Log-spiral Failure Mechanism Research Articles

Seismic Bearing Capacity of Strip Footings with Modified Pseudo-dynamic Method

Current research has shown a nonlinear trend in the failure of soil, and the single tangent method is commonly adopted when coping with nonlinear problems of soil failure. However, the method equates a nonlinear criterion to an optimizable linear criterion, which may differ from the actual situation, resulting in conservative results. In this paper, two types of piece-wise log-spiral failure mechanisms for bearing capacity estimations, including symmetrical and unilateral mechanisms were proposed with the nonlinear Mohr-Coulomb criterion. The static bearing capacity of foundations was evaluated using the symmetric failure mechanism, while the seismic bearing capacity of foundations was evaluated adopting a modified pseudo-dynamic method based on the unilateral failure mechanism. The result shows that the bearing capacity calculated in the paper is smaller compared to the result using the linear Mohr-Coulomb criterion. For London clay, the static bearing capacity is reduced by about 45% at a foundation width equal to 1m. From the comparisons, it is found that the proposed approach of piece-wise log-spiral failure mechanism for bearing capacity estimation is effective. In addition, parametric studies show that the nonlinear parameters, the initial factor of seismic acceleration, the normalized frequency, and the damping ratio all have obvious effects on the seismic bearing capacity. A significant reduction in the seismic bearing capacity of the foundation occurs when the normalized frequency ωsH/Vs is equal to (0.5 + n)π (n = 0, 1, 2, …). Considering that the approach proposed provides a strict upper bound to the bearing capacity, the result imparts confidence in the approach of analysis presented.

Optimal stability analysis of homogenous soil slopes with an irregular geometric morphology

The common morphologies of slope surfaces in nature include linear, stepped, convex, concave, and their combination types. Many researchers have investigated the stability of slopes with simple linear, stepped convex, or concave geometric morphologies, disregarding the effect of combination of convex and concave morphology. In this paper, slope surfaces with convex-concave characteristics are considered. A model of a slope surface composed of n segments is constructed to realize the arbitrary generation of irregular geometric morphologies. Based on the upper bound limit analysis and the log-spiral failure mechanism, a formula for the factor of safety of slopes with irregular geometric morphology is obtained. Optimal stability analysis of convex, concave and convex-concave combination slopes with different characteristics is carried out. This paper mainly focuses on the effect of the location and extent of convex-concave sections on slope stability and sliding surfaces. In addition, a comparative analysis is carried out from both theoretical and numerical perspectives. The local stability of convex and convex-concave combination slopes is discussed. The results show that the effect of convex-concave characteristics on slope stability is related to the equivalent straight-slope angle. Moreover, some abnormal phenomena have been identified. For example, under certain conditions, the stability of a convex slope is better than that of a straight slope, and a concave morphology is not conducive to slope stability. In addition, when the equivalent straight-slope angle is small, convex-concave combinations can yield the worst or best slope stability. Therefore, the location and extent of convex-concave sections should be comprehensively considered to achieve an optimal design scheme in slope reinforcement design and construction.

Seismic bearing capacity of rock foundations subjected to seepage by a unilateral piece-wise log-spiral failure mechanism

Most of the current studies on the bearing capacity of rock foundations follow the Hoek-Brown (HB) criterion, but all adopt the generalized tangent technique or the multi-tangent approach, which does not reflect the essence of the nonlinear dependence of the Hoek-Brown criterion. Therefore, a modified unilateral failure mechanism is proposed in the paper, using which the bearing capacity of shallow strip footings considering seepage and seismic forces is evaluated. Use of a statics-like approach for seepage condition and a modified pseudo-dynamic method for seismic condition. The comparison with the results of other literature confirms the feasibility and effectiveness of the study in the paper, while the parametric analysis shows that a smaller upper bound solution is yielded based on the failure mechanism proposed in this paper, and the horizontal gradient ratio, the horizontal factor of seismic acceleration, the normalized frequency, the geological strength index, the disturbance coefficient, and the rock type-dependent parameter all have significant effects on the bearing capacity of rock foundations. In addition, the analysis of the working conditions considering both seepage and seismic forces confirmed the dominance of seismic forces. The results of the superposition treatment between different working conditions are inaccurate, which will underestimate the foundation bearing capacity and cause a waste of cost. This paper develops a more accurate method of assessing the bearing capacity of rock foundations and gives a table of coefficients that can be adopted in engineering practice.

