Translational Failure Mechanism Research Articles

An Improved Approach of Classical Upper Bound Theory for Stability Analysis of Layered Slopes

The equations for the critical height of layered slope were derived by a related researcher, but they lack details and do not agree with the method of limit equilibrium. So this topic was reinvestigated. Considering the possible global or local failure modes of the layered slope, the equations for the critical height of the above modes are derived based on the upper limit theorem by using rotational failure mechanisms or rotational and translational failure mechanisms. Based on the above theory, the stability coefficients of layered slope are investigated. The results show that the presented upper bound approach has better performance than other methods mentioned in the literature and is consistent with the limit equilibrium method. In combination with the strength reduction method, the global and local stability of the layered slope are analyzed using the several examples. The high-calculation accuracy of presented method and the specific measures to improve the smoothness of the sliding surface are reviewed. From the perspective of the combination of sliding surfaces, the dimensionless parameter vector of the layered slope is introduced. The possible limitations of the upper bound limit approach with log spirals are pointed out and the conditions which must be fulfilled in order to achieve a higher computational accuracy are mentioned.

Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming

Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is.

UPPER-BOUND SOLUTIONS FOR BEARING CAPACITY OF STRIP FOOTINGS OVER ANISOTROPIC NONHOMOGENEOUS CLAYS

All available solutions for the problem of bearing capacity on clays of anisotropic and nonhomogeneous strength are based on the assumption of either circular or Prandtl-type failure mechanisms. Although these solutions are rigorous within the concept of limit analysis or limit equilibrium methods, the formulations are too mathematical and exceedingly cumbersome and the bearing capacity value can only be determined through numerical optimization for each given combination of soil and failure mechanism parameters. By means of the upper bound approach of limit analysis, and adopting translational failure mechanisms, this paper presents analytical solutions for the bearing capacity of surface strip footings on clays of strength anisotropic and linearly increasing with depth. Closed-form expressions for bearing capacity factors in the case of smooth and rough footings, have been derived by considering two newly introduced kinematically admissible translational failure mechanisms with varying wedge angles. It was remarkable to find that the two mechanisms would render closed-form expressions for the bearing capacity factor if and only if the deformed region underneath the footing is set to be bounded by two vertical discontinuity surfaces. The derived formulas are expressed in terms of degree of strength anisotropy and a nondimensional parameter that reflects strength nonhomogeneity. Besides being the only closed-form solutions yet available for the bearing capacity of strip footings on clays with anisotropic and nonhomogeneous strength, the derived expressions have been found to not only provide upper bound values for the bearing capacity factor that compared favorably with available solutions, but also yield the best upper bound values when strength increase with depth becomes predominant.

Seepage on local stability of slurry trench in deep excavation of diaphragm wall construction

The stability of slurry trench is of importance in diaphragm wall construction. The local stability of slurry trench under seepage application is investigated in this research. In the current research, the local instability of slurry trench is identified as the soil collapse in an instable sublayer and a three-dimensional translational failure mechanism is developed. In this mechanism, the local stability is initialed by the movement of a single rigid block and the seepage application is accounted by introducing the analytical model of semi-confined seepage. The stability is analyzed through kinematic approach and the upper bound solution of safety factor is deduced as a result. The stability is evaluated by optimizing the mechanism for the local failure. Using the current solution, the seepage effect on the stability is analyzed. Regardless of seepage, the stability is mainly dependent on the shear strength of the sublayer. Under seepage application, the failure zone is enlarged and the safety factor decreases as a result. The effect of seepage on the stability is significantly influenced by piezometric head difference Δp and leakage ratio λ of the sublayer. The validity of the current solution is examined by investigating the case of diaphragm wall installation in Suzhou, China.

Ultimate Bearing Capacity of Rock Mass Foundations Subjected to Seepage Forces Using Modified Hoek–Brown Criterion

The experimental data shows that most rocks behave nonlinearly in nature. The modified nonlinear Hoek–Brown failure criterion was considered to investigate the bearing capacity problem of shallow rigid foundations on rock masses subjected to horizontal seepage forces. Two multi-wedge translational failure mechanisms, including symmetrical and non-symmetrical mechanisms were used in the closed-form of the upper bound method of the limit analysis theory. The symmetrical failure mechanism was used in the case of no seepage, while the seepage effect was considered in the non-symmetrical mechanism. The variation of seepage forces was obtained as a function of gradient ratio i(γw/γsub) in the developed formulation. The bearing capacity coefficients Nγ, Nq and Nσ are introduced for the case of seepage flow condition. The results show that the magnitude of the bearing capacity coefficients reduces continuously with an increase in the value of gradient ratio i(γw/γsub). The obtained results were compared and offered for functional use in foundation engineering.

