Many engineered and natural slopes have complex geometries and are multi-layered. For these slopes traditional stability analyses will tend to predict critical failure surfaces in layers with the lowest mean strength. A move toward probabilistic analyses allows a designer to account for uncertainties with respect to input parameters that allow for a more complete understanding of risk. Railway slopes, which in some cases were built more than 150 years ago, form important assets on the European rail network. Many of these structures were built at slope angles significantly higher than those allowed in modern design codes. Depending on the local geotechnical conditions these slopes may be susceptible to deepseated failure; however, a significant number of failures each year occur as shallow translational slips that develop during periods of high rainfall. Thus, for a given slope, two potential failure mechanisms might exist with very similar probabilities of failure. In this paper a novel multimodal optimisation algorithm (‘Slips’) that is capable of detecting all feasible probabilistic slip surfaces simultaneously is presented. The system reliability analysis is applied using polar co-ordinates, as this approach has been shown to be less sensitive to local numerical instabilities, which can develop due to discontinuities on the limit state surface. The approach is applied to two example slopes where the complexity in terms of stratification and slope geometry is varied. In addition the methodology is validated using a real-life case study involving failure of a complex slope.@en

Lateral loading is often the governing design criteria for piles supporting offshorewind turbines and with the recent growth of this sector, the reliability of traditional design approaches is receiving renewed interest. To accurately abeb the behavior of a laterally loaded pile requires a detailed understanding of the soil reaction that ismobilized as the lateral deflection of the pile occurs. Currently, the p-y curvemethod iswidely adopted tomodel the response of laterally loaded piles. The limitations of existing p-y formulations arewidely known, and there is acceptance that load tests on large-diameter stiff monopiles are urgently required to formulate appropriate designmethods. However, interpretation of the data frominstrumentation placed on stiffmonopiles is not straightforward. This paper proposes an optimization technique to derive the soil reaction profile along the shaft of instrumented piles, fromwhich the correlated p-y curves can then be obtained. Themethod considers force equilibrium, pile deflection, and additional boundary conditions. A set of fourth-order polynomial equations are abumed to model the soil reaction profile under each load step during a monotonic load test. By minimizing the difference between themeasured and calculated bendingmoment and considering equilibriumof the shear forces acting on the pile, the soil reaction profile and the concentrated tip resistance can be obtained simultaneously. A stiff instrumented test pile installed in over-consolidated sand was load tested and the resultswere used to test the performance of the proposed method. The results are compared with othermethods used in literature and practice. Themethod provides a consistent framework to derive p-y curves from measured strain data. The results of the field test and derived p-y curves confirmed that existing designmethods do not accurately capture the lateral loading response of piles in dense sand.@en

Lateral loading is often the governing design criteria for piles supporting offshorewind turbines and with the recent growth of this sector, the reliability of traditional design approaches is receiving renewed interest. To accurately abeb the behavior of a laterally loaded pile requires a detailed understanding of the soil reaction that ismobilized as the lateral deflection of the pile occurs. Currently, the p-y curvemethod iswidely adopted tomodel the response of laterally loaded piles. The limitations of existing p-y formulations arewidely known, and there is acceptance that load tests on large-diameter stiff monopiles are urgently required to formulate appropriate designmethods. However, interpretation of the data frominstrumentation placed on stiffmonopiles is not straightforward. This paper proposes an optimization technique to derive the soil reaction profile along the shaft of instrumented piles, fromwhich the correlated p-y curves can then be obtained. Themethod considers force equilibrium, pile deflection, and additional boundary conditions. A set of fourth-order polynomial equations are abumed to model the soil reaction profile under each load step during a monotonic load test. By minimizing the difference between themeasured and calculated bendingmoment and considering equilibriumof the shear forces acting on the pile, the soil reaction profile and the concentrated tip resistance can be obtained simultaneously. A stiff instrumented test pile installed in over-consolidated sand was load tested and the resultswere used to test the performance of the proposed method. The results are compared with othermethods used in literature and practice. Themethod provides a consistent framework to derive p-y curves from measured strain data. The results of the field test and derived p-y curves confirmed that existing designmethods do not accurately capture the lateral loading response of piles in dense sand.@en

Probabilistic slope stability analysis typically requires an optimisation technique to locate the most probable slip surface. However, for many slopes particularly those containing many different soil layers or benches several distinct critical slip surfaces may exist. Furthermore, in large slopes these critical slip surfaces may be located at significant distances from each other. In such circumstances, finding and rehabilitating the most probable failure surface is of little merit, as rehabilitating that surface does not improve the safety of the slope as a whole. Unfortunately, existing slip surface search techniques were developed to converge on one global minimum. Therefore, to implement such methods to evaluate the stability of a slope with multiple failure mechanisms requires the user to define probable slip locations prior to calculation. This requires extensive engineering experience and places undue responsibility on the engineer in question. This paper proposes the use of a locally informed particle swarm optimisation method which is able to simultaneously converge to multiple critical slip surfaces. This optimisation model when combined with a reliability analysis is able to define all areas of concern within a slope. A case study of a railway slope is presented which highlights the benefits of the model over single objective optimisation models. The approach is of particular benefit when evaluating the stability of large existing slopes with complicated stratigraphy as these slopes are likely to contain multiple viable slip surfaces.@en