Calculation method for reinforcement spacing of bilaterally wrapped reinforced embankments under seismic force

The vertical spacing among reinforcements in geosynthetic-reinforced earth embankment is crucial to its overall stability. Based on the upper bound theorem of plastic limit analysis and pseudo-static approach, an overall stability analysis method for bilaterally wrapped reinforced embankments under strip surcharge and seismic action is put forward in view of the planar and log-spiral failure mechanism of the reinforced embankments, which quantitatively expresses the relationship between the reinforcement spacing and the factor of safety of the embankments. Some examples show that the maximum relative error of the factor of safety between the proposed method and some existing methods is around 10% under a specified reinforcement spacing. The factor of safety is nonlinearly decreasing as the reinforcement spacing increases, and the results by the log-spiral mode are slightly more conservative than those by the planar mode. The proposed method can quantitatively reflect the influence of the filling properties, reinforcement strength, seismic forces, strip surcharge, and embankment geometry on the reinforcement spacing. The nonlinear negative relationship between the factor of safety and the reinforcement spacing is noticeable under different reinforcement strengths. The reinforcement spacing is almost linearly reducing with the increase of the vertical seismic coefficient increases, while it decreases clearly nonlinearly as the horizontal seismic coefficient increases.

A log-spiral limit equilibrium analysis for passive earth pressure under the effect of unsaturated seepage conditions

In the current state of the study regarding passive earth pressure, the majority of literature was limited in scope to dry or saturated cases. However, most soils in practical engineering are unsaturated. Based on the log-spiral failure mechanism, this paper develops a limit equilibrium (LE) analysis to evaluate the passive earth pressure under the effect of steady unsaturated seepage conditions. For assessing the effect of suction stress on passive earth pressure, a suction stress-based effective stress representation is incorporated into a limit equilibrium analysis. The analytical formula of passive earth pressure coefficient is derived using the moment equilibrium equation for the backfill defined by a log-spiral slip surface. An optimization procedure is developed to search for the minimum passive earth pressure coefficient and the critical failure surface via MATLAB. A parametric analysis is performed to investigate the effects of some key parameters on passive thrust. Besides, examples of two different cases are given to verify the effectiveness of theoretical results. Results indicate that suction stress can increase the magnitude of the passive earth pressure coefficient and the suction-induced effect highly depends on the seepage conditions and soil types.

Passive resistance of unsaturated backfill under steady state flow conditions

ABSTRACT This paper presents a unified semi-analytical solution to investigate the passive earth resistance of unsaturated soils retained by a rigid wall in the framework of limit-equilibrium approach based on a rotational log-spiral failure mechanism. Coupled influences of unit weight and suction stress changes in unsaturated soils under different steady vertical flow conditions have been considered to provide a more realistic solution. The impact of different parameters such as effective internal friction angle soil, inclination of backfill surface and wall back face, surcharge pressure, height of wall, location of water table, and soil–wall interface friction has been explored by performing a parametric study. It has been found that the changes in the suction stress and unit weight of unsaturated soils under different input parameters have a greater effect on modifying the critical slip surface, and magnitude and point of application of passive earth resistance on the retaining walls. The results obtained from the present study compare reasonably well with the solutions in the literature.

A New Approach for Evaluating the Soil Slope Reinforcement Tensile Forces Using Limit Equilibrium Methods

Limit equilibrium methods have been extensively used in the design of reinforced soil structures using various types of failure surfaces. A significant problem in limit equilibrium analysis of reinforced soil is the need to know the force at each reinforcement layer in the limit state. Limit equilibrium analysis with log spiral failure mechanism has been employed to locate the critical failure surfaces emerging at or above the toe and to study the behavior of geosynthetic-reinforced soil slopes. This paper describes a numerical procedure, using limit equilibrium methods, to evaluate the distribution of the soil slope reinforcement tensile forces. Both, log spiral and circular slip surfaces are considered. The effect on the required tensile forces of the target safety factor value, the ratio of the mobilized soil shear strength, and the reinforcement layer spacing are examined. Results show that the distribution of reinforcement tensile forces is dependant on reinforcement layer spacing; however, the total reinforcement force is not. The total reinforcement force required to ensure equilibrium is strongly dependant on the target safety factor value and the ratio of the mobilized soil shear strength. Modified Bishop Method with circular failure surface and Shiwakoti–Leshchinsky log spiral failure surface led to comparable results.