Seismic stability of earth slopes with tension crack

Cracks at the crest of slopes frequently occur during earthquakes. Such cracks result from limited tension strength of the soil. A tension cut-off in Mohr-Coulomb shear strength can represent this limited strength. Presented is an extension of variational analysis of slope stability with a tension crack considering seismicity. Both translational and rotational failure mechanisms are included in a pseudo-static analysis of slope stability. Developed is a closed-form to assess the seismic stability of slopes with zero tensile strength. The results indicate that the presence of the tension crack has significant effects on the seismic stability of slopes, i.e., leading to small value of the yield acceleration. Considering soil tension strength in seismic slope analysis may lead to overestimation on the stability, as much as 50% for vertical slopes. Imposing tension crack results in transit of the critical failure mode to a straight line from a log-spiral, except for flat slopes with small soil cohesion. Under seismic conditions, large cohesion may increase the depth of crack, moving it closer to the slope.

Seismic stability analysis of gravity retaining wall supporting c–φ soil with cracks

This article presents an analytical approach for the seismic stability analysis of gravity retaining wall with c–φ backfill soil. Cracks which are pre-existing (open before the collapse) and are form as part of slope collapse are considered. For a translational failure mechanism assumed, formulas are provided to calculate directly the yield acceleration and the inclination of failure surface. Factors such as cracks and cracks opening, wall back inclination, soil-wall friction, backfill slope are easily to be coupled into the formulations. Both the depth and most adverse location of the crack can be determined from the optimization procedure. Comparisons are made with existing methods and the influences of cracks opening are discussed. The influence of a crack presence on seismic stability of soil-wall system is distinct and pre-existing (opened) cracks have more adverse effect.

Displacement of Pile-Reinforced Slopes with a Weak Layer Subjected to Seismic Loads

The presence of a weak layer in a slope requires special attention because it has a negative impact on slope stability. However, limited insight into the seismic stability of slopes with a weak layer exists. In this study, the seismic stability of a pile-reinforced slope with a weak thin layer is investigated. Based on the limit analysis theory, a translational failure mechanism for an earth slope is developed. The rotational rigid blocks in the previous rotational-translational failure mechanism are replaced by continuous deformation regions, which consist of a sequence ofnrigid triangles. The predicted static factor of safety and collapse mechanism in two typical examples of slopes with a weak layer compare well with the results obtained from the available literature and by using the Discontinuity Layout Optimization (DLO) technique. The lateral forces provided by the stabilizing piles are evaluated using the theory of plastic deformation. An analytical solution for estimating the critical yield acceleration coefficient for the pile-reinforced slopes is derived. Based on the proposed translational failure mechanism and the corresponding critical yield acceleration coefficient, Newmark’s analytical procedure is employed to evaluate the cumulative displacement. Considering different real earthquake acceleration records as input motion, the effect of stabilizing piles and varying the spacing of piles on the cumulative displacement of slopes with a weak layer is investigated.

Governing failure mode of unsaturated soil slopes under rainwater infiltration

Due to rainwater infiltration and loss of matric suction above the wetting font, both translational and rotational slips may occur in an unsaturated soil slope. It is useful to know which failure mode is more critical. The governing failure mode is likely to be affected by soil properties, slope geometry, depth of wetting front and contribution of matric suction to shear strength, which were investigated in this study. Specifically, upper bound limit analysis was adopted to develop stability charts based on rotational failure mechanism, and infinite slope model was used to develop stability charts based on translational failure mechanism. For a slope, the failure mechanism which gives the lower factor of safety is the governing failure mode. It was found that the failure mode of an unsaturated soil slope under rainfall is determined by parameter group c ′/γ H tanϕ ′ for a given slope angle, depth of wetting front and contribution of matric suction to shear strength. With the increase in depth of wetting front and greater contribution of matric suction to shear strength, a slope is more prone to translational failure. Slopes with angle β = 45° are most vulnerable to translational failure, while gentler slopes (e.g. β = 15°) and steeper slopes (e.g. β = 75°) are more susceptible to rotational failure.

Soluciones de forma cerrada para la capacidad de carga de zapatas en suelos anisotrópicos cohesivos

Simple closed-form solutions for the undrained bearing capacity of strip footings on anisotropic cohesive soils are derived employing kinematical approach of limit analysis. Both modified Hill-type and translational failure mechanisms, with variable wedge angles, are attempted and the best upper bound for each mechanism has been analytically determined leading to an analytical expression for the bearing capacity factor. The influence of degree of soil anisotropy on the corresponding value for the bearing capacity factor has also been evaluated. For a wide range of degree of anisotropy, the improvement in the predicted upper bound values does not warrant the use of the modified Hill-type mechanism. Instead, the conventional Hill-type failure mechanism, with a fixed wedge angle of p/4, provides a simple and concise analytical expression for the bearing capacity factor that is analytically equivalent to the conventional Prandtl - Reissner bearing capacity factor for the case of isotropic soil multiplied by the average of the sum of degree of anisotropy plus unity. Rev. ing. constr. [online]. 2015, vol.30, n.2, pp. 109-125. ISSN 0718-5073. http://dx.doi.org/10.4067/S0718-50732015000200003