Probabilistic slope stability analysis typically requires an optimisation technique to locate the most probable slip surface. However, for many slopes particularly those containing many different soil layers or benches several distinct critical slip surfaces may exist. Furthermore, in large slopes these critical slip surfaces may be located at significant distances from each other. In such circumstances, finding and rehabilitating the most probable failure surface is of little merit, as rehabilitating that surface does not improve the safety of the slope as a whole. Unfortunately, existing slip surface search techniques were developed to converge on one global minimum. Therefore, to implement such methods to evaluate the stability of a slope with multiple failure mechanisms requires the user to define probable slip locations prior to calculation. This requires extensive engineering experience and places undue responsibility on the engineer in question. This paper proposes the use of a locally informed particle swarm optimisation method which is able to simultaneously converge to multiple critical slip surfaces. This optimisation model when combined with a reliability analysis is able to define all areas of concern within a slope. A case study of a railway slope is presented which highlights the benefits of the model over single objective optimisation models. The approach is of particular benefit when evaluating the stability of large existing slopes with complicated stratigraphy as these slopes are likely to contain multiple viable slip surfaces.@en

Probabilistic slope stability analysis typically requires an optimisation technique to locate the most probable slip surface. However, for many slopes particularly those containing many different soil layers or benches several distinct critical slip surfaces may exist. Furthermore, in large slopes these critical slip surfaces may be located at significant distances from each other. In such circumstances, finding and rehabilitating the most probable failure surface is of little merit, as rehabilitating that surface does not improve the safety of the slope as a whole. Unfortunately, existing slip surface search techniques were developed to converge on one global minimum. Therefore, to implement such methods to evaluate the stability of a slope with multiple failure mechanisms requires the user to define probable slip locations prior to calculation. This requires extensive engineering experience and places undue responsibility on the engineer in question. This paper proposes the use of a locally informed particle swarm optimisation method which is able to simultaneously converge to multiple critical slip surfaces. This optimisation model when combined with a reliability analysis is able to define all areas of concern within a slope. A case study of a railway slope is presented which highlights the benefits of the model over single objective optimisation models. The approach is of particular benefit when evaluating the stability of large existing slopes with complicated stratigraphy as these slopes are likely to contain multiple viable slip surfaces.@en

Probabilistic slope stability analysis typically requires an optimisation technique to locate the most probable slip surface. However, for many slopes particularly those containing many different soil layers or benches several distinct critical slip surfaces may exist. Furthermore, in large slopes these critical slip surfaces may be located at significant distances from each other. In such circumstances, finding and rehabilitating the most probable failure surface is of little merit, as rehabilitating that surface does not improve the safety of the slope as a whole. Unfortunately, existing slip surface search techniques were developed to converge on one global minimum. Therefore, to implement such methods to evaluate the stability of a slope with multiple failure mechanisms requires the user to define probable slip locations prior to calculation. This requires extensive engineering experience and places undue responsibility on the engineer in question. This paper proposes the use of a locally informed particle swarm optimisation method which is able to simultaneously converge to multiple critical slip surfaces. This optimisation model when combined with a reliability analysis is able to define all areas of concern within a slope. A case study of a railway slope is presented which highlights the benefits of the model over single objective optimisation models. The approach is of particular benefit when evaluating the stability of large existing slopes with complicated stratigraphy as these slopes are likely to contain multiple viable slip surfaces.@en

This paper presents a new method for applying reliability-based design approaches to slope stability analysis. In this method the soil properties are considered to be random variables. The factor of safety of the slope is found using Bishop's simplified method for noncircular slip surfaces. By considering the variability of the soil properties, the probability of failure is determined from the reliability index (β). The minimization problem (determination of the lowest β value for the range of variables and possible slip surfaces considered) is solved using a genetic algorithm approach, which simultaneously locates the critical slip surface and determines the reliability index. The performance of the new method is compared to some existing reliability approaches when applied to case histories of slope failures from the geotechnical literature. The new approach is seen to provide reasonable and consistent estimates of the reliability index and critical slip surface.@en

This paper presents a new method for applying reliability-based design approaches to slope stability analysis. In this method the soil properties are considered to be random variables. The factor of safety of the slope is found using Bishop's simplified method for noncircular slip surfaces. By considering the variability of the soil properties, the probability of failure is determined from the reliability index (β). The minimization problem (determination of the lowest β value for the range of variables and possible slip surfaces considered) is solved using a genetic algorithm approach, which simultaneously locates the critical slip surface and determines the reliability index. The performance of the new method is compared to some existing reliability approaches when applied to case histories of slope failures from the geotechnical literature. The new approach is seen to provide reasonable and consistent estimates of the reliability index and critical slip surface.@en

