Upper Bound Method Of Limit Analysis Research Articles

A Calculation Method for Reliability Index of a Deep–Bedded Karst Tunnel Construction with Cavity Located Ahead of Tunnel Working Face

For the purpose of reliability quantitative assessment of the surrounding rock of the deeply embedded karst tunnel and the geological body around the cavern in the case of the cavern in the forepart of the tunnel face, on the basis of the upper bound limit analysis method, the energy dissipation theory, as well as the reliability theory, the dimensionless performance function of each damage area of the deeply buried karst tunnels could be established in the case of the cavern in the front of the tunnel face. Subsequently, the probability of failure and the reliability index of each damage region of the deep–bedded karst tunnel in the case of the cavern in the front of this tunnel face should be calculated through the Monte Carlo simulation sampling approach. The investigation has demonstrated that the larger the cohesion of the geotechnical body and the larger the internal friction angle within the geotechnical body, the larger the reliability indexes of the geotechnical bodies around the tunnel. The larger the diameter of the cavern and the larger the tunnel burial depth, the greater the probability of failure in the left part of the geotechnical body around this cavern, and the smaller the reliability indexes of these damage areas.

Pseudo-static analysis of 3D unsaturated bench slopes stabilized by multiple rows of piles

Bench slopes incorporated with multiple rows of anti-slide piles remain an effective technique in landslide disaster preventions and are widely employed in the design of new subgrades and embankments. To provide more realistic results for engineering guidance, the three-dimensional (3D) effect and suction in soils require explicit considerations. Employing the upper bound limit analysis method, a 3D limit analysis of bench slopes stabilized by multiple rows of piles is performed in this paper. The upper bound solutions of several illustrative slopes are optimized and compared with the published ones, indicating the validity of the optimization program and the proposed method. A series of parameter analyses are conducted regarding the roles of suction and anti-slide piles in slope safety assessments. The results show that the suction effect and pile reinforcement increase continually as the pile location increases and the influence of bench width can be ignored. The stability of bench slopes stabilized by multiple rows of piles differ with that of slopes stabilized by single row of piles dramatically. The maximum pile reinforcement reaches 70% for sandy soil slopes but only 30% for clayey soil slopes. The influences of surcharge load and seismic load on the pile reinforcement can nearly be neglected.

Seismic stability analysis of high embankments retained by assembled multi-step cantilever retaining walls pulled locally with geogrids

ABSTRACT This paper introduces a new retaining structure, multi-step cantilever retaining walls pulled locally with geogrids, which has advantages of light weight, quick installation and good applicability for high fill earthworks. Considering log-spiral rotation failure mechanism passing by the heel of the lowest wall members as well as pull-out failure and tensile rupture of the flexible reinforcements, an analytical procedure for seismic overall stability of the retained embankment is proposed based on the upper-bound limit analysis method combined with pseudo static approach. Analysis results of a practical example show that the proposed safety factor and critical slip surface are identical with those by numerical simulation method via FLAC3D. The safety factor increases approximately linearly with the ultimate tension force and the number of reinforcements and nonlinearly with the length of reinforcements within a certain range. Horizontal seismic force has noticeable effect on the slope stability, and vertical seismic effect becomes significant under high horizontal acceleration coefficient. The safety factor is decreasing and the critical slip surface develops obviously towards the embankment exterior as the total number of vertical wall members increases. Besides, the distribution width and setback distance from the walls of the strip surcharge have certain effects on the retained slope stability.

A 3-D analytical continuous upper bound limit analysis for face stability of shallow shield tunneling in undrained clays

For face stability of shallow shield tunneling in undrained clays, a 3-D analytical continuous upper bound limit analysis method is developed. A set of empirically based analytical expressions for tunneling induced ground displacement field is employed within the upper bound theorem, and a particle swarm optimization technique is applied to determine the least favorable collapse domain and the corresponding minimum required tunnel face support pressure and maximum permissible stability number. Verification is conducted by using a finite element limit analysis software and a finite element simulation software, and by comparing with previous theoretical upper bound schemes, and it is found that the method is reliable, less conservative than the finite element limit analysis software and previous theoretical upper bound schemes. Parametric analysis indicates that when the soil unit weight is sufficiently large and/or the soil cohesion sufficiently small, tunnel face support pressure is necessary, and the larger the tunnel cover, the larger the soil unit weight and/or the smaller the soil cohesion, the larger the minimum required support pressure.