Tunnel face stability and ground settlement in pressurized shield tunnelling

An analysis of the stability of large-diameter circular tunnels and ground settlement during tunnelling by a pressurized shield was presented. An innovative three-dimensional translational multi-block failure mechanism was proposed to determine the face support pressure of large-shield tunnelling. Compared with the currently available mechanisms, the proposed mechanism has two unique features: (1) the supporting pressure applied to the tunnel face is assumed to have a non-uniform rather than uniform distribution, and (2) the method takes into account the entire circular excavation face instead of merely an inscribed ellipse. Based on the discrete element method, a numerical simulation of the Shanghai Yangtze River Tunnel was carried out using the Particle Flow Code in two dimensions. The immediate ground movement during excavation, as well as the behaviour of the excavation face, the shield movement, and the excavated area, was considered before modelling the excavation process.

Rotational–translational mechanism for the upper bound stability analysis of slopes with weak interlayer

The presence of a weak interlayer has usually an adverse effect on the slope stability. However, the rotational failure mechanism in the conventional upper bound limit analysis cannot rationally describe the sliding of the failure mass along the weak interlayer. Therefore, a new failure mechanism was proposed in this study to evaluate the stability of slopes with weak interlayers using the upper bound limit analysis and the associated factor of safety was determined by the shear strength reduction technique. The new failure mechanism is comprised of rigid blocks undergoing rotational or translational movements, instead of the rotational movement in the conventional failure mechanism. It has also been extended to the stability analysis of slopes in presence of stabilizing piles and pore water pressures. Case studies were carried out on actual slopes with weak interlayers. The proposed rotational–translational failure mechanism was verified by the shear strength reduction finite element method (SSRFEM). Comparisons demonstrate the reliability of limit analysis method with the proposed rotational–translational failure mechanism for slopes with weak interlayers and therefore it can be used as a simple evaluation method for the engineering design.

Failure Mechanics of the Nile Valley Landslide, Yakima County, Washington

Research Article| November 01, 2011 Failure Mechanics of the Nile Valley Landslide, Yakima County, Washington THOMAS C BADGER; THOMAS C BADGER Washington State Department of Transportation, Geotechnical Division, P.O. Box 47365, Olympia, WA 98504-7365 Search for other works by this author on: GSW Google Scholar ERIC L SMITH; ERIC L SMITH Washington State Department of Transportation, Geotechnical Division, P.O. Box 47365, Olympia, WA 98504-7365 Search for other works by this author on: GSW Google Scholar STEVE M LOWELL STEVE M LOWELL Washington State Department of Transportation, Geotechnical Division, P.O. Box 47365, Olympia, WA 98504-7365 Search for other works by this author on: GSW Google Scholar Environmental & Engineering Geoscience (2011) 17 (4): 353–376. https://doi.org/10.2113/gseegeosci.17.4.353 Article history first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation THOMAS C BADGER, ERIC L SMITH, STEVE M LOWELL; Failure Mechanics of the Nile Valley Landslide, Yakima County, Washington. Environmental & Engineering Geoscience 2011;; 17 (4): 353–376. doi: https://doi.org/10.2113/gseegeosci.17.4.353 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyEnvironmental & Engineering Geoscience Search Advanced Search Abstract On October 11, 2009, a very large translational landslide, referred to as the Nile Valley Landslide (NVL), destroyed more than 2500 ft (750 m) of State Route 410 near the community of Nile, located about 25 mi northwest of Yakima, Washington. Based on eyewitness accounts, Pacific Northwest Seismic Network records, and an intensive subsurface investigation, we infer two translational failure mechanisms: an initial shallow failure within the unconsolidated surficial deposits, followed by failure within a deep, adversely dipping, claystone interbed between two Grand Ronde Basalt flows. The underlying basalt flow contains a highly pressurized aquifer that significantly reduces the effective stress within the inferred deep failure zone and its stability. Recent inclinometer data showing slope movement within both the shallow and deep failure zones support this interpretation. The NVL is located at the base of Cleman Mountain, an anticlinal ridge that hosts the enormous and currently dormant Sanford Pasture landslide complex (SPLC). Geochemical analyses of basalts encountered in the numerous borings and outcrops within and around the NVL suggest that the basal failure zones of the NVL and SPLC are stratigraphically different, and that the NVL is likely not a reactivation of the SPLC. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Seismic stability analysis of gravity retaining walls

A new approach based on the category of upper bound theorem of limit analysis is presented in this study to consider the seismic stability of gravity retaining walls. The retaining wall and the backfill soil were taken as a whole system. For a translational failure mechanism assumed, formulas are provided to calculate directly the yield acceleration and the inclination of the failure surface. An example is shown to illustrate the method. Comparisons are made with limit equilibrium method, and the results are found consistent. Based on a limited parametric study, it is shown that the wall roughness has remarkable influence on the yield acceleration.

