Modeling Hydraulic Fracturing and Blow-Out Failure of Tunnel Face During Shield Tunneling in Soft Soils

Acknowledgments

Notation

a

radius of the cylindrical cavity (m);

c

cohesion of soils (kPa);

D

diameter of the shield machine (m);

d

thickness or diameter of fractures (m);

g

stagnation gradient of slurry (kP/m);

K₀

coefficient of earth pressure;

L

fracture length at the current time (m);

L_s

final length of fractures (m);

P

slurry pressure in the excavation chamber (kPa);

P₀

slurry pressure at the tunnel face (kPa);

P_w

water pressure at the fracture tip (kPa);

p

radial stress acts along the inner wall of the cavity (kPa);

p_c

fracture initiation pressure (kPa);

p_t

fracturing pressure determined by the tensile failure mode (kPa);

p_s

fracturing pressure determined by the shear failure mode (kPa);

q

flow volume of slurry per unit time (m³/s);

r

radial coordinates in the cylindrical coordinate system (m);

V

flow velocity of slurry (m/s);

W

width of slurry-induced fractures (m);

α

empirical coefficient of fracture shape;

γ_m

specific weight of slurry (kN/m³);

μ

dynamic viscosity of slurry (cp);

φ

friction angle of soils (°);

θ

angle between the fracture and horizontal direction (°);

σ₁

maximum principal stress (kPa);

σ₃

minimum principal stress (kPa);

σ_r

radial stress in the cylindrical coordinate system (kPa);

σ_t

tensile strength of soils (kPa);

${\sigma }_{\theta }$

circumferential stress in the cylindrical coordinate system (kPa);

τ_rθ

shear stress in the cylindrical coordinate system (kPa); and

τ

yield stress of slurry (kPa).

References