Upper Bound Method Of Limit Analysis Research Articles

Improved limit analysis method of piled slopes considering the pile axial forces

For the analysis and design of piled slopes using the upper-bound limit analysis method, the axial force on the pile cross-section, where the pile is intersected by the slip surface, contributes to a resistant work rate of the pile; yet this has been omitted in past investigations. Based on analysis of the related work rate and energy dissipation rate of the piled slope, a closed-form solution to internal forces of the pile on the cross-section and some characteristic parameters of the critical slip surface under a specified factor of safety are provided with full consideration of the axial force. The calculation results for two examples show that the axial force has a possibly minor and non-conservative effect on the shear force and bending moment in some cases, but has a major effect on the location of the slip surface, which naturally causes additional design length of the pile. The existing methods without considering the axial force are less conservative or safer than the proposed method in terms of the requisite pile length, particularly under a smaller design factor of safety.

An Analytical Continuous Upper Bound Limit Analysis of Pore Water Effect on the Tail Stability of Underwater Shield Tunnels during Construction

An analytical continuous upper bound limit analysis is developed to analyse the effects of seepage on the transverse stability of underwater shield tunnels. The approach is based on an analytical continuous upper bound limit analysis method for cohesive-frictional soils. It employs the complex variables solution of the displacement field due to tunnel deformation and movement, and the analytical solution of the pore water pressure field for steady state seepage due to pore water influx at the tunnel perimeter. The most critical slip line position and the minimum required tunnel support pressure are determined by using a particle swarm optimization scheme for various generic situations. The method is verified via finite element simulation and comparison with the solution from using rigid block upper bound limit analysis. The parametric analysis revealed among other things that both the infimum of the necessary tunnel support pressure and the most critical plastic zone increase when the hydraulic head at the ground surface increases, but decrease when the tunnel influx increases due to the fact that pore water pressure at the tunnel perimeter decreases with the tunnel influx.

3D Limit Analysis of the Transient Stability of Slope during Pile Driving in Nonhomogeneous and Anisotropic Soil

To evaluate the stability of a slope subjected to pile driving in nonhomogeneous and anisotropic soils, an upper‐bound limit analysis method is employed in this paper. A 3D rotational failure mechanism for soil slope is extended to account for different failure patterns (i.e., toe failure and base failure). In order to avoid missing the global minimum, an efficient optimization method is simultaneously employed to find the least upper bound to the factor of safety (FS). The effectiveness and accuracy of the proposed method is well demonstrated by comparing the results obtained from the proposed approach with the solutions from published literatures. The effects of key designing parameters are presented and discussed. The optimal pile location and the three‐dimensional effect of the slope are discussed. In addition, these results highlight that the adverse effects of pile driving on slope stability should be highly concerned during the design of geotechnical infrastructures, rather than emphasizing the reinforcement effect of a pile only.

Quantitatively assessing the pre-grouting effect on the stability of tunnels excavated in fault zones with discontinuity layout optimization: A case study

Pre-grouting is a popular ground treatment strategy utilized to enhance the strength and stability of strata during the excavation of a tunnel through a fault zone. Two important questions need to be answered during such an excavation. First, how should the grouting size be determined? Second, when should excavation begin after grouting? These two questions are conventionally addressed through empirical experience and standard criteria because a reliable quantitative approach, which would be preferable, has not yet been developed. To address these questions, we apply a recently proposed numerical approach known as discontinuity layout optimization, an efficient node-based upper bound limit analysis method. A case study is provided utilizing a tunnel located in a stratum characterized by complicated geological conditions, including soft soil and a fault zone. The factor of safety is used to quantitatively assess the stability of the tunnel section. The influences of the grouted zone thickness and the time-dependent material properties of the grouted zone on the stability of the tunnel section are evaluated, thereby assisting designers by quantitatively assessing the effects of pre-grouting.

Stability study of slope reinforced with piles under steady unsaturated flow conditions

In this study, based on the log-spiral upper bound limit analysis method that integrated with the generalized effective stress, a new formula for calculating the lateral stabilizing force provided by a row of piles required to increase the slope safety factor to a desired value under vertical steady unsaturated flow was developed, and the most critical solutions were obtained by the optimization method. Moreover, the proposed method can be simplified to the case without piles for computing the stability number for a slope in the limit state of failure. By comparing the results of the proposed method to others for some examples, its feasibility was verified. Numerical study for the parametric effects was presented, indicating that limit lateral stabilizing force depends strongly on the soil types, the slope geometry, the seepage conditions and that in routine design without consideration of suction stress can lead to a less conservative result in clay and sand, but can obtain a relatively safe result in silt and loess. This paper gives some useful suggestions for engineering application and provides a useful method for further study.

