A New Analytical Model for Trapdoor Tests Considering Effect of Incomplete Soil Arching and Principal Stress Deflection

Data Availability Statement

Acknowledgments

Notation

B

width of trapdoor;

c

cohesion;

F_i

horizontal thrust acting on the ith structural arch foot in phase II;

F_Pi

horizontal thrust acting on the ith structural arch foot in phase III;

f

arch height of structural arch;

f_ia

average arch height of the ith structural arch in phase II;

$f_{ia}^{\mathrm{\prime }}$

average arch height of the ith structural arch in phase I;

f_Pia

average arch height of the ith structural arch in phase III;

H

cover depth of the trapdoor;

H₁

height of unloading area;

H₂

height of parabola at top of failure zone in phase II and III;

$H_2^{\mathrm{\prime }}$

height of parabola at top of failure zone in phase I;

H₃

height of shear band;

K₀

coefficient of static earth pressure;

K_A

lateral pressure coefficient at point A;

K_a

coefficient of active earth pressure;

K_ia

average lateral pressure coefficient of the ith structural arch in phase II;

$K_{ia}^{\mathrm{\prime }}$

average lateral pressure coefficient of the ith structural arch in phase I;

K_L

lateral pressure coefficient on shear band;

$K_L^{\mathrm{\prime }}$

lateral pressure coefficient at the bottom of the unloading zone in phase I;

K_P0

lateral pressure coefficient of the ground surface in phase III;

K_Pia

average lateral pressure coefficient of the ith structural arch in phase III;

K_s

lateral pressure coefficient at the boundaries on both sides of different zones;

L_i

length of the ith structural arch foot in phase II;

$L_i^{\mathrm{\prime }}$

length of the ith structural arch foot in phase I;

L_Pi

length of the ith structural arch foot in phase III;

m

distribution factor of vertical earth pressure;

q

surcharge on the ground surface;

q_i

load acting on the (i + 1)th structural arch in phase II;

$q_i^{\mathrm{\prime }}$

load acting on the (i + 1)th structural arch in phase I;

q_(i−1)

load acting on the ith structural arch in phase II;

$q_{(i-1)}^{\mathrm{\prime }}$

load acting on the ith structural arch in phase I;

q_iG

self-weight stress of the ith structural arch in phase II;

$q_{iG}^{\mathrm{\prime }}$

self-weight stress of the ith structural arch in phase I;

q_n

load acting on the top of the failure zone in phase II;

$q_n^{\mathrm{\prime }}$

load acting on the top of the failure zone in phase I;

q_P(i−1)

load acting on the ith structural arch in phase III;

q_Pi

load acting on the (i + 1)th structural arch in phase III;

q_PiG

self-weight stress of the ith structural arch in phase III;

q_Pn

load acting on the top of the failure zone in phase III;

q_S

load acting on the self-weight zone;

q_U

load acting on the top of the failure zone;

V

volume of failure zone;

V₁

volume of parabolic-shape in phase II and III;

$V_1^{\mathrm{\prime }}$

volume of parabolic-shape in phase I;

V₂

volume of rectangle;

V_T

volume of space formed by trapdoor displacement;

W_F

self-weight of soil inside the parabolic-shape in phase II and III;

$W_F^{\mathrm{\prime }}$

self-weight of soil inside the parabolic-shape in phase I;

W_s

self-weight of self-weight zone;

α

soil volume bulking factor;

β

angle between horizontal plane and fracture surface at the top of failure zone, it can be taken as θ₀ in phase II and III;

γ

unit weight of soil;

γ_e

unit weight of failure zone in phase II and III;

${\gamma }_e^{\mathrm{\prime }}$

unit weight of failure zone in phase I;

δ

normalized displacement of trapdoor;

η

displacement of trapdoor;

θ

angle between the direction of the maximum principal stress and the horizontal plane;

θ₀

principal stress deflection angle on shear band or the angle between horizontal plane and fracture surface at the top of failure zone in phase II and III;

θ_ia

average principal stress deflection angle of the ith structural arch in phase II;

${\theta }_{ia}^{\mathrm{\prime }}$

average principal stress deflection angle of the ith structural arch in phase I;

θ_P0

principal stress deflection angle of the ground surface in phase III;

θ_Pia

average principal stress deflection angle of the ith structural arch in phase III;

ρ

normalized pressure acting on the trapdoor;

σ₁

maximum principal stress of the element in the arch;

σ₃

minimum principal stress of the element in the arch;

σ_av

average vertical stress;

σ_h

horizontal stress;

σ_Tv

average vertical stress acting on the trapdoor;

σ_v

vertical stress;

σ_vA

vertical stress at point A;

τ

shear stress on shear band;

φ

internal friction angle; and

ω

principal stress deflection angle at the boundaries on both sides of different zones.

References