Seismic analysis of slope considering log-spiral failure surface with numerical validation

This paper presents the solution of c-φ soil slope stability problem using the pseudo-dynamic method assuming the log-spiral failure mechanism. The vertical slice analysis methodology is introduced to analyze the stability of the slope under vertical and horizontal seismic loads. The adopted pseudo-dynamic method in the present analysis considers the effect of phase difference and primary and shear wave velocity which travel through the soil medium during an earthquake. Considering the limit equilibrium method, the moment equilibrium condition for each slice was established and a factor of safety of the slope is evaluated. Results are presented in a tabular and graphical form to understand the effect of different parameters of slope soil. Comparisons of the present analysis are highlighted with the existing solutions. A numerical solution is also done by PLAXIS 2D to compare the present study under earthquake loading conditions.

Upper bound seismic limit analysis of geosynthetic-reinforced unsaturated soil walls

The assessment of the internal stability of geosynthetic-reinforced earth retaining walls has historically been investigated in previous studies assuming dry backfills. However, the majority of the failures of these structures are caused by the water presence. The studies including the water presence in the backfill are scarce and often consider saturated backfills. In reality, most soils are unsaturated in nature and the matric suction plays an important role in the wall's stability. This paper investigates the internal seismic stability of geosynthetic-reinforced unsaturated earth retaining walls. The groundwater level can be located at any reinforced backfill depth. Several nonlinear equations relating the unsaturated soil shear strength to the matric suction and different backfill type of soils are considered in this study. The log-spiral failure mechanism generated by the point-to-point method is considered. The upper-bound theorem of the limit analysis is used to evaluate the strength required to maintain the reinforced soil walls stability and the seismic loading are represented by the pseudo-dynamic approach. A parametric study showed that the required reinforcement strength is influenced by several parameters such as the soil friction angle, the horizontal seismic coefficient, the water table level, the matric suction distribution as well as the soil types and the unsaturated soils shear strength.

Impact of Embedment Resistance on Required Reinforcement Force in MSE Walls

This paper presents a limit equilibrium (LE) method to quantify the impact of the embedment resistance on the maximum mobilization reinforcement force required for global stability of the mechanically stabilized earth wall. This LE method is based on the log spiral failure mechanism and is rigorous in the sense that it satisfies equilibrium at the limit state. The presented formulation yields required reinforcement force, not taking into consideration limitations of the stiffness of the facing. Results show that the reinforcement would be eliminated when having enough embedment depth from an analytical parametric study standpoint. However, when the embedment depth is shallow, more reinforcements should be required on account of insufficient embedment resistance.

Seismic rotational stability analysis of reinforced soil retaining walls

Reinforced soil retaining walls have been widely constructed all over the world. Although the limit equilibrium (LE) method is common practice in design, a growing body of experimental and analytical evidence has demonstrated that it could lead to overly conservative (and hence, uneconomical) design. In this paper, a kinematic limit analysis method, combined with a pseudo-dynamic method of analysis, is developed for rotational stability analysis of reinforced soil retaining walls based on the log-spiral failure mechanism. The proposed analysis method is validated against the results from different pseudo-static methods. However, the rotational stability and the corresponding yield acceleration coefficients from the proposed method are shown to vary with time, and with factors such as the backfill shear modulus and the frequency of ground motion. Parametric analyses are also conducted to study the influences that pseudo-dynamic analysis parameters, reinforcement properties, wall height, and soil strength have on rotational stability and failure geometry of reinforced soil retaining walls. Results indicate that optimum value of ultimate reinforcement strength is greater when the reinforcement is more widely spaced. Additionally, the cross-sectional area of the rotational failure mass is smaller for walls with lower-strength reinforcement and larger vertical spacing.