Dimensionless Parameter Diagrams for the Active and Passive Stability of a Shallow 3D Tunnel Face

The methods for calculating the elliptical cone’s geometric parameters of multiple elliptical cone sliders were improved by introducing expression of elliptical path in 3D space. This elliptical path is the intersecting line of a cone and inclined cutting plane. Based on upper-bound limit analysis method and an improved method, Sequential Quadratic Programming (SQP) method was employed to obtain optimal upper bound solutions of failure pressure. The effectiveness of this method was verified by a comparative analysis, and a detailed parametric study on the failure pressure and failure modes was presented. In this study, the stability and failure modes of tunnel face are significantly affected by internal friction angle ϕ and dimensionless parameter C/D for both active and passive failure; by contrast, dimensionless parameters γD/c and σs/c have small effects. It is also found that dimensionless parameters C/D and σs/c have no effect on the results if the failure region does not reach the ground surface.

Seismic stability analysis of slopes with pre-existing slip surfaces

In analyzing seismic stability of a slope with upper bound limit analysis method, the slip surface is often assumed as a log-spiral or plane slip surface. However, due to the presence of a weak layer and unfavorable geological structural surface or a bedrock interface with overlying soft strata, the preexisting slip surface of the slope may be irregular and composed of a series of planes rather than strictly log-spiral or plane shape. A computational model is developed for analyzing the seismic stability of slopes with pre-existing slip surfaces. This model is based on the upper bound limit analysis method and can consider the effect of anchor bolts. The soil or rock is deemed to follow the Mohr-Coulomb yield criterion. The slope is divided into multiple block elements along the slip surface. According to the displacement compatibility and the associated flow rule, a kinematic velocity field of the slope can be obtained computationally. The proposed model allows not only calculation of the rate of external work owing to the combined effect of self-weight and seismic loading, but also that of the energy dissipation rate caused by the slip surface, interfaces of block elements and anchorage effect of the anchors. Considering a direct relationship between the rate of external work and the energy dissipation rate, the expressions of yield acceleration and permanent displacement of anchored slopes can be derived. Finally, the validity of this proposed model is illustrated by analysis on three typical slopes. The results showed that the proposed model is more easily formulated and does not need to solve complex equations or time consuming iterations compared with previous methods based on the conditions of force equilibrium.

Limit Analysis Method for Evaluating Soil Resistance to Lateral Motions of Pipelines Partially Embedded in a Seafloor

The lateral soil resistance available to pipelines partially embedded in a seafloor is of interest in evaluating pipeline lateral buckling capacity, stability under forces resulting from current loads, or route pullout loads. An upper-bound limit analysis method, including equilibrium requirements in a manner common to lower-bound theories, was used to evaluate lateral soil resistance to pipe displacements. The method is applicable to sand and clay foundations with homogeneous or layered conditions. Comparisons with results from physical tests and other limit analysis and finite-element investigations are presented. The numerical limit analysis procedure was implemented through numerical-computing software. An optimization procedure was used to identify the minimum resistance satisfying the governing objective equations. The seafloor surface geometry may include soil berms or other features. The soil strength may be described by a linear Mohr-Coulomb criterion or a curved criterion representing a varying material friction angle.

Three-dimensional upper bound stability analysis of slopes with weak interlayer based on rotational-translational mechanisms

The slope stability is greatly affected by the weak interlayer and pore-water pressure, which can change the failure mechanism of the slope as well. Compared to the two-dimensional method for the slope stability analysis, the three-dimensional method can reflect the actual slope condition better. Based on the upper bound theorem, a three-dimensional combined rotational-translational mechanism is proposed to study the stability of slopes with the weak interlayer and pore-water pressure in this paper. The proposed mechanism consists of the curvilinear cone rotational mechanism and the cone translational mechanism. The combined mechanism can be expended longitudinally by the plane inserted, so that the method can be used to analyze the slope stability with different lengths. The distribution of the pore-water pressure obtained from the two-dimensional seepage finite element analysis is incorporated into the limit analysis. Case studies were carried out by the upper bound limit analysis method with the proposed mechanism and results were compared with those by the limit equilibrium method in the literature. Comparisons demonstrate the reliability of the proposed rotational-translational failure mechanism for slopes with the weak interlayer, which can be used as a simple method for preliminary evaluation of slope stability in practical application.

