Determination of Stabilizing Forces Acting on Piles to Reinforce Slurry Trench against Globe Collapse

Acknowledgments

Notation

D_s

slurry height from the top of the trench;

D_w

groundwater depth from the top of the trench;

$\dot{D}$

rate of work dissipation;

F_p

stabilizing forces acting on the piles;

F_s

safety factor of the trench;

H

final excavation depth of trench;

H_r

H/r₀;

H_s

slurry height from the bottom of the trench;

H_w

groundwater height from the bottom of the trench;

h_p

height of the stabilizing forces provided by piles and h_p = H in this paper;

L_r

L/r₀;

m

height of the resultant of stabilizing forces as a percentage of the length of the reinforcing piles above the sliding surface;

q

surcharge applying on the top of the ground surface;

r_s

γ_s/γ;

r₀, r_h, r

circular radius corresponding to different rotational angles θ in Fig. 1;

S_u

undrained shear strength of soil;

S_u0

undrained shear strength at the ground surface;

W_p

work rate supplied by the reinforcing piles;

W_q

work rate applied by ground surface surcharge;

W_r

external work rate of soil weight (region BECB in Fig. 1);

W_s

external work rate of slurry pressure;

X

x/H;

x

length of BE in Fig. 1;

Y

y/H;

y

excavation depth of the trench;

z

depth below the ground surface;

γ

unit weight of soil;

γ_s

unit weight of slurry;

θ₀, θ_h, θ_s, θ_p

angle in the polar coordinate in Fig. 1.

λ

ratio of the distance between the location of the surcharge and the edge of the trench to the excavation depth H;

ρ

undrained shear strength gradient that the shear strength of ground surface increases linearly with depth; and

ω

rotational angular velocity.

References