitudinal inclination angle can help researchers to explore more appropriate methods in the decision of support parameters. Some researcher found that the influence of longitudinal inclination angle on the face stability of shield tunnel cannot be neglected. Zhao et al. (2017) derived the active and passive failure pressures during tunneling using the upper-bound limit analysis method, in which the effects of tunnel inclination angle and tunneling length were taken into account. It was found that the tunnel inclination angle had a significant effect on the calculated results for both the active and passive failures. From the model tests of Weng et al. (2020), it was obtained that the active limit support pressures in front of tunnel face exhibited a significant linear increasing pattern with the longitudinal slope angle.

In this paper, a new experimental equipment is designed, through which a series of 1-g model tests is conducted to investigate the failure mechanism of tunnel face under different longitudinal inclination angle in dense sand. Based on the results of model tests and numerical simulations, three new models for predicting the face support pressure are proposed and compared.