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In this paper the static and seismic values of bearing capacity factors for shallow strip foundations adjacent to slopes have been evaluated using the method of characteristics, accounting, through the pseudo-static approach, for the effect of horizontal and vertical inertia forces arising in the soil and transmitted by the superstructure. Differently from most of the available studies, the effect of the inertia forces in the soil, due to the seismic wave propagation, and the effect of inertia forces acting in the superstructure, due to the structural seismic response, are dealt with independently. It was also demonstrated that the above-mentioned effects can be superimposed without significant error. Original empirical formulas and, in some cases, closed-form solutions, have been provided to calculate bearing capacity factors or suitable corrective coefficients which allow accounting for slope inclination and for horizontal and vertical seismic accelerations in the soil and in the superstructure. The proposed solutions, obtained assuming Hill's and Prandtl's failure mechanisms, have been checked against those obtained through finite-element analyses and compared with results already available in the literature.

The investigation of soil response to dynamic loads is necessary to predict site-specific seismic hazard. This paper presents the results of cyclic and dynamic laboratory tests carried out after the 2016–2017 Central Italy Earthquake sequence, within the framework of the seismic microzonation studies of the most damaged municipalities in the area. The database consists of 79 samples investigated by means of dynamic resonant column tests, cyclic torsional shear tests or cyclic direct simple shear tests. Results are firstly analysed in terms of field and laboratory values of small-strain shear wave velocity, highlighting the influence of the sample disturbance and of the mean effective consolidation pressure. The cyclic threshold shear strains as a function of plasticity index are then compared with findings from the published literature and the outliers are analysed. Subsequently, the dynamic soil behaviour is investigated with reference to the small-strain damping ratio. Differences between results from different tests are analysed in the light of the loading frequencies. Finally, the database is used to develop a predictive model for soil nonlinear curves according to plasticity index, mean effective confining stress, and loading frequency. The model represents a useful tool to predict the nonlinear stress–strain behaviour of Central Italy soils, necessary to perform site-specific ground response analyses.

A rigorous and practical solution aimed at accounting for the effect of groundwater in the assessment of bearing capacity of shallow strip footings in plane strain conditions has been developed using the method of characteristics. A steady water table in the foundation soil is considered and a bearing capacity factor Nγw to be used in the classical trinomial bearing capacity equation is introduced. The proposed bearing capacity factor depends on the angle of shear strength, on the footing roughness and on the water table depth and is also influenced by the soil unit weight. Normalizing Nγw with respect to the bearing capacity factor Nγ computed for the case of dry foundation soil, a corrective coefficient has been introduced for which best-fit empirical relationships have been proposed for both smooth and rough foundations. The size of the plastic mechanism under the footing has also been investigated and equations allowing to evaluate its relevant dimensions have been provided. The proposed solutions have been checked against results obtained via finite element analyses, finding a perfect agreement in terms of both corrective coefficients and shape and size of the soil plastic volume. Finally, the actual bearing capacity problem was solved showing that the trinomial formula, even in presence of a steady water table, still yields conservative values of the bearing capacity.

This paper investigates the combined effect of the vertical component of the input motion and of the weakening effect associated to pore-pressure build-up with reference to a zoned earth dam for which the most recent probabilistic seismic hazard analyses promoted the need of evaluating its seismic performance. The two effects were studied through advanced plane-strain non-linear dynamic analyses using a finite-difference numerical model calibrated on an accurate geotechnical characterisation. The occurrence of ultimate limit states in the dam embankment is checked using sets of horizontal and vertical input motions properly selected to account for possible frequency coupling with the dam. The analysis results are presented and discussed in the paper focusing on (i) the main features of the plastic mechanisms temporarily induced by the seismic actions, (ii) the amplification of the horizontal and vertical accelerations acting in the dam body, (iii) the role of the energy and frequency content of the input motion on the magnitude of earthquake-induced permanent displacements, (iv) the combined effect of frequency coupling and non-linear soil behaviour on the overall dam response.

The paper describes the results of numerical analyses carried out for the assessment of the seismic behavior of the Menta Bituminous Faced Rockfill Dam, located in Italy. The computer code FLAC based on the finite difference method was used to build a numerical model using the standard input data provided in the framework of the 15th ICOLD International Benchmark Workshop on Numerical Analysis of Dams. The behavior of the rockfill material was modelled using an elasto-plastic constitutive model, taking into account the shear modulus reduction and the hysteretic damping caused by the development of cyclic shear strains in the dam body. Constitutive parameters for rockfill were calibrated using the available laboratory data. Dam seismic behavior with respect to the assigned input accelerograms was inspected; in particular, the seismic performance of the dam was assessed evaluating its response in terms of dam crest acceleration and displacements: the latter turned out to be relatively small at the selected shaking scenario. Finally, the dam seismic behavior was analyzed focusing also on the role of the temperature-dependent bituminous facing stiffness and the return period of the seismic input.

The availability of easily accessible databases of earthquake records allows the use of large sets of accelerograms for dynamic analyses of geotechnical systems. However, the selection of acceleration records is influenced by multiple sources of uncertainty related also to the geotechnical properties of the soil deposit which strongly affect the site seismic response. The authors recently proposed a procedure for a proper selection of the input ground motion to be used in 1D seismic site response analyses. An application of the procedure is presented and discussed in the paper highlighting the relevant influence of soil heterogeneity on the results of the accelerograms selection procedure.