Probabilistic analysis and design at the ultimate limit state of obliquely loaded strip footings

This paper presents a probabilistic approach for the analysis and design of a strip footing subjected to an inclined load. Both the punching and sliding modes of failure were considered. The deterministic model of the soil punching mode was based on the kinematic approach of limit analysis using a non-symmetrical translational multiblock failure mechanism. The vertical and horizontal components of the footing load were considered as random variables. The soil shear strength parameters were first modelled as random variables and then as random fields to take into account the soil spatial variability. Spatial averaging was used to transform the random field problem to a simple problem of correlated random variables. The reliability index of each failure mode and the system failure probability were calculated. When the soil shear strength parameters were modelled as random variables, it was shown that the coefficient of variation of the angle of internal friction and that of the horizontal footing load have a non-negligible effect on the system failure probability. On the other hand, when the shear strength parameters were modelled as random fields, it was found that the case of (a) a finite (i.e. non-infinite) autocorrelation distance and/or (b) an anisotropic soil regarding the autocorrelation distance, leads to a greater reliability of the foundation with respect to the reference case of isotropic and infinite autocorrelation distances (i.e. the case of random variables). For both cases of random variables or random fields, it was shown that the negative correlation between the shear strength parameters gives a greater reliability of the foundation in comparison to the uncorrelated shear strength parameters. Finally, for design, an iterative procedure was performed to determine the breadth of the footing for a target system failure probability.

Limit analysis of cantilever retaining walls with spaced piles

A modified method is proposed for designing cantilever retaining walls with spaced piles. The approach used is based on a new translational three-dimensional failure mechanism within the framework of the upper-bound theorem of limit analysis. Numerical optimisation of the mechanism is performed by a minimisation procedure for the critical three-dimensional passive earth pressure coefficient. Internationally accepted analytical methods for designing these types of retaining structure assume a simplified rectilinear earth pressure distribution, not only for non-spaced piles but also for spaced piles, where the earth pressure distribution is multiplied by the pile spacing. The results of the proposed method indicate that the pile-to-pile spacing, depending on the input soil parameters, strongly influences the shape of the three-dimensional failure mechanism and the passive pressure along the embedment depth to the point of moment equilibrium. Distribution of the passive earth pressure is no longer rectilinear, but the earth mass contributing to the soil–pile interaction on the dredged side of the embedment depth is reduced, which leads to longer piles and higher inner forces in the retaining structure.

Influences of nonassociated flow rules on seismic bearing capacity factors of strip footing on soil slope by energy dissipation method

Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient concept was adopted for seismic bearing capacity calculations. A multi-wedge translational failure mechanism was used to obtain the seismic bearing capacity factors for different seismic coefficients and various inclined angles. Employing the associated flow rule, numerical results were compared with the published solutions. For bearing capacity factors related to cohesion and equivalent surcharge load, the maximum difference approximates 0.1%. However, the difference of bearing capacity factor related to unit weight is larger. With the two flow rules, the seismic bearing capacity factors were presented in the form of design charts for practical use. The results show that seismic bearing capacity factors related to the cohesion, the equivalent surcharge load and the unit weight increase greatly as the dilatancy angle increases, and that the nonassociated flow rule has important influences on the seismic bearing capacity.

Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e.g. Tresca or Mohr–Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined ‘discontinuity layout optimization’ (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e.g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained.

Bearing capacity of foundation on slope determined by energy dissipation method and model experiments

To determine the ultimate bearing capacity of foundations on sloping ground surface in practice, energy dissipation method was used to formulate the bearing capacity as programming problem, and full-scale model experiments were investigated to analyze the performance of the soil slopes loaded by a strip footing in laboratory. The soil failure is governed by a linear Mohr-Coulomb yield criterion, and soil deformation follows an associated flow rule. Based on the energy dissipation method of plastic mechanics, a multi-wedge translational failure mechanism was employed to obtain the three bearing capacity factors related to cohesion, equivalent surcharge load and the unit gravity for various slope inclination angles. Numerical results were compared with those of the published solutions using finite element method and those of model experiments. The bearing capacity factors were presented in the form of design charts for practical use in engineering. The results show that limit analysis solutions approximate to those of model tests, and that the energy dissipation method is effective to estimate bearing capacity of soil slope.

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.