Numerical simulation of slurry fracturing during shield tunnelling

Highlights

• Numerical simulation for evaluating tunnelling-induced slurry fracturing.

• Numerical model considered the couplings of stress distribution, fluid flows, and fracturing.

• The fracture initiation, branching, and propagation are reproduced numerically.

Abstract

The slurry type shield method is an important tunnelling method, especially for underwater tunnels in soft soil. If the slurry pressure is too high, it may lead to slurry fracturing of the stratum in front of the excavation face and cause water inrush accidents. Controlling the face stability of shallow shield tunnels is difficult owing to the inadequate understanding of the slurry induced fracturing mechanism. Most importantly, understanding the details of the slurry fracturing propagation process is not enough, as the process is especially complicated. However, the propagation process cannot be directly observed in the field or in small-scale laboratory tests because it occurs in bodies of soil. Thus far, an effective approach to investigate the slurry fracturing mechanism in the surrounding stratum of a slurry shield tunnel has not been reported. In this paper, a numerical simulation method for evaluating tunnelling-induced slurry fracturing is presented. The developed numerical model considered the couplings of stress distribution, fluid flows, and fracturing. The fracture initiation, branching, and propagation in the stratum could be reproduced numerically. A series of simulations for different ratios of cover depth to tunnel diameter were carried out to investigate the propagation process of slurry fracturing. The effects of slurry pressure at the tunnelling face and the cover depth above the tunnel were investigated. The results of the fracturing process induced by slurry, such as the fracture propagation velocity, slurry pressure distribution along the fracture, fracture initiation pressure, fracture extending pressure, and stratum deformations, were analyzed.

Introduction

Shield tunnelling has many advantages, such as high degree of mechanization, fast driving, little disturbance on the surrounding environment, and a high degree of safety during construction. In comparison to other shield methods, the slurry pressure balance shield method has notable features. As the uniform transmission of the slurry pressure has high speed, high control accuracy of the earth pressure balance of the excavation face, small cutter head torque, minor tool wear, etc., slurry shield tunnelling is suitable to soft soil ground with a high moisture content, and especially suitable to cross-river tunnelling, subsea tunnelling, large diameter shield tunnelling, and tunnelling under strict ground deformation restrictions. Therefore, many large diameter underwater tunnels in soft soils have been constructed by the slurry shield method.

Injecting a relatively low viscosity fluid into soils can create fractures owing to the tensile or shear failure of the soil skeleton, which is known as hydraulic fracturing. The stability of the excavation face in slurry shield tunnelling is maintained by slurry pressure. When the shield machine is driven on the underwater, the stability control of the excavation face is difficult owing to the small cover depth and large water pressure. Hydraulic fracturing induced by a high slurry pressure is likely to occur in the excavation face and cause slurry eruption to the river or seabed, and thus result in bed collapse and water intrusion into the tunnel. This phenomenon is known as slurry fracturing. One of the most important considerations in order to ensure safety during tunnelling is to maintain an appropriate slurry pressure so as to ensure the stability of the excavation face.

Investigations on the slurry fracturing of the slurry shield began at Japan's Tokyo Bay subsea tunnel. Kurihara et al. (1988) investigated the possibility of slurry fracturing phenomena by shield model experiments and proposed an empirical formula of slurry fracturing. However, the slurry viscosity was not considered because the pressurized liquid used in these experiments was water. Additionally, the propagation of hydraulic fracturing was not investigated because the scale of the model was small. Therefore, it was difficult to evaluate the results of fracturing and propagation phenomena that occur in actual projects. Mori and Tamura (1990) investigated the fracturing phenomena of grouting at the shield tail through laboratory experiments and established a relationship between fracturing pressure and grout viscosity. Yuan (2002) completed a large number of triaxial experiments on slurry fracturing and shield model experiments in order to investigate the effects of slurry viscosity and the location of fracturing. However, the propagation process could not be observed directly because it occurred inside the soil body, and also because it was not possible to observe it with a small-scale laboratory test. Therefore, our understanding of the slurry induced fracturing mechanism is inadequate. Especially, the details of the slurry fracturing propagation process are almost absent. Thus far, there has been no effective way to investigate the slurry fracturing mechanism in a slurry shield tunnel. Owing to our inadequate understanding, controlling the face stability of shallow shield tunnels is difficult. Therefore, in this study, a numerical approach was adopted.

Slurry fracturing is a hydraulic fracturing phenomenon. Hydraulic fracture initiation has been researched extensively because fracturing is a liability in several engineering projects such as horizontal directional drilling and dam construction. On the other hand, fracture propagation and geometry has been largely ignored. Thus far, little is known about the physical appearance and mechanical behavior of hydraulic fracture in soil and about methods to analyze fracture propagation. However, only fracture propagation and its geometry should be investigated when studying slurry fracturing in shield tunnelling, as the purpose is to control and limit the opening of fractures in order to prevent the eruption of slurry to the ground surface.

