A three-dimensional analytical solution to the arching effect in inclined backfilled stopes

ABSTRACT

The stress state in backfilled mine stopes is an important issue to assess the behavior of the interaction between the backfill and the surroundings or barricades. Most previous arching analyses have considered only the vertical backfilled stopes in both 3D and 2D conditions, and the 3D stress distribution that results from the arching effect in inclined mine stopes remains unclear. In this paper, based on the limit equilibrium theory, a 3D stress solution that is applicable to vertical and inclined backfilled stopes is proposed to further examine the arching effect. The solution is validated against an available centrifuge model by changing the inclination of the model. The proposed analytical solution is consistent with the numerical simulations, and it is suggested that neglecting the wall inclination causes one to underestimate the arching phenomenon. In other words, the vertical stresses at the bottom of the stope can decrease when the wall inclination is considered. Hence, when the stope is assumed in plain strain conditions, both the vertical and horizontal stresses exerted on the barricades are overestimated.

KEYWORDS:

• Inclined backfilled stope
• arching effect
• limit equilibrium theory
• numerical simulation

Acknowledgments

This work is funded by the National Science Foundation of China (Grant Nos. 51222401, 51374049 and 51534003) and the Fundamental Research Funds for the Central Universities of China (Grant Nos. N140105001, N140104007 and N170106003). These supports are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notation

The following symbols are used in this paper:

B = Stope width (m);

c = Cohesion of the backfill (kPa);

c_i = Cohesion of the fill-wall interface (kPa);

dh = The height of the layer element (m);

F_ni = Normal forces acting on stope walls (kN);

g = The gravity acceleration of backfill (m/s²);

K = Backfill pressure coefficient for inclined backfill stope and defined as the ratio of transverse horizontal stress to vertical stress at the hanging wall;

k = The Rankine’s earth-pressure coefficient;

K_a = Active backfill pressure coefficient for inclined backfill stope;

k_a = Rankine’s active earth-pressure coefficient;

k_L = The ratio between longitudinal normal stress σ_hL and average vertical stress σ_av;

K_o = Backfill pressure coefficient at-rest condition for inclined backfill stope;

k_o = Rankine’s earth-pressure coefficient at rest;

K_p = Passive backfill pressure coefficient for inclined backfill stope;

k_p = Rankine’s passive earth-pressure coefficient;

k_T = The ratio of horizontal stress to vertical stress for vertical stope;

L = Stope longitudinal length (m);

q = Surcharge on the top surface of the backfill (kPa);

S_i = Shear forces acting along stope walls (kN);

V = Internal vertical force (kN);

W = Self-weight of the backfill (kN);

β = Wall inclination of backfilled stope to the horizontal plane (°);

γ = Unit weight of the backfill (kN/m³);

γ⁺ = Values obtained by multiplying the backfill density by the centrifuge acceleration (MN/m³);

δ_i = Internal friction angle of the fill-wall interface (°);

δ = Friction angle of the backfill (°);

σ_av = Average vertical stress of the stope cross section at position h, (kPa);

σ_hL = Longitudinal horizontal stress (kPa);

σ_hT = Transversal horizontal stress (kPa);

σ_ni = Normal stress on stope walls (kPa);

τ_i, τ_j = Shear stresses acting along stope walls (kPa); and

φ = Internal friction of backfill (°).

Additional information

Funding

This work was supported by the the National Science Foundation of China [51525402, 51874069, 51534003]; Fundamental Research Funds for the Central Universities of China [, N170108028, N170106003].