A. V. Lyamin

Stability of an undrained plane strain heading revisited

The stability of an idealised heading in undrained soil conditions is investigated in this paper. The heading is rigidly supported along its length, while the face, which may be pressurised, is free to move. The problem approximates any flat wall in an underground excavation. Failure of the heading is initiated by a surface surcharge, acting with the self-weight of the soil. Finite element limit analysis methods, based on classical plasticity theory, are used to derive rigorous bounds on load parameters, for a wide range of heading configurations and ground conditions. Solutions for undrained soils with constant strength, and increasing strength with depth are presented. Recent improvements to finite element limit analysis methods, developed at the University of Newcastle, have allowed close bounds to be drawn in most cases. Previous research in this area has often been presented in terms of a stability ratio, N that combines load and self-weight into a single parameter. The use of a stability ratio for this problem is shown not to be rigorous, a finding that may be applicable to other stability problems in underground geomechanics.

Undrained stability of footings on slopes

Solutions for the ultimate bearing capacity of footings on purely cohesive slopes are obtained by applying finite element upper and lower bound methods. In a footing-on-slope system, the ultimate bearing capacity of the footing may be governed by either foundation failure or global slope failure. The combination of these two factors makes the problem difficult to solve using traditional methods. The importance of a dimensionless strength ratio in determining the footing capacity is broadly discussed, and design charts are presented for a wide range of parameters. In addition, the effect of footing roughness and surface surcharge are briefly quantified.

Undrained Stability of Dual Circular Tunnels

In this paper,numericallimit analysis and semianalytical rigid blocktechniques are used toinvestigate the effectof the tunnelspac- ingonthestabilityoftwocirculartunnelsexcavatedsidebyside.Thetunnelsaremodeledunderplane-strainconditions,whichimpliesthatthey are assumed to be infinitely long. Bounds on the stability of the tunnels are obtained using finite-element limit analysis, the numerical formu- lation of which is based on the upper and lower bounds theorems of classical plasticity. Solutions are obtained using advanced conic program- mingschemes tosolvethe resultingoptimization problems,and upperand lowerboundestimates on thestabilityof thetunnels areobtained for arangeofgeometries.Thesebounds,whichbracketthetruecollapseloadfromaboveandbelow,arefoundtodifferbyatmost5%forthecases where the solution does not approach zero. Results from this study are summarized in stability charts for use by practitioners. DOI: 10.1061/ (ASCE)GM.1943-5622.0000288.

Trench Stability under Bentonite Pressure in Purely Cohesive Clay

AbstractTrench stability is a conventional geotechnical problem; however, current evaluations are often based entirely on empiricism. This paper uses numerical finite-element upper and lower bound limit analysis to produce stability charts for two-dimensional and three-dimensional homogeneous and inhomogeneous undrained diaphragm wall trenches. Using the limit theorems cannot only provide a simple and useful way of analyzing the stability of the trench, but also avoid the shortcomings and arbitrary assumptions underpinning the limit equilibrium method. By considering the effects from the bentonite slurry pressures, the collapse load in this study has been bracketed to within ±8.5% or better by the numerical upper and lower bound limit analyses. The chart solutions can be used to predict either the critical depth or the safety factor of the trench and provide a convenient tool for preliminary designs by practicing engineers.

Mesh generation for lower bound limit analysis

This paper describes a general strategy for generating lower bound meshes in D-dimensions. The procedure is based on a parametric mapping technique, coupled with midpoint splitting of subdomains, and permits the user to control the distribution of the discontinuities and elements precisely. Although it is not fully automatic, the algorithm is fast and automatically generates extension zones for problems with semi-infinite domains.

