An improved analytical solution to estimate the stress state in subvertical backfilled stopes

2008 ◽  
Vol 45 (10) ◽  
pp. 1487-1496 ◽  
Author(s):  
Li Li ◽  
Michel Aubertin
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Surrounding Rock ◽  
Underground Mines ◽  
Good Representation ◽  
Normal Stresses ◽  
Numerical Investigations ◽  
Backfilled Stopes ◽  
Buried Conduits ◽  
Opening Width

The increasing use of backfill in underground mines requires a better understanding of the interaction between the relatively soft fill material and the surrounding rock mass. In recent years, it has been shown that stresses in backfilled stopes can be estimated using an approach based on Marston’s arching formulation developed initially for buried conduits in trenches. However, despite its advantages, this approach has some shortcomings. For instance, it postulates that both the vertical and horizontal normal stresses are uniformly distributed across the opening width. Numerical investigations conducted by the authors have shown that this assumption is not always valid. This paper presents a modification to the Marston-based solution, which leads to a nonuniform vertical stress distribution across the opening. This modification of the analytical solution involves parameters that have been calibrated against some numerical modelling results. The same equations and parameters are then shown to provide a good representation of additional modelling cases for which the stress state is correctly predicted.

scholarly journals Узагальнення моделі Голанда і Рейсснера на випадок осьової симетрії

2021 ◽  
pp. 12-19
Author(s):  
Костянтин Петрович Барахов
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Bessel Functions ◽  
Classical Model ◽  
Adhesive Bond ◽  
Radial Coordinate ◽  
Round Hole ◽  
Normal Stresses

The purpose of this work is to create a mathematical model of the stress state of overlapped circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. To solve the problem, a simplified model of the adhesive bond of two overlapped plates is proposed. The simplification is that the movement of the layers depends only on the radial coordinate and does not depend on the angular one. The model is a generalization of the classical model of the connection of Holland and Reissner in the case of axial symmetry. The stresses are considered to be evenly distributed over the thickness of the layers, and the adhesive layer works only on the shift. These simplifications allowed us to obtain an analytical solution to the studied problem. The problem of the stress state of the adhesive bond of two plates is solved, one of which is weakened by a round hole, and the other is a round plate concentric with the hole. A load is applied to the plate weakened by a round hole. The discussed area is divided into three parts: the area of bonding, as well as areas inside and outside the bonding. In the field of bonding, the problem is reduced to third- and fourth-order differential equations concerning tangent and normal stresses, respectively, the solutions of which are constructed as linear combinations of Bessel functions of the first and second genera and modified Bessel functions of the first and second genera. Using the found tangential and normal stresses, we obtain linear inhomogeneous Euler differential equations concerning longitudinal and transverse displacements. The solution of the obtained equations is also constructed using Bessel functions. Outside the area of bonding, displacements are described by the equations of bending of round plates in the absence of shear forces. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations concerning the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

scholarly journals Total and Effective Stresses in Backfilled Stopes during the Fill Placement on a Pervious Base for Barricade Design

Minerals ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 38 ◽  
Author(s):  
Jian Zheng ◽  
Li Li ◽  
Yuchao Li
Keyword(s):  
Analytical Solution ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
The Self ◽  
Underground Mines ◽  
Filling Rate ◽  
Effective Stresses ◽  
Arching Effect ◽  
The Stability ◽  
Backfilled Stopes

Backfill is increasingly used in underground mines worldwide. Its successful application depends on the stability of the barricades built at the base of the stopes to hold the backfill in place, which in turn depends on the knowledge of the pore water pressure (PWP) and stresses during, or shortly after, the placement of the slurried backfill. Until now, self-weight consolidation is usually considered for the estimation of the PWP. There is no solution available to evaluate the total and effective stresses during, and shortly after, the filling operation. As excess PWP can simultaneously be generated (increased) and dissipated (decreased) during the backfilling operation, effective stresses can develop when the filling rate is low and/or hydraulic conductivity of the backfill is high. The arching effect has to be considered to evaluate the effective and total stresses in the backfilled stopes. In this paper, a pseudo-analytical solution is proposed to evaluate the effective and total stresses in backfilled stopes during the backfill deposition on a permeable base, by considering the self-weight consolidation and arching effect. The proposed solution is validated by numerical results obtained by Plaxis2D. A few sample applications of the proposed solution are shown.

Numerical investigation of the geomechanical response of adjacent backfilled stopes

2015 ◽  
Vol 52 (10) ◽  
pp. 1507-1525 ◽  
Author(s):  
Nooshin Falaknaz ◽  
Michel Aubertin ◽  
Li Li
Keyword(s):  
Rock Mass ◽  
Stress State ◽  
Friction Angle ◽  
Critical Issue ◽  
Surrounding Rock ◽  
Filling Sequence ◽  
Natural Stress ◽  
Simulation Results ◽  
Backfill Strength ◽  
Backfilled Stopes

Backfilling of mine stopes helps provide a safe workplace underground. The interaction between the backfill and surrounding rock mass has to be evaluated to ensure the secure application of backfill. This critical issue has led to much research on the stress state in single (isolated) backfilled stopes. However, the stress distribution in multiple openings that interact with each other has not yet been investigated as thoroughly. In this paper, the authors are using numerical simulations to evaluate the response of two adjacent backfilled stopes created in sequence, with a new assumption that is based on an explicit relationship between Poisson’s ratio and the internal friction angle of the backfill; as shown here, the use of this relationship can significantly modify the stress state in backfilled stopes. The simulation results, presented in terms of stresses, displacements, and strains, illustrate the influence of different parameters including backfill strength, pillar width, stope depth, rock mass stiffness, natural stress state, and excavation and filling sequence. Complementary aspects are also considered. A discussion follows on some of the characteristics and limitations of this investigation.

