Slurry Support Mechanism for Shield Tunneling Considering Slurry Infiltration and Cutter-Disk Cutting Effect

Data Availability Statement

Acknowledgments

Notation

A

cross-sectional area of the elementary volume;

a

empirical coefficient obtained from the test;

C

slurry concentration;

C_r

stagnation rate of slurry particles within the elementary volume, i.e., the volume of slurry particles stagnated in a unit slurry volume;

C_s

volume fraction of slurry particles in the slurry suspension inside the elementary volume of porous media;

C_w

slurry suspension volume fraction inside the elementary volume;

C₀

initial slurry particles volume fraction;

dx

elementary thickness;

d₁₀

effective particle size of soil mass;

F_i,j

triangular surface element;

f_sg

slurry stagnation gradient;

g

gravity acceleration;

k

soil permeability coefficient;

k_G

slurry pressure gradient coefficient;

k_w

soil permeability coefficient to water;

L

length of the soil skeleton;

L_f

slip failure zone width;

l

slurry infiltration distance;

l_max

maximum penetration distance of the slurry;

M_sr

stagnated slurry particles mass in soil pores;

M_su

stagnated slurry particles mass in suspension state in the soil;

M_w

mass of the slurry carrier fluid flowing in from the left boundary of the elementary volume;

M_s

slurry particle mass flowing in from the left side of the elementary volume;

$M_s^{\mathrm{\prime }}$

slurry particle mass flowing out from the right side of the elementary volume;

$M_w^{\mathrm{\prime }}$

mass of the slurry carrier fluid flowing in from the right boundary of the elementary volume;

M_wp

water mass change due to the pore-water pressure change within the elementary volume;

M_wr

water mass change in the elementary volume of porous media;

ΔM_s

mass difference between the inflow and outflow of bentonite slurry particles;

ΔM_w

mass difference between the inflow and outflow of the slurry carrier fluid on both sides of the elementary volume;

$N_{\gamma }$

dimensionless parameter reflecting the soil gravity;

N_c

dimensionless parameter reflecting the soil cohesion;

n

soil porosity in the infiltration zone;

n₀

initial soil porosity before the slurry infiltration;

p

pore-water pressure within the elementary volume;

p_A

constant slurry overpressure;

p_x

seepage force;

p₀

original pore-water pressure in the layers;

Δp

slurry pressure difference between the slurry chamber and the layers;

R_i,j

pole diameter corresponding to the triangular surface element F_i,j at the center of gravity on the slip surface (Fig. 14);

S

cutter's penetration degree;

t_cut

time interval of cutter cycle cutting;

t_f

specific time;

t_fil

time used for slurry film formation and development;

t_pen

time used for deep penetration in each cutting time interval t_cut;

v

slurry macroscopic penetration velocity inside the elementary volume;

v_cr

critical tunneling speed;

v_f

corresponding slurry penetration speed;

W_D

internal dissipation work of the slip system;

W_P

power generated by the slurry seepage force generated by the pore-water pressure gradient applied to the slip damage zone in front of the tunnel working face;

$W_{\gamma }$

gravity power of the slip system in the slip region below the water table when considering groundwater action;

Wσ_vH

equivalent load power of the possible additional load on the ground surface;

α

compression coefficient of the soil skeleton;

β

compression coefficient of the water;

β_i,j

angle between the motion velocity of the slip system and the horizontal direction;

γ_w

unit weight of water;

γ′

soil buoyant unit weight;

ɛ_i,j

angle between the velocity and the vertical direction;

λ

filtration coefficient of the stratum;

μ

dynamic viscosity coefficient of slurry;

μ_s

water storage coefficient of the porous medium;

μ_w

dynamic viscosity coefficient of water;

ρ_w

slurry carrier fluid (water) density;

σ_A

limit slurry support pressure;

σ_E

equivalent load that integrates the surface additional load and soil arch effect;

τ_s

slurry static yield strength; and

ω

rotational angular velocity of the slip system.

References