Multi-stage slope displacement analysis based on real-time dynamic Newmark slider method

Based on the upper-bound limit analysis method and the real-time dynamic Newmark slider method, the internal and external power of the multi-stage slope under earthquake action is calculated at each moment, and the real-time yield acceleration coefficient and the horizontal displacement of the slope toe are obtained. The influence of soil parameters and geometric characteristics of the slope on the horizontal displacement of the slope toe under the seismic action is analyzed with a typical three-stage slope. The results indicate that the yield acceleration coefficient of the landslide shows an increasing trend during the sliding process, and the value of the horizontal displacement of the slope toe considering the real-time dynamics is smaller than the result without considering. Changing the geometric characteristics of the slope can improve the seismic performance of the multi-stage slope to a certain extent.

Calculation Method of Loose Pressure in Surrounding Rock Mass

With the implementation of the regional coordinated development strategy, traffic flow has grown explosively. The construction of a larger tunnel section becomes an effective way to solve the highway network’s insufficient transport capability problem. Currently, there is little research on the factors influencing and methods of calculating the loose pressure in the surrounding rock mass for highway tunnels with super-large cross-sections. Based on the Bifurcation Tunnel, which is one of the sign projects in the past five years, this paper discusses the influencing factors for the range of loose zone in deeply buried tunnels using a combination of a numerical analysis and an orthogonal test. The weight of influencing factors is calculated via an efficiency evaluation method. This paper establishes a limit analysis model of the loose pressure in the surrounding rock mass under a non-linear failure criterion based on the fitted boundary function and upper bound limit analysis method and deduces the correlations of the loose pressure. The distribution law of the loose pressure, obtained via the limit analysis method, is consistent with the pressure-monitoring results, verifying the correctness of the proposed calculation method. This study can provide a calculation basis for the design of a supporting structure and the selection of similar super-section tunnel projects.

Research on Upper Bound Limit Stability Analysis of Multi-Step High Steep Slope

In order to explore the stability of multi-step high steep slope, this paper considers layer distribution of soil and builds a slope failure mechanism which meets requirements of velocity separation based on plastic mechanics principles, then derives the calculation method of external force power and internal energy dissipation power in failure area using numerical analysis theory, and proposes a loop algorithm for slope stability analysis combining upper bound limit analysis theorem and strength reduction principle. At the same time, in order to enhance the applicability of the upper bound limit analysis method, this paper develops a slope stability calculation system of upper bound limit analysis combined with computer programming technology and evaluates the accuracy of the calculation system through slope engineering practice in open-pit mine. The results show that stability factor by calculation system of upper bound limit analysis is an upper limit solution compared with limit equilibrium method, but the error rate of two methods is less than 5%, which indicates that the slope stability calculation system established in this paper has high accuracy in stability analysis of multi-step high steep slope in the practice of open-pit mine. On the other hand, the most dangerous sliding surface searched by upper bound limit analysis can fully solve velocity problems of multi-step high steep slope failure, so it has stronger reference values in engineering practice.

Upper bound solution of passive instability on the face of longitudinal inclined shallow buried shield tunnel based on rotation–translation mechanism

To better evaluate the passive failure mode of shallow shield tunnel faces in sandy soil strata, tunnel faces passive failure mode was investigated considering the longitudinal inclination in this study. A three-dimensional rotation–translation mechanism that simultaneously considers the longitudinal inclination of the tunnel and partial failure of the tunnel face based on the upper bound limit analysis method was presented. The mechanism comprised two rigid translation blocks and one rigid rotation block. Subsequently, the reliability of the proposed mechanism was verified using the horizontal rigid translation mechanism and numerical simulation considering the longitudinal inclination. Finally, the effects of tunnel longitudinal inclination (δ), cover depth ratio (C/D), soil internal friction angle (ϕ), and the possible presence of uniform surface surcharge (σS) on the limit support pressure of the tunnel face and the partial failure range was assessed. The results indicated that the partial failure range of the tunnel face gradually increased with δ When C/D<1. Conversely, global failure of the tunnel face occurred at different longitudinal inclinations when C/D≥1. The rotation angle (θ) of the rotational failure zone was sensitive to the longitudinal inclination (δ) and decreased with δ at the same coverage depth ratio.

Analysis of the effects of isolation piles on the basal stability of foundation pits against upheaval based on continuous velocity fields.

The upper bound limit analysis method is one of the main approaches to check the basal stability of foundation pits against upheaval. However, existing studies have often failed to consider the effects of external supporting structures, including isolation piles and others, on basal stability against upheaval. This study derives a formula for the coefficient of basal stability against upheaval under the action of isolation piles by simplifying the pile-soil relationship and systematically examines the impact of isolation pile parameters on basal stability against upheaval using the theory of continuous velocity fields and the upper bound limit analysis method. A comparison of simulation results indicates that this technique can accurately identify the variation trend of basal stability against upheaval under the influence of isolation piles and achieve high calculation precision under the operating conditions of wide foundation pits and short isolation piles. Accordingly, a moderate increase in isolation pile parameters produces a significant supporting effect for narrowed foundation pits. Whereas for wide foundation pits, the supporting capacity of isolation piles can be maximized when pile length equals excavation depth.