Influence of Pipe Ramming on Stress State of Surrounding Soil and Nearby Tunnel Lining

2016 ◽  
Vol 843 ◽  
pp. 81-86 ◽  
Author(s):  
Alexandr A. Pankratenko ◽  
Nguyen Quang Huy ◽  
Nguyen Duyen Phong ◽  
Andrey S. Samal ◽  
Abdrahman B. Begalinov ◽  
...  
Keyword(s):  
Rock Mass ◽  
Stress State ◽  
Analytical Solution ◽  
Surrounding Rock ◽  
Tunnel Lining ◽  
Circular Tunnel ◽  
Under Construction ◽  
Pipe Ramming ◽  
Plane Problem Of Elasticity ◽  
Surrounding Soil

ANNOTATIONThis article proposes an approach to the prediction of stress state and assessing the strength of a circular tunnel lining and the surrounding rock mass under construction near the production used by the micro-tunneling technology of pipe ramming. The basis of this method is an analytical solution of the corresponding plane problem of elasticity theory.

scholarly journals Analytical Solution of a Circular Opening considering Nonuniform Pressure and Its Engineering Application

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Peng Wu ◽  
Yanlong Chen ◽  
Liang Chen ◽  
Xianbiao Mao ◽  
Wei Zhang
Keyword(s):  
Analytical Solution ◽  
Plastic Zone ◽  
Young’S Modulus ◽  
Lateral Pressure ◽  
Young's Modulus ◽  
Pressure Coefficient ◽  
Surrounding Rock ◽  
Engineering Practice ◽  
Circular Opening ◽  
Lateral Pressure Coefficient

Based on the Mohr–Coulomb criterion, a new analytical solution of a circular opening under nonuniform pressure was presented, which considered rock dilatancy effect and elastic-brittle-plastic failure characteristics. In the plastic zone, the attenuation of Young’s modulus was considered using a radius-dependent model (RDM), and solution of the radius and radial displacement of plastic zone was obtained. The results show that many factors have important impact on the response of the surrounding rock, including lateral pressure coefficient, dilation coefficient, buried depth, and Young’s modulus attenuation. Under nonuniform pressure condition, the distribution of plastic zone and deformation around the opening show obvious nonuniform characteristic: with the increasing of lateral pressure coefficient, the range of plastic zone and deformation decrease gradually at side, while they increase at roof and floor, and the location of the maximum value of support and surrounding rock response curve transfers from side to roof. Based on the analytical results and engineering practice, an optimization method of support design was proposed for the circular opening under nonuniform pressure.

scholarly journals Semi-analytical solution for the problem of extended Pom-Pom fluid flow in a round pipe

2021 ◽  
Vol 2057 (1) ◽  
pp. 012007
Author(s):  
A I Kadyirov ◽  
E K Vachagina
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Solution Method ◽  
Parametric Method ◽  
Single Equation ◽  
Weissenberg Number ◽  
Normal Stresses ◽  
Rheological Equation ◽  
Rheological Equation Of State

Abstract A semi-analytical solution to the problem of the steady flow of viscoelastic single equation eXended Pom-Pom (XPP) fluid in a round pipe using the four-mode rheological equation of state of XPP is presented. An original parametric method for solving the set problem is used. The resulting method is applicable for solving a similar problem in a flat slit. The developed solution method is tested by comparing it with numerical results and experimental data. Using a polyacrylamide solution as an example, the influence of the Weissenberg number on the axial velocity profiles and the components of normal stresses is studied.

An Analytical Solution to Metal Plane Problem in Terms of Orthotropic Anisotropy and Strain Hardening

2010 ◽  
Vol 97-101 ◽  
pp. 348-356
Author(s):  
Yao He Liu ◽  
Guo Feng Yi ◽  
Jian Ming Xiong
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Plane Stress ◽  
Yield Criterion ◽  
Research Result ◽  
Yield Condition ◽  
Plane Stress State ◽  
Yield Function ◽  
Anisotropic Parameter ◽  
Symmetric Plane

In this paper, the yield condition of Hill’s orthotropic yield criterion under axial symmetric plane stress state was discussed. The yield function of orthotropic material was proposed and the analytical solution to meet the condition of equations of equilibrium and compatibility under axial symmetric plane stress state is obtained, in which the conditions of power hardening materials was considered. The research result indicates that hardening coefficient and anisotropic parameter have substantial influence over stress and strain. However, in the presence of the coefficient R90=H/F，the influence appears to be quite weak.

A New Analytical Solution for the Stress State in Inclined Backfilled Mine Stopes

2017 ◽  
Vol 35 (3) ◽  
pp. 1151-1167 ◽  
Author(s):  
Abtin Jahanbakhshzadeh ◽  
Michel Aubertin ◽  
Li Li
Keyword(s):  
Stress State ◽  
Analytical Solution
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