Assessment of the stability of embankment and cut slopes over the life of a project are critical issues for railway and motorway infrastructure projects. Experience has shown that many slope failures occur during or shortly after rainfall. Analyses show that failure is initiated by the reduction in near surface suction over some critical depth in the slope. A simple method is proposed in this paper to estimate the time needed for a wetting front to develop. The method which is a modification of the traditional Green-Ampt infiltration model assumes that ponding of water cannot occur on soil slopes and as a consequence soil in the wetted zone remains partially saturated at the point of slope failure. It differentiates between cases where the initial suction in the slope is high and the rate of infiltration is controlled by the rainfall intensity (supply controlled) and, situations where the suction is low, and the rate of infiltration is controlled by the infiltration capacity of the soil (demand controlled). When applied to a case history where field measurements of infiltration into a slope were available the new method provided a reasonable approximation of the measured infiltration time.@en

Assessment of the stability of embankment and cut slopes over the life of a project are critical issues for railway and motorway infrastructure projects. Experience has shown that many slope failures occur during or shortly after rainfall. Analyses show that failure is initiated by the reduction in near surface suction over some critical depth in the slope. A simple method is proposed in this paper to estimate the time needed for a wetting front to develop. The method which is a modification of the traditional Green-Ampt infiltration model assumes that ponding of water cannot occur on soil slopes and as a consequence soil in the wetted zone remains partially saturated at the point of slope failure. It differentiates between cases where the initial suction in the slope is high and the rate of infiltration is controlled by the rainfall intensity (supply controlled) and, situations where the suction is low, and the rate of infiltration is controlled by the infiltration capacity of the soil (demand controlled). When applied to a case history where field measurements of infiltration into a slope were available the new method provided a reasonable approximation of the measured infiltration time.@en

This paper describes the development of a probabilistic design approach to analyse the stability of unsaturated soil slopes. Instability of unsaturated soil slopes is caused by the downwards progression of a wetting front, which reduces the near-surface suctions, increases the weight of soil in the failure zone and reduces the soil strength. Assuming the slip surface forms parallel to the slope surface (at a depth equal to the wetting front depth) the probability of failure is determined in this paper through the reliability index determined using a computationally efficient genetic algorithm method.@en

This paper describes the development of a probabilistic design approach to analyse the stability of unsaturated soil slopes. Instability of unsaturated soil slopes is caused by the downwards progression of a wetting front, which reduces the near-surface suctions, increases the weight of soil in the failure zone and reduces the soil strength. Assuming the slip surface forms parallel to the slope surface (at a depth equal to the wetting front depth) the probability of failure is determined in this paper through the reliability index determined using a computationally efficient genetic algorithm method.@en

Simple limit equilibrium analyses can be performed to determine the Factor of Safety (FOS) against slope failure of unsaturated soil slopes. However, many of the input parameters needed for these analyses are highly variable, and the FOS value obtained is critically dependent on assumptions made by the designer. This paper describes a suite of reliability analyses on unsaturated soil slopes performed using an invariant reliability model. The results are presented in design charts from which a designer can choose the FOS value required to ensure a given target reliability index for a slope. The approach ensures that despite the variability of input parameters the slope will have a probability of failure of 2.23% or less.@en

Simple limit equilibrium analyses can be performed to determine the Factor of Safety (FOS) against slope failure of unsaturated soil slopes. However, many of the input parameters needed for these analyses are highly variable, and the FOS value obtained is critically dependent on assumptions made by the designer. This paper describes a suite of reliability analyses on unsaturated soil slopes performed using an invariant reliability model. The results are presented in design charts from which a designer can choose the FOS value required to ensure a given target reliability index for a slope. The approach ensures that despite the variability of input parameters the slope will have a probability of failure of 2.23% or less.@en

Modern engineered slopes are designed to exceed certain safety targets set out in design codes. This is in stark contrast to earthen infrastructure inherited from the 18th century which typically was constructed in a haphazard manner without design. This infrastructure seldom meets modern deterministic guidelines yet clearly exhibits some degree of safety, as a failure has not occurred in the intervening years. This paper highlights the use of reliability theory for evaluating the stability of existing engineered slopes. A comprehensive review of geotechnical uncertainty and existing reliability based techniques are outlined. Furthermore, the paper highlights the issue of finding the critical slip surface and gives a brief summary of the current state of the art. Finally a case study of an Irish railway embankment is presented and both a deterministic and reliability analysis is performed on it highlighting the benefits of probabilistic methods over traditional techniques.@en

This paper describes a simple model which can be used to estimate the time needed for a wetting front to develop in an unsaturated soil slope. The model is an extended form of the traditional Green-Ampt method. The first extension recognises that ponding of water cannot occur on a soil slope. It further allows the user to indirectly account for antecedent rainfall conditions by separating slopes into two categories depending on their initial suction profiles. In the first category, where the initial suctions are large, the rate of the development of the wetting front depth is controlled by the rainfall intensity. In the second, where the initial suction is low, the time taken for a wetting front to develop to a given depth depends on the infiltration capacity of the soil. In the final section of the paper results from the new model are compared to numerical predictions of wetting front depth in a fine sand slope.@en