Energy Response Characteristics of Laterally Loaded Piles

A bounding surface plasticity p − y model is used to examine the internal energy responses of a laterally loaded pile in static and dynamic simulations. The model response is first compared with those observed in physical centrifuge tests, including monotonic and cyclic loading, in a normally consolidated fine-grained soil. Then, the model is used to examine hypothetical static and dynamic situations. The monotonic load capacities determined by the model and an upper-bound limit analysis method are in agreement with that inferred from the physical test. The work done by external loads in static conditions is principally balanced by the plastic work in the p − y springs and the elastic strain energy in the structural pile elements, which are comparable in the cases examined. The numerical model is capable of reproducing accurately the observed test structural responses as well as the characteristics of plastic energy dissipation. In a dynamic free-vibration simulation, the pile is highly damped as a result of the significant plastic energy dissipation. The simple work-hardening elastic–plastic p − y model is theoretically sound, applicable to arbitrary loading histories, and requires the same level of effort to use as traditional p − y methods.

A comparison study of face stability between the entering and exiting a shallow-buried tunnel with a front slope

Worldwide, it is a great challenge to tunnel in portal section, where excessive deformation, cracking, or even collapse often occurs during the construction process. This paper presents a comparison study of face stability between entering and exiting a shallow-buried tunnel with a front slope. Firstly, the theoretical solutions of support pressure σT and safety coefficient FS of the excavation face considering surface slope are derived by upper-bound limit analysis method. Secondly, for different slope angles, buried depth and surrounding rocks of the exit and entrance sections, the σT and FS are obtained. The results show that when the burial depth of the tunnel crown h remain constant, the σT increased first and then decreased while the FS increased gradually, and both become steady when the slope angle α arrive at a certain value. In addition, the thicker the h is, the smaller the certain value α is. When the h and α remain constant, the loose area in front of the excavate face will decreased apparently with the increase of the internal friction angle φ, thus the σT will decrease and FS will increase. Moreover, the σT decreased linearly with the increase of cohesion c and unit weigh γ of surrounding rock, while the FS is the opposite. Compared with the entrance section, the construction risk at the exit section is greater.

Virtual displacement based discontinuity layout optimization

AbstractDiscontinuity layout optimization (DLO) is a relatively new upper bound limit analysis method. Compared to classic topology optimization methods, aimed at obtaining the optimum design of a structure by considering its self‐weight, building cost, or bearing capacity, DLO optimizes the failure pattern of the structure under specific loading conditions and constraints by minimizing the dissipation energy. In this work, we present a modified DLO algorithm that contains all of the advantages of DLO. It is referred to virtual displacement‐based discontinuity layout optimization (VDLO). VDLO takes the stress state of a loaded structure as a snapshot and correspondingly provides the optimum failure pattern, which greatly extends the application potential of DLO. Numerical examples indicate the effectiveness and flexibility of VDLO. It is regarded as a highly promising supplemental tool for other numerical methods in element‐/node‐based frameworks.

Stability Analysis of the Horseshoe Tunnel Face in Rock Masses.

Accurately estimating the stability of horseshoe tunnel faces remains a challenge, especially when excavating in rock masses. This study aims to propose an analytical model to analyze the stability of the horseshoe tunnel face in rock masses. Based on discretization and “point-by-point” techniques, a rotational failure model for horseshoe tunnel faces is first proposed. Based on the proposed failure model, the upper-bound limit analysis method is then adopted to determine the limit support pressure of the tunnel face under the nonlinear Hoek–Brown failure criterion, and the calculated results are validated by comparisons with the numerical results. Finally, the effects of the rock properties on the limit support pressure and the 3D failure surface are discussed. The results show that (1) compared with the numerical simulation method, the proposed method is an efficient and accurate approach to evaluating the face stability of the horseshoe tunnel; (2) from the parametric analysis, it can be seen that the normalized limit support pressure of the tunnel face decreases with the increasing of geological strength index, GSI, Hoek–Brown coefficient, mi, and uniaxial compressive strength, σci, and with the decreasing of the disturbance coefficient of rock, Di; and (3) a larger 3D failure surface is associated with a high value of the normalized limit support pressure.

Stability Analysis of Pressurized 3D Tunnel Face with Tensile Strength Cutoff

The aim of this study is to propose an effective approach to evaluate the stability of a shield tunnel face with tensile strength cutoff by using the upper-bound limit analysis method. Based on the discretization and “point by point” techniques, two improved rotational failure mechanisms, namely the improved collapse failure mechanism and the improved blowout failure mechanism, are developed with the tensile cutoff for the first time. Based on these improved failure mechanisms, the critical collapse and blowout pressures of tunnel faces are then determined by using the upper-bound limit analysis method. The proposed method is then validated by comparisons with previous analytical solutions and numerical results, showing that the proposed method is an effective approach to evaluate the stability of shield tunnel faces. The influences of model parameters on the critical support pressures and the failure feature of the proposed mechanisms are finally presented.