Passive earth pressure under the log-spiral failure mechanism

Under either convex or concave log-spiral failure mechanism, the passive earth pressure may be overestimated. This paper develops a new formula satisfying the moment limit equilibrium condition, which combines a new procedure to determine the passive earth pressure. The procedure could consider convex and concave log-spiral failure mechanisms simultaneously and figure out which failure mechanism is critical. The present method can investigate the influence of the inclination of wall, the slope of backfill or the wall friction on the shape of the critical slip surface. Additionally, the comparisons illustrate that the critical slip surface is concave log-spiral under certain conditions.

Modified Pseudo-dynamic Bearing Capacity of Shallow Strip Footing Considering Fully Log-Spiral Passive Zone with Global Center

The subject seismic bearing capacity is one of the most important aspects of geotechnical earthquake engineering. As the existing pseudo-dynamic method has certain drawbacks, this paper presents a modified pseudo-dynamic approach to evaluate the seismic bearing capacity of shallow strip footing resting on c–Φ soil considering the log-spiral failure mechanism. Since damping is present in all materials, more realistic results can be obtained by modeling the soil as a visco-elastic material. Here, the passive failure region is considered a fully log-spiral zone with an arbitrary location of the center of log-spiral. A single seismic bearing capacity coefficient (Nγe) is evaluated for the simultaneous resistance of unit weight, surcharge and cohesion, which is more practical to simulate the field failure mechanism. The effects of soil and seismic parameters are taken into account to evaluate the seismic bearing capacity of the foundation. The results obtained from the present analysis are presented in both tabular and graphical non-dimensional form. Results are thoroughly compared with the existing values in the literature, and a reasonably good agreement is found with the existing studies.

Stability of Unsaturated Soil Slopes with Cracks under Steady-Infiltration Conditions

Most classical approaches for evaluating the stability of soil slopes with tension cracks are performed under dry and/or saturated conditions. The suction-induced effect of unsaturated soils is generally neglected in assessing slope stability. This article presents an analytical framework for assessing the stability of unsaturated soil slopes with tension cracks under one-dimensional (1D) steady-infiltration conditions using the limit-analysis method. The boundary-value problem was formulated based on the log-spiral failure mechanism by taking the effects of suction stress, effective unit weight of soil, and tension cracks into account. A simplified method was developed to calculate the external work rate of unsaturated soil weight. Detailed investigations of the effects of suction, Poisson’s ratio, steady infiltration, and water in tension cracks on the slope stability are presented.

Upper Bound Analysis for Collapse Failure of Shield Tunnel Face Excavated in Unsaturated Soils Considering Steady Vertical Flow

Natural soils are mostly in an unsaturated state and the corresponding mechanical properties differ significantly from a saturated one. In traditional stability analysis for a shield tunnel face, the soil mass is typically assumed to be dry or saturated for convenience of analysis. In this work, based on the upper bound theorem of classical plasticity theory and the log-spiral failure mechanism, face stability of the shield tunnel excavated in unsaturated soils under vertical steady flow is studied. The profile of shear strength is determined by virtues of the unified effective stress approach and the analytical solution of matric suction under unsaturated steady flow. On this basis, the analytical expression for the supporting pressure is deduced and the sequential quadratic programming is employed to search for the optimal upper bound solution. Through parametric analysis it is found the fitting parameters of SWCC and the groundwater level affect the supporting pressure notably. Besides, the relevant influence of vertical discharge is also significant when clayey soils are concerned.

Investigation of the stability of submarine sensitive clay slopes underwave-induced pressure

The exploration and exploitation of marine georesources ordinarily disturbs the submarine soft clay surrounding construction areas and leads to a significant decrease in the shear strength of structured and sensitive clayey soils in submarine slopes. Under wave action, local slides can even trigger large-scale submarine landslides, which pose a serious threat to offshore infrastructure such as pipelines and footings. Therefore, accurately evaluating the stability of submarine sensitive clay slopes under wave-induced pressure is one of the core issues of marine geotechnical engineering. In this paper, a kinematic approach of limit analysis combined with strength reduction technique is presented to accurately evaluate the real-time stability of submarine sensitive clay slopes based on the log-spiral failure mechanism, where external work rates produced by wave-induced pressure on slopes are obtained by the numerical integration technique and then are applied to the work-energy balance equations. The mathematical optimization method is employed to achieve the safety factors and the critical sliding surfaces of submarine slopes at different time in a wave cycle. On this basis, the stability of submarine sensitive clay slopes under various wave parameters is systematically investigated. In particular, extreme wave conditions and special cases of slope lengths no more than one wavelength are also discussed. The results indicate that waves have some negative effects on the stability of submarine sensitive clay slopes.