Limit analysis approach for accessing stability of three-dimensional (3-D) slopes reinforced with piles

ABSTRACTThe stabilization of slopes by placing piles is one of the most innovative and effective slope reinforcement techniques in the coastal engineering in recent years. Due to the simplicity and efficiency, limit analysis method is the most common approach for assessing the stability of slopes. However, the majority of existing limit analysis methods is limited to slope without the presence of piles. In this technical note, a novel upper-bound limit analysis method was proposed to access the stability of three-dimensional slopes reinforced with piles incorporating the admissible rotational failure mechanism where toe failure, face failure, and base failure were taken into account. The effects of key designing parameters, e.g., pile location, pile spacing, slope angle, slope width on the stability of earth slopes, and geometry of critical slip surface were presented and discussed. The results demonstrate that the proposed approach is more appropriate for assessing the stability of slopes reinforced with piles and can be also utilized in the design of piles stabilizing the unstable slopes.

Stability Analysis and Design of Cantilever Retaining Walls with Regard to Possible Failure Mechanisms: An Upper Bound Limit Analysis Approach

This study presents a new algorithm for design of cantilever retaining walls based on the proposed failure mechanisms and considers the effects of wall geometric parameters using an upper-bound limit analysis approach. All previous work on this subject has only focused on the optimum design of the retaining walls assuming constant forces, irrespective of the total stability and critical conditions of failure mechanisms. In the present study, the upper-bound limit analysis method was used to determine the shape of the critical failure mechanisms for a retaining wall simultaneously with its optimal dimensions. The safety factors against overturning, sliding, and bearing capacity failure were assessed by the limit analysis approach. The current results show good agreement with the results obtained using the limit equilibrium methods and finite element analyses. The results obtained based on the proposed failure mechanism show that the geometry and dimensions of the wall affect its stability safety factors, the shape of the critical failure mechanisms and the active pressure on the wall; therefore, the process of determining the shape of the critical failure mechanisms, checking the stability of the wall and the procedure of finding its optimal dimensions should be performed simultaneously.

Effects of shear strength reduction strategies on safety factor of homogeneous slope based on a general nonlinear failure criterion

Safety factor of slope is often calculated based on the conventional linear Mohr–Coulomb failure criterion. However, many experimental results show that the strength envelopes of almost all of geomaterials are characteristically nonlinear. This paper presents a method (upper bound limit analysis method) to analyze the stability of a homogeneous slope based on a general nonlinear failure criterion, in which different shear strength reduction strategies (SSRS) can be used. Based on the presented method, three SSRSs (i.e. by factoring the unconfined shear strength c0 only, by factoring the tensile strength σt only, by factoring both the unconfined shear strength c0 and the tensile strength σt) are used to calculate the safety factors of a homogeneous slope under a general nonlinear failure criterion. Compared results show different SSRSs have significant influence on the calculated safety factor.

Limit Analysis of Slopes Reinforced with Multi-Directional Anchors

The upper-bound method of limit analysis combined with strength reduction technique is employed to analyze the stability of an earth slope reinforced with multi-directional anchors. A homogeneous and isotropic earth slope reinforced with two rows of anchors is considered. Attempts are made to obtain the optimal angles of anchors. Parametric studies show that, for homogeneous and isotropic slopes, the optimal angle of the first row of anchors is 0°; while the optimal angle of the second row of anchors varies with anchor positions, and generally is less than 15°.

Strength properties of jointed rock masses based on the homogenization method

This paper aims to determine the strength properties of jointed rock masses by means of the homogenization method. To reflect the microstructure of jointed rock masses, a representative element volume (REV) is selected. Assuming being rigid and perfectly plastic and utilizing the Mohr-Coulomb yield criterion for rock and joints, an upper bound limit analysis method is proposed based on the homogenization theory. By using the finite element method and Goodman joint element, a nonlinear mathematical programming with equality constraints is formulated, which can be solved by a direct iterative algorithm. Numerical results show the strength of jointed rock masses behaves anisotropy with different joint directions. This method presents an effective tool for the strength analysis of jointed rock masses.

Seismic bearing capacity of shallow foundations near slopes using the upper-bound method

The seismic bearing capacity factors of spread and embedded foundations near slopes have been analytically investigated. The pseudo-static approach was used and the seismic forces consisted of a horizontal load applied to the foundation and the inertia of the soil mass. The upper-bound method of limit analysis was employed and a non-symmetrical failure mechanism was proposed. This mechanism comprises a triangular active wedge, a logarithmic spiral shear zone and a passive wedge. The shear transfer coefficient was introduced to calculate the seismic bearing capacity of spread foundations with variable shear transfer at the base of foundations. The validity of the results from the present analysis was confirmed by comparing with the results proposed by other investigators. Finally, the lowest upper-bound solutions of the seismic bearing capacity factors of shallow foundations near slopes were presented in the form of design charts for practical use in geotechnical engineering. It has been shown that the seismic bearing capacity factors reduce considerably with the increase of horizontal seismic coefficient. In addition, the magnitude of bearing capacity factors decreases further with increase in slope inclination and increase with the embedment and the distance of slope crest from the beginning of loading.