The Influence of Hydraulic Conditions on the Stability of Dual Circular Tunnels in Unsaturated Soils

The performance of geotechnical structures in unsaturated soils is affected significantly by the hydraulic conditions. In the present paper, a unified computational upper bound limit analysis method is applied to study the stability of dual circular tunnels located in unsaturated soils. The linings are substituted by an equivalent uniform pressure exerted on the periphery of the tunnel. The main focus is put on the effect of ground water table and surface water infiltration on the required supporting pressure and collapse mechanisms of dual tunnels. The critical center-to-center spacing above which the interaction of the tunnels disappears is also discussed.

Stability Analysis of Deep Rectangular Tunnels Using Adaptive Finite Element Limit Analysis with Hoek–Brown Failure Criterion

The purpose of this study is to investigate the stability of deep rectangular tunnels excavated in a jointed rock mass using adaptive finite element limit analysis (AFELA) method. The rock mass is assumed to obey the generalized Hoek–Brown failure criterion. The numerical results from parametric studies are presented in the form of dimensionless tables and figures concerning stability numbers (Ns). Typical failure mechanisms are depicted and discussed based on visualized results from AFELA. The results demonstrate that Ns decreases with geological strength index (GSI), increases with disturbance factor (D), stays nearly unchanged with the intact rock yield parameter (mi) and is less sensitive to GSI as D decreases. Besides, an analytical upper bound limit analysis method is also applied to provide a check on the validity of the results from AFELA. The influence of the excavation-induced disturbance on the stability of deep rectangle tunnels is investigated by introducing a disturbance coefficient (ζ).

Dynamic Stability Analysis of Slope Subjected to Surcharge Load considering Tensile Strength Cut-Off

Surcharge slopes are more vulnerable to instability under the effects of earthquake ground shaking, especially considering the tensile stress. In order to account for the adverse factors of seismic forces and tensile stress, the theory of soil with tensile strength cut-off is deduced and analyzed using the upper bound limit analysis method in this paper. Combined with the quasistatic analysis, the equation of critical acceleration expression for surcharge slope subjected to the dynamic conditions has been evaluated. By using the improved Newmark method, permanent displacements have been analyzed in the case of the classical earthquake ground motions. In addition, optimization algorithm has been undertaken, in which several influencing factors such as slope inclination, internal friction angle, surcharge factor, seismic load, and tension cut-off coefficient have been taken into account, and some results are verified with the classical solutions and FEM results. The results concluded the following: (1) The outcomes of verification results are accurate. (2) The critical acceleration of the slope is significantly affected by tension cut-off with the increasing of surcharge factor and seismic effects. (3) The permanent displacements of surcharge slope considering the tensile strength cut-off can be even 2 times of the traditional analysis; meanwhile, with more reduction of tensile strength, the cumulative displacements increase rapidly. Therefore, considering the influence of tensile strength cut-off is fundamental to the dynamic stability design of surcharge conditions.

Seismic Reliability Investigation of Bearing Capacity of Foundations Based on Limit Analysis and Limit Equilibrium Methods

In this paper, by considering the upper-bound limit analysis method in calculating the seismic bearing capacity of foundations, the comparison between a limit equilibrium method such as Hansen and limit analysis method in terms of reliability is investigated. Limit equilibrium has been the oldest method for performing bearing capacity of foundations. However, it seems that theoretical equations proposed by the majority of old limit equilibrium methods to calculate the bearing capacity of foundations (such as Hansen) do not consider the effects of inertial forces of the earthquake in the soil mass. These methods only take into account the horizontal load applied to the foundation and disregard the earthquake forces applied to the soil. By comparing the results of this study, it can be inferred that the reliability of the Hansen approach is very close to the limit analysis method that ignores the impact of horizontal earthquake forces applied to rigid soil blocks. Since the upper-bound limit analysis takes into account the seismic effect of inertial forces in an earthquake, its results may be considered more accurate than Hansen. This study shows that in both granular and cohesive soils in high seismicity-prone areas, usage of a more realistic method as the limit analysis is more reasonable. Considering the facility of RBD by Hansen method using EXCEL spreadsheet in comparison to the seismic reliability-based design using MATLAB programming following the upper-bound limit analysis method, graphs that offer coefficients for obtaining the equivalent value of target reliability in the limit analysis by using the Hansen formulation are presented. Additionally, this study shows that the horizontal seismic coefficient (kh) is an impressive parameter that affects the differences between the two mentioned approaches.

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.

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.