Search

The conventional pseudo-dynamic (CPD) and modified pseudo-dynamic (MPD) methods are invoked to obtain the seismic bearing capacity of strip foundations using the limit equilibrium method, with a two-wedge failure mechanism. A spectral version of the conventional pseudo-dynamic method (SPD) is also invoked by considering the ground motion amplification factor, to be a function of the non-dimensional frequency λ/B and soil damping. Numeric analyses show that bearing capacity results obtained by the MPD and SPD methods are generally consistent. Both experience the same general reduction in bearing capacity with the increase of λ/B, with successive ups and downs corresponding to soil’s natural frequencies. For 5

The evaluation of slope stability of a three-dimensional slope requires identifying the critical slip surface with the minimum factor of safety, which is a complex optimization problem. Failure to identify the critical slip surface can lead to unconservative conclusions about the stability of a slope. This paper proposes a novel 3D surface-altering optimization method, which iteratively alters the geometry of a 3D slip surface to find the critical slip surface representing the minimum factor of safety in a slope. The geometry of the slip surface is defined via nonuniform rational basis spline (NURBS) curves formed over a plan grid of control points. The proposed method includes a series of five subroutines that apply various forms of transformations to the control points. These subroutines include minimization problems, which determine the optimal transformation parameters for minimizing the obtained factor of safety of the resulting slip surfaces. Given that any geometrically defined slip surface can be approximated using an equivalent series of NURBS control points, the proposed method can be used in efforts to further reduce the global factor of safety first obtained via conventional search methods, such as those involving spherical or ellipsoidal slip surfaces. To demonstrate its effectiveness, the proposed method was applied to further optimize the critical ellipsoidal slip surfaces reported in some numerical examples. Comparing the results with those limited to ellipsoidal slip surfaces, the proposed method was consistently able to identify slip surfaces with significantly lower factors of safety. The postaltered slip surfaces also matched closely with finite element shear strength reduction results. As such, the proposed method is effective in searching for critical slip surfaces and can be used as a final step in the critical surface searching routine.

Objective:Spatial variability is one of the largest sources of uncertainty in geotechnical applications. This variability is primarily characterized by the scale of fluctuation, a parameter that describes the distance over which the parameters of a material are similar. Spatial variability is generally described with traditional methods of time series analysis. In statistics, the Auto-Regressive Moving Average (ARMA) model is commonly used to describe the relationship between two points in time. Instead of assuming an autocorrelation model, the ARMA model calculates the necessary auto-regressive components (AR), as well as a decaying Mean Structure (MA). The advantage of this method is that it is calculated for each specific field study, so that the data is not forced to fit into a fixed autocorrelation model (e.g. Markovian, Gaussian,etc).Methods:In this study, the ARMA model is introduced as a means of measuring scale of fluctuation, and two case studies and a simulation are used to compare the scale of fluctuation values from the ARMA model to the other estimates.Results:In the first case study, the ARMA model estimated a value of 0.26 m while the other methods ranged from 0.22-0.29 m. In the second case study, the ARMA model estimated a value of 0.40 m while the other methods ranged from 0.40-0.54 m. In the simulated example, where the true value was 5.0 m, the ARMA model estimated a value of 4.73 m while the other methods ranged from 3.24-3.51 m.Conclusion:This paper concludes that ARMA is a promising new method for estimating the scale of fluctuation but requires a considerable amount of research before it can become established in the geotechnical sphere.

Shear strength parameters in naturally alluvial deposits bear variation with depth (non-stationarity). Probabilistic analysis of simple slopes with linearly increasing (mean) undrained shear strength with depth and spatial variability is explored using the 2D random limit equilibrium method (RLEM) along with the non-circular failure surface assumption. A deterministic factor of safety design chart method is extended to express margins of safety as probability of failure for soils with random variability and positive correlation between shear strength parameters and unit weight. The effects of isotropic and anisotropic spatial variability and cross-correlation of soil properties on probability of failure are also investigated. Combinations of low correlation length and positive cross-correlation between strength parameters are shown to reduce the probability of failure. This offers the possibility to bring probabilistic estimates of failure into alignment with expectations of slope stability based on experience with factors of safety. The results of a limited number of RLEM analyses are compared with some other results using the 2D random finite element method (RFEM). The influence of different involved parameters and assumptions, more specifically the nonlinear variation of the undrained cohesion and also the non-circular slip surface, on the embedded uncertainty and probability of failure was elaborated. The research has emphasized the importance of non-circular failure surface assumption along with the consideration of non-stationarity in shear strength parameters.