Collapse Analysis of Square Tunnels in Cohesive–Frictional Soils

ABSTRACT The stability of a long square tunnel in a Mohr-Coulomb soil with a uniform friction angle, cohesion, and self-weight is investigated. This problem corresponds to drained loading of a tunnel in clay or rock, is difficult to analyse, and has been addressed rarely in the literature. For a range of tunnel geometries and material properties, rigorous bounds on the internal tunnel pressure required to prevent collapse are obtained using two numerical methods which are based on the bound theorems of classical plasticity and finite elements. The results are presented in terms of dimensionless stability charts and closely bracket the true collapse load for most cases of practical interest. The bounding methods used in the analyses have recently been developed at the University of Newcastle, and lead to large nonlinear programming problems that can be solved very efficiently using special purpose algorithms. The formulations are natural successors to techniques based on linear programming, and are fast enough to be used for large scale stability problems in three-dimensions. The upper and lower bound finite element solutions differ by less than a few per cent for most of the cases studied and, as an additional check, are compared against the analytical upper bound estimates derived from several assumed rigid block collapse mechanisms.

Slope stability charts for two-layered purely cohesive soils based on finite-element limit analysis methods

AbstractStability charts for soil slopes, first produced in the first half of the twentieth century, continue to be used extensively as design tools, and draw the attention of many investigators. This paper uses finite-element upper and lower bound limit analysis to assess the short-term stability of slopes in which the slope material and subgrade foundation material have two distinctly different undrained strengths. The stability charts are proposed, and the exact theoretical solutions are bracketed to within 4.2% or better. In addition, results from the limit-equilibrium method (LEM) have been used for comparison. Differences of up to 20% were found between the numerical limit analysis and LEM solutions. It also shown that the LEM sometimes leads to errors, although it is widely used in practice for slope stability assessments.

Three-dimensional slope stability charts for frictional fill materials placed on purely cohesive clay

This paper investigates slope stability and produces a set of stability charts for three-dimensional (3D) slopes for a specific case in which frictional fill materials are placed on purely cohesive clay. As slopes are not usually plane strain in nature and are influenced by physical boundaries, this study uses a 3D analysis using the finite-element LB limit analysis method. Stability charts are convenient tools for geotechnical engineers during design in practice. For comparison purposes, the results from two-dimensional (2D) analyses are also discussed. The results from this study quantify the increase in the factors of safety obtained when 3D conditions are analyzed as opposed to the more traditional 2D.

Ultimate Bearing Capacity of a Strip Footing on Ground Reinforced by a Trench

AbstractThe ultimate bearing capacity of a strip footing on soil reinforced by a trench has been studied in the framework of limit analysis. Existing contributions were reviewed and were compared with numerical results predicted by two methods. The main finding was how the numerical tools performed in predicting closed lower-bound (LB) and upper-bound (UB) solutions of the ultimate bearing capacity of a strip footing on soil reinforced by a trench, for four cases of reinforcement. As a result, by analytical methods, the gap between the LB and UB solutions becomes significant as the difference in shear strength characteristics of the reinforcing material and initial soil increases. Assessment of the suggested quasi-exact solutions of the ultimate bearing capacity of a strip footing on soil reinforced by a trench is strongly recommended.

Slope-stability assessments using finite-element limit-analysis methods

AbstractThis paper utilizes finite-element limit-analysis methods to investigate the stability of slopes of various properties and in nature. Specifically, a slope with a soft (weak material) band, a postquake slope, and rock slopes were investigated. The conventional Mohr-Coulomb failure criterion and the Hoek-Brown failure criterion are utilized for soil and rock slopes, respectively. The Hoek-Brown failure criterion can be applied directly in the finite-element limit-analysis methods without the need for conversion to the equivalent Mohr-Coulomb parameters. The applicability of the numerical limit-analysis methods in both soil and rock slopes is clearly demonstrated. It is also significant to note that the results presented in this paper have two distinct solutions: the upper- and lower-bound solutions. In addition, the failure mechanisms of the slopes are also shown. Prior assumptions of the failure mechanisms are not required for these finite-element limit-analysis methods, therefore providing a more...