The direct observation of the propagation processes of hydraulic fractures enveloped in soil layers is difficult both by field observation and by experiment, and the details of fracture growth inside the soil have generally been inferred from indirect measurements. During the past few years, with the rapid increase of computing power, numerical tools have become an attractive option for gaining insight into the fracturing process. The simulation of the hydraulic fracturing process is complicated, because it involves the coupling of four processes (Adachi et al., 2007, Kumar et al., 2017): (i) the mechanical deformation induced by fluid pressure on fracture surfaces, (ii) fluid flow within the fracture, (iii) fracture propagation, (iv) coupling of seepage and stress in the computational domain around the fracture. The simulation of hydraulic fracturing in the rock and soil mass is arguably one of the most challenging computational problems in geoengineering, and has been the subject of numerous investigations since the pioneering work of Khristianovic and Zheltov (1955). Many numerical methods have been developed for hydraulic fracturing simulation (Peirce and Siebrits, 2005, Lecampion and Detournay, 2007, Imoimo, 2012, Lei et al., 2017). Among them, the finite element method (FEM) is the most robust one, in comparison to boundary element method (BEM), discrete element method (DEM), and displacement discontinuity method (DDM), which cannot efficiently solve the elasticity-plasticity equation that relates fluid pressure to the fracture opening (Dusseault and McLennan, 2011).

Two approaches, namely, the discrete crack model and the smeared crack model have been used with the FEM, and have been proposed by Ngo and Scordelis (1967), and Rashid (1968), respectively. The discrete crack model aimed to simulate the initiation and propagation of dominant cracks. In contrast, the smeared crack model was based on the idea of many small cracks nucleating, and only linking up to form one or more dominant cracks at a later stage of the loading process.

In its original form, the discrete crack approach had several disadvantages (Borst et al., 2004). In this approach, the cracks were forced to propagate along the element boundaries; thereby, a mesh bias was introduced. Although, automatic remeshing with sophisticated computer code reduced the mesh bias, a computational difficulty consisting of the continuous change in topology was inherent in the discrete crack approach and was even aggravated by the remeshing procedures, up to a certain extent.

Given that each individual crack was not solved numerically, the smeared crack model captured the deterioration process through a constitutive relationship. Thus, it smeared out the cracks over the continuum and described a cracked solid by an equivalent anisotropic continuum with degraded material properties in a direction normal to the crack orientation and without requiring remeshing. Although the discrete crack approach is occasionally preferred because of its mature theoretical foundation, the analysis of smeared cracks seems to be more often applicable to common FEM analyses in engineering practice.

However, many assumptions and simplifications have been made in previous numerical studies, such as the requirement of placing fissures inside the analyzed domain prior to analysis (Wisser et al., 2005, Carrier and Granet, 2012). A numerical model for the coupled analysis of flow, stress, and fracturing was proposed in order to overcome the shortcoming of pre-setting the fractures (Yang et al., 2017). The proposed approach is similar to the smeared crack method. The simulated domain was discretized into large numbers of tiny elements in order to consider the small local variations of material properties. At each loading step, the stress and strain in the elements were calculated and examined against the predefined soil strength. The elements with stresses above the material’s strength were considered to be in fracture. The material properties of the fractured elements were reduced and the fracture width in the element could be calculated. This approach could effectively simulate hydraulic fracturing (Wang et al., 2009, Yang et al., 2017) in rocks, and has been extended to simulate hydraulic fracturing in soil (Chen et al., 2014).

This study investigated the macroscopic slurry fracturing of soil at tunnel engineering scale. Two-dimensional (2D) modeling was carried out and spatial discretization was performed by the FEM. However, the elements representing the soil were treated differently to those representing the fracture. The soil was assumed to follow the Biot equations for poromaterials. The elements containing the fracture were modelled with a pressure equation, where the fracture volume was considered by the fracture porosity.

The representation of both the soil and the fracture by the same regular grid simplified the numerical formulation and fully integrated the slurry flow in the fracture into the water flow in the soil. During fracturing, the slurry front will encounter an opposing pressure from water. Therefore, there will be two fluids present in the fracture channels or in soils, and it will be necessary to keep track of the slurry influx flow front. In this study, the volume of fluid (VOF) technique (Li, 2016) was used to keep track of the water-slurry interface.

In this paper, the Biot equations are introduced after the presentation of fracture discretization, fracture criterion, fluid pressure in fracture, and permeability of fractured elements. A simulation of slurry fracturing around the excavation face of the shield tunnelling was carried out, and the effect of slurry pressure at the tunnel face and the cover depths above the tunnel were investigated. The intention of these simulations was to provide a numerical simulation method of slurry fracturing in shield tunnelling.