The main objective of this study is to evaluate the ultimate seismic bearing capacity of a shallow strip footing resting on a frictional soil stratum containing a weak intervening layer. The majority of the studies throughout the literature pertain to the static loading condition. The previous seismic analyses have also been devoted to the studies on the bearing capacity of shallow strip footings resting on a two-layered soil. The influence of weak middle layer on the pseudo-static seismic bearing capacity of shallow foundations is the main focus of the present study. To determine the seismic bearing capacity, the limit equilibrium method (LEM) was combined with the pseudo-static seismic loading approach. Bearing capacity was defined by a single equivalent coefficient which combines the contributions of cohesion, surcharge and soil weight. A two-wedge failure surface, known as the Coulomb failure mechanism, was adopted to model the slip lines in each layer to calculate the seismic bearing capacity of the overlying shallow strip footing. The Particle Swarm Optimization (PSO) algorithm was invoked to seek the optimal bearing capacity value under different strength and loading conditions. In order to verify the validity of the presented formulations, the results were compared with some Finite Elements Method (FEM) analyses available in literature. Furthermore, the influence of the embedment depth, thickness, and strength of the weak inter-layer on the seismic bearing capacity of the shallow footing is investigated in the presence of different seismic loading arrangements. The results of this study could be very helpful in the seismic analysis and design of shallow foundations overlying a soil medium containing a weak layer of various strengths.

The purpose of this study is to examine the behavior of simple soil slopes reinforced with geosynthetics using deterministic and stochastic as well as circular and noncircular limit equili...

Spectral seismic bearing capacity of strip foundations is evaluated by the limit equilibrium method (LEM). In this study, the pseudo-dynamic approach is followed to take into account seismic accele...

In limit equilibrium slope stability analysis, surface altering optimisation (SAO) is a novel approach to minimise the factor of safety for a given slip surface using spline curves in 2D. It is a local search algorithm that when combined with a global search method, can form a powerful hybrid optimisation technique used in slope stability analysis. Probabilistic analysis of a slope with spatial variability is a computationally intensive example that would demonstrate the accuracy and speed of optimisation techniques. In this paper, the probabilistic analysis results of three different slopes with both complicated and straightforward geometries are presented, and the application of SAO in spatial variability analysis using random limit equilibrium method (RLEM) is demonstrated. It was found that SAO combined with a global search method provides fairly accurate results and yields curtailed computational effort.

In this study, the well-established pseudo-static approach along with the horizontal slices method (HSM) is employed to investigate the seismic internal stability of geosynthetic-reinforced earth slopes. Previous simple HSM analyses were based on a primary assumption stating that the normal inter-slice forces are exerted on the mid-length of horizontal sections. However, this simplifying assumption could give rise to substantial errors in the calculation of design parameters, specifically in the case of high seismic excitations or low soil strength parameters. To address this deficiency, a balancing moment is considered as a new variable to account for the corresponding eccentricity. In the current HSM, two sets of unknown variables, including horizontal inter-slice forces and shear forces along failure surface, are determined using the well-known λ coefficient and the Mohr-Coulomb failure criterion. In this new technique, the traditional ‘5N-1ʹ type of HSM analysis is reduced to a robust and rigorous ‘3N’ one with the same predictive capability. The influence of various parameters, including soil characteristics, slope geometry and different earthquake coefficients are rigorously examined. Moreover, a number of useful graphs is provided to help engineers in the preliminary seismic design of geosynthetic-reinforced earth slopes.

Spatial variability is one of the major sources of uncertainty in geotechnical applications. This variability is characterized customarily by the scale of fluctuation. Scale of fluctuation ...