Upper-bound solutions of three-dimensional passive earth pressures

This paper presents a novel approach to the determination of passive soil pressures: using the upper-bound method within the framework of limit analysis theory. It is based on a three-dimensional, kinematically admissible, rotational, hyperbolical failure mechanism. The failure mechanism is composed of the central and two lateral bodies, which are connected by a common velocity field. This approach is similar to two-dimensional stability analyses, where the log spiral potential failure surface is considered. The front surface of the central body interacts with the retaining wall; the upper surface can be loaded by surcharge loading; and the log spiral segment defines the curved failure surface of the central part. The cross sections of the lateral bodies are in agreement with the cross section of the central body. On the outer side, they are laterally bounded by a curved and kinematically admissible hyperbolic surface, which is defined by enveloping the hyperbolical half cones and part of the case surface of the leading half cone. The results give values for the passive soil pressure coefficients that are for most cases lower than the values determined by the upper-bound method of limit analysis for a translational failure mechanism, as published in the literature.Key words: limit analysis, earth pressure, passive pressure, failure surface, soil–structure interaction.

A three-dimensional upper-bound approach to slope stability analysis based on RFEM

An upper-bound limit analysis method based on rigid finite elements has been developed recently. Numerical procedures for implementing the three-dimensional upper-bound slope stability analysis using rigid finite elements are presented in the paper. The search for the minimum value of the factor of safety can be set up as a non-linear programming problem. Because of the existence of non-linear equalities, a special sequential quadratic programming (SQP) algorithm, CFSQP, is applied to obtain the optimal solution in the paper. Two test problems are used to examine the validation and capability of the present rigid element upper-bound limit analysis method by comparison with results obtained by other methods. A practical example illustrates the application of the present method in three-dimensional slope stability analysis.

Rigid Finite Element Method for Upper Bound Limit Analysis of Soil Slopes Subjected to Pore Water Pressure

The traditional approach for assessing the stability of slopes is using limit equilibrium methods. Recently, many efforts have been made to utilize limit analysis methods based on the upper bound and lower bound limit theorems in plasticity. In this paper, an upper bound limit analysis method using rigid finite elements is presented. Rigid finite elements are used to discretize the slope media. Kinematically admissible velocity discontinuities are permitted to occur at all interelement boundaries. The traditional definition of factor of safety is adopted in the present method so that the results from the limit analysis can be directly compared with those from methods of slices. The presence of water can be considered through work terms in the energy–work balance equation. To do this effectively, the pore water pressure is considered as an external force, similar to gravity and surface tractions. The proposed method formulates the slope stability problem as a nonlinear optimization problem with constraints...

SEISMIC BEARING CAPACITY OF SHALLOW STRIP FOOTINGS IN SEISMIC CONDITIONS.

The seismic bearing capacity factors of shallow strip footings are calculated. The approach used is pseudo-static, where the seismic effects are considered by taking into account static inertia forces. The upper-bound method of limit analysis is used. Two failure mechanisms, referred to as the M1 and M2 mechanisms, are considered for the calculation schemes. These mechanisms are non-symmetrical. M1 consists of a log sandwich composed of a triangular active wedge, a log-spiral radial shear zone and a triangular passive wedge. M2 consists of an arc sandwich composed of a triangular active wedge, a circular radial shear zone and a triangular passive wedge. The solutions obtained are rigorous upper-bound ones in the framework of the limit analysis theory for an associated flow rule Coulomb material. For the static case, the numerical results of the bearing capacity factors show that the M1 mechanism gives the exact well-known solutions of both the Ncs and Nqs factors. This is not the case with the M2 mechanism. However, for the Nys factor, the lowest upper-bound solutions are obtained from the M1 mechanism for angle of internal friction of the soil greater than 30 degrees and from the M2 mechanism for angle of internal friction of the soil less than 30 degrees. For the seismic case, the lowest upper-bound solutions of the seismic bearing capacity factors obtained from both the M1 and M2 mechanisms are presented in the form of design charts for practical use in geotechnical engineering. These results are compared with other authors' results. (A)