Upper Bound Solution for Required Supporting Pressure Applied on a Deep Shield Tunnel Face Under Different Groundwater Levels

The construction of shield tunnels is greatly influenced by the presence of groundwater. Based on the upper bound theorem of limit analysis, this paper presents an analytical investigation on the stability of shield tunnel face subjected to the impact of pore water pressure. Considering the nonlinear strength feature of soil mass, the nonlinear failure criterion of power-law type is employed, and the tangential technique is utilized to determine its equivalent Mohr–Coulomb strength parameters. The log-spiral failure mechanism for shield tunnel face is constructed, and three different cases of the relation between groundwater level and this mechanism are summarized. After that, rates of work of external forces and rate of internal energy dissipation are computed and analytical expression for the supporting pressure is deduced. Numerical solution with respect to specified parameters is calculated through optimization. Parametric analysis is performed and the variation of required supporting pressure with increasing height of groundwater level is presented.

Bearing capacity analysis of a saturated non-uniform soil slope with discretization-based kinematic analysis

In contrast to conventional kinematic analysis postulating a log-spiral failure mechanism, this study adopts a discretization technique to generate a kinematically admissible failure mechanism, using the forward difference method. A vertical infinitesimal trapezoidal element, similar to that in slices method of limit equilibrium, is chosen so as to consider pore water effect within slopes. The work rate-based balance equation yields the optimal kinematic solution of limiting surcharge near the crest of the slope. The bearing capacity of a saturated non-uniform slope is sought through optimization and verified with conventional kinematic analysis.

Active earth pressures from a log-spiral slip surface with arching effects

The distribution of active earth pressures behind retaining structures is typically inferred from simplified Rankine or Coulomb analyses, both of which are triangular in shape and assume a planar slip surface. However, various experiments and numerical models have demonstrated an earth pressure distribution that is non-linear in shape, typically attributed to a phenomenon called ‘soil arching’. Existing analytical solutions have typically evaluated arching with planar slip surfaces; however, slip surfaces that form behind retaining structures are often curvilinear, tending to follow a log-spiral shape, particularly when considering wall batter or interface friction between the backfill and wall. In this letter, the arching effect is considered using a log-spiral failure mechanism that has been developed by deriving a first-order differential equation and subsequently solved using a numerical approach. A series of charts are presented accounting for varying soil strengths, interface friction and wall batters.

Solutions for stability of anchored earth slopes subjected to seismic loading

The limit analysis approach is paid more attention to in the stability analysis of slopes subjected to seismic loading. However, the solutions obtained from the approaches are in general limited to a designated slope or the same kind of slopes. It seems that a wide applicability of the solutions in their present form is rather difficult. Based on the kinematic theorem and the assumption of combined log-spiral rotational failure mechanism, the integral formulation for expressing the rate of external work rate due to soil weight and seismic loading is derived under the framework of pseudo-static method considering the complex geometrical configurations and the multilayer soils in slopes with multi-row anchors. Further, the work-energy balance equation is established, and the analytical expressions for the global factors of safety (FS) and the yield acceleration coefficient of anchored slopes are obtained by using the strength reduction technique combined with the optimization method. Moreover, the permanent displacement with Newmark's method is also solved. Several representative examples are employed to validate the analytical solutions, and some comparisons of the FSs and the corresponding critical sliding surfaces obtained by various methods are also made. The results show that the analytical approach can yield the high-accuracy solutions and is widely applicable to the seismic stability analysis of complex slopes with multi-row anchors. Finally, a practical case is analyzed using the proposed approach. ©2016, Editorial Office of Chinese Journal of Geotechnical Engineering. All right reserved.