A general closed-form solution to compute the reliability index of a simple limit state function with two load terms and one resistance term is derived. The formulation considers contributions to margins of safety expressed in probabilistic terms due to the choice of load and resistance models, bias values, dependencies between nominal values and bias, uncertainty in estimates of nominal values for uncorrelated load and resistance terms at time of design, and average margin of safety expressed as the operational factor of safety. A sensitivity analysis and example application demonstrate the quantitative influence of the contributing random variables on reliability index.

Reinforced slopes with horizontal layers of geosynthetic reinforcement can have different mechanisms of failure. In this paper two major mechanisms of failure of reinforced slopes are investigated. External mechanisms occur when the critical slip surface passes beyond the reinforced zone. Internal mechanisms are characterised by failure surfaces that intersect all of the reinforcement layers. For a target value of the factor of safety and a specific value of the reinforcement length, there is a minimum value of the reinforcement tensile strength that will generate only external mechanism types. For greater reinforcement strength values, there is no change in the mechanism of failure and the value of the factor of safety. On the other hand, increasing the minimum reinforcement length, while keeping the reinforcement tensile strength equal to or less than the minimum value obtained for an external failure mechanism, will generate an internal mechanism type with the same mean value of factor of safety. In this study, probabilistic slope stability analysis of these two mechanisms is carried out using Monte Carlo simulation of slopes with different purely frictional and cohesive-frictional (c − ϕ) soils and different slope angles. Margins of safety are expressed in terms of a conventional factor of safety and in terms of maximum probability of failure. Cross correlation between soil strength parameters is also considered in this paper. It is shown that considering practical values of cross correlation coefficient reduces the maximum probability of failure for both internal and external failure mechanisms.

Uncertainty in the predicted ultimate pullout strength of soil nails can be significant due to the complexity of nail–soil interactions, inherent variability in soil properties and the effects of nail installation. The paper first presents a statistical evaluation of the accuracy of ultimate bond strength of soil nails using the effective stress method (ESM) equation that has been adopted in Hong Kong. A total of 113 ultimate nail capacity data points from field pullout tests were collected from the literature and used to estimate the accuracy of the current ESM. Based on the available data, the current ESM default pullout model is found to be excessively conservative (on average) by at least a factor of three. The spread in prediction accuracy measured by the coefficient of variation (COV) of bias is in the range of 36–43 % after removing anomalous test data. Here, bias is the ratio of measured to predicted pullout load capacity. In addition, the accuracy of the current ESM equation for prediction of nail bond strength is shown to be dependent on the magnitude of predicted ultimate bond strength and magnitude of nominal vertical effective stress which is undesirable. The paper examines four candidate-modified bond strength equations with empirical coefficients that have been back-fitted to measured bond strengths to improve the overall accuracy of the equation and to reduce or remove the undesirable dependencies noted above. One equation with an empirically corrected stress-dependent term is judged to be the best candidate model based on the mean of bias values, spread (COV) of bias values, lack of dependencies and simplicity. Finally, the relative contributions of random variability in soil shear strength to measurement bias in bond strength (prediction accuracy) for each soil type are computed for the best bond strength model. Analysis of the contribution of soil shear strength to prediction accuracy showed that the combination of variability due to factors other than soil shear strength was greater than the variability in soil shear strength alone, where the latter is defined by the soil secant friction coefficient.

Probabilistic slope stability analyses of simple geosynthetic reinforced soil slopes were carried out using the shear strength reduction method in combination with the finite element method (FEM). An existing open-source FEM code was modified to include bar elements to model horizontal layers of geosynthetic reinforcement. Analysis results using the modified code (mFEM) demonstrate that large reductions in probability of failure can be realized by adding geosynthetic reinforcement layers to constructed slopes. The modified code was also used to investigate the effect of variability of soil friction angle on probabilistic outcomes for constructed unreinforced and reinforced purely frictional soil slopes.

This paper focuses on the calculation of probability of failure of simple unreinforced slopes and the influence of the magnitude of cross correlation between soil parameters on numerical outcomes. A general closed-form solution for cohesive slopes with cross correlation between cohesion and unit weight was investigated and results compared with cases without cross correlation. Negative cross correlations between cohesion and friction angle and positive cross correlations between cohesion and unit weight, and friction angle and unit weight were considered in the current study. The factors of safety and probabilities of failure for the slopes with uncorrelated soil properties were obtained using probabilistic slope stability design charts previously reported by the writers. Results for cohesive soil slopes and positive cross correlation between cohesion and unit weight are shown to decrease probability of failure. Probability of failure also decreased for increasing negative cross correlation between cohesion and friction angle, and increasing positive correlation between cohesion and unit weight, and friction angle and unit weight. Probabilistic slope stability design charts presented by the writers in an earlier publication are extended to include cohesive-frictional (c-[Formula: see text]) soil slopes with and without cross correlation between soil input parameters. An important outcome of the work presented here is that cross correlation between random values of soil properties can reduce the probability of failure for simple slope cases. Hence, previous probabilistic design charts by the writers for simple soil slopes with uncorrelated soil properties are conservative (safe) for design. This study also provides one explanation why slope stability analyses using uncorrelated soil properties can predict unreasonably high probabilities of failure when conventional estimates of factor of safety suggest a stable slope.

A general closed-form solution for the true probability of failure of a simple limit state function with one load term and one resistance term is derived. The formulation considers contributions due to model type, uncertainty in method bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety. Example calculations are presented using different load and resistance models for the pullout internal stability limit state of steel strip reinforced soil walls together with matching bias data reported in the literature.

Non-circular Random Limit Equilibrium Method (RLEM) uses a combination of non-circular limit equilibrium method, 2D random field theory, and Monte Carlo simulation. Non-circular RLEM has the ability to seek out the weakest failure path in a slope stability analysis using optimization techniques such as Surface Altering, while considering spatial variability of soil properties. This study is a probabilistic analysis of the stability of the Sugar Creek embankment fill slope using non-circular RLEM. This example has been investigated in the literature with other probabilistic methods such as the non-circular limit equilibrium method together with 1D spatial variability analysis. The results of this study show that the values of probability of failure are in good agreement for the 1D and 2D spatial variability cases, while the mean factor of safety values for 2D spatial variability tend to be higher with smaller standard deviations of factor of safety.

A general closed-form solution for the reliability index (or probability of failure) of a simple linear limit-state design function with one load term and one resistance term is used to com...

The 2D random finite element method and the one-dimensional and 2D random limit equilibrium method are used to investigate the influence of spatial variability of soil strength parameters on the probability of failure of simple soil slopes with cohesive undrained shear strength. The combined influence of spatial variability of soil properties and cross-correlation between undrained soil strength and unit weight on the computed probability of failure is explored. The paper identifies conditions where numerical outcomes are similar and where they are not. The limitations of each analysis method are described and implications to analysis and design are identified. Abbreviations: FEM: finite element method; LEM: limit equilibrium method; RFEM: random finite element method; RLEM: random limit equilibrium method

ABSTRACT: The disturbance factor (D) is a parameter in the Generalized Hoek-Brown failure criterion for rock slopes in slope stability. It represents the subsurface damage to the rock material properties resulting from blasting and stress relaxation during excavations. Within the region of assumed damage, a number between zero (undisturbed) and unity (very disturbed) is prescribed as the value of the disturbance factor. Most commonly a uniform value of D is assumed within the entire region of damage, but little research has been done to study the impact of the variation in the D parameter on stability. Through use of an example, this paper examines the effect of various distribution functions of D through the damaged region, such namely, as constant, linearly varying, and exponentially varying. The failure surfaces and factors of safety for the slope as determined via limit equilibrium are also compared with finite element analyses. Varying the distribution of the damage function was found to significantly affect the failure surface and factor of safety. It is recommended that practitioners adopt care to select an appropriate distribution for slope stability analysis. 1. BACKGROUND The Generalized Hoek-Brown method (Hoek and Brown 2018) is widely used for determining rock mass strength in rock mechanics. One application of this method is in the design of open pits in rock masses which requires the evaluation of factor of safety against overall sliding. During excavation, subsurface damage can occur to the surrounding rock masses and cause fracturing. The damage can be caused by two sources: (a) blasting and (b) stress relaxation (Hoek et al. 2002), and can be quantified in the form of a disturbance factor, D, which ranges from a zero (undisturbed) to unity (disturbed) within the rock masses. For slope stability, the shear strength of the rock activated along the slip surface can be obtained by solving Eq. (1) to Eq. (4) (Hoek et al. 2018).