In this study, the evaluation of static and seismic bearing capacity factors for a shallow strip footing was carried out by using the method of characteristics, which was extended to the seismic condition by means of the pseudo-static approach. The results, for both smooth and rough foundations, were checked against those obtained through finite element analyses. Under seismic conditions the three bearing capacity problems for N c , N q and N γ were solved independently and the seismic bearing capacity factors were evaluated accounting separately for the effect of horizontal and vertical inertia forces arising in the soil, in the lateral surcharge and in the superstructure. Empirical formulae approximating the extensive numerical results are proposed to compute the static values of N γ and the corrective coefficients that can be introduced in the well-known Terzaghi׳s formula of the bearing capacity to extend its applicability to seismic design of foundations.

In this paper, a method for generating samples of a fully non-stationary zero-mean Gaussian process, having a target acceleration time-history as one of its own samples, is presented. The proposed method requires the following steps: i) divide the time axis of the target accelerogram in contiguous time intervals in which a uniformly modulated process is introduced as the product of a deterministic modulating function per a stationary zero-mean Gaussian sub-process, whose power spectral density (PSD) function is filtered by two Butterworth filters; ii) estimate, in the various time intervals, the parameters of modulating functions by least-square fitting the expected energy of the proposed model to the energy of the target accelerogram; iii) estimate the parameters of the PSD function of the stationary sub-process, once the occurrences of maxima and of zero-level up-crossings of the target accelerogram, in the various intervals, are counted; iv) obtain the evolutionary spectral representation of the fully non-stationary process by adding the various contribution evaluated in the various intervals.

Many existing earth dams have been designed and built worldwide before the establishment of a seismic code, so that it is of relevant interest to evaluate their seismic performance and post-seismic operational conditions. This requires an accurate geotechnical characterisation of the dam and foundation soils, a proper definition of the seismic scenarios at the site of the dam, the use of simplified procedures for screening-level seismic analyses and advanced non-linear dynamic analyses to study the most critical seismic scenarios. This process has been used for the evaluation of the seismic performance of a zoned earth dam located in a high seismic hazard area of Southern Italy. In this paper the available data of historical seismicity at the site of the dam and the results of a probabilistic seismic hazard analysis are first discussed and input ground motions are selected using compatibility criteria with the energy and frequency content of the expected target motion in a range of vibration period relevant for the non-linear response of the dam. Seismic performance of the dam is then evaluated through procedures based on Newmark-type computations, in which permanent displacements are related to ground motion characteristics and to the seismic resistance of the dam, the latter evaluated detecting the earthquake-induced plastic mechanisms and the corresponding critical accelerations. Also, an original improvement of the well-known Makdisi & Seed procedure, was proposed to better capture the actual influence of non-linear soil behaviour in the evaluation of horizontal acceleration and permanent displacements of the crest of the dam. The analysis results pointed out the relevant role of the earthquake-induced shear strength reduction on the dam permanent displacements.

Seismic performance of natural slopes, earth structures and solid-waste landfills can be evaluated through displacement-based methods in which permanent displacements induced by earthquake loading are assumed to progressively develop along the critical sliding surface as a result of transient activation of plastic mechanisms within the soil mass. For sliding mechanisms of general shape the earthquake-induced displacements should be computed using a model that provides a closer approximation of sliding surface. When large permanent displacement are induced by seismic actions, due to substantial shear strength reduction, and significant changes in ground surface occur, an improved estimate of permanent displacement can be obtained using a model which accounts for shear strength reduction and mass transfer between adjacent portions of the slope resulting from geometry changes of ground surface during the seismic event. In this paper, a GLE-based model is proposed for seismic displacement analysis of slopes that accounts for shear strength degradation and for geometry rearrangement. Model accuracy is validated against experimental results obtained from shaking table tests carried out on small scale model slopes. Comparison of computed and experimental results demonstrates the capability of the proposed approach in capturing the main features of the observed seismic response of the model slopes.

In this paper the seismic response of simple slope geometries under vertically propagating in-plane shear waves (SV waves) is assessed through two-dimensional finite element analyses to investigate the amplification of the ground motion induced by soil topography. Topographic horizontal and vertical amplification factors were evaluated through different sets of analyses focused on slopes in homogeneous half space and on slopes overlying either a rigid or a compliant bedrock. Soil was assumed to behave as a linear visco-elastic or as an equivalent-linear visco-elastic material. In the analyses the effects of slope inclination and of the characteristics of the input motion were also investigated. In order to calibrate the numerical model, the results obtained in linear visco-elastic analyses were compared with the results of parametric numerical analyses available in the literature, showing a good agreement. The results confirmed that a complex interaction exists between stratigraphic and topographic effects on the amplification of the ground motion and that the two effects cannot be evaluated independently and easily uncoupled. In the case of compliant bedrock the effect of the impedance ratio was also investigated. The results of the equivalent-linear analyses pointed out the remarkable dependence on soil non-linear behavior and, when compared to the results of linear visco-elastic analyses, showed that without accounting for soil non-linear behavior, topographic amplification factors may result underestimated.

The paper describes a comparison between in situ measurements and theoretical predictions of the ground settlements induced by preloading and vertical drains on a heterogeneous soil deposit. Settlement measurements, normalized with respect to the final value of the consolidation settlements computed using the hyperbolic approach, were compared with an average degree of consolidation predicted by a rigorous theoretical solution accounting for radial and vertical consolidation induced by a time-dependent loading history and including the smear effect. The comparison allowed estimating proper values of the diameter describing the smeared zone and revealed the remarkable influence of the lithological and mechanical heterogeneity of the soil deposit.

The paper presents the results of a physical and mechanical characterization of a compressible and crushable volcanic ash collected during a recent eruptive event of Mount Etna. The characterization of this complex natural material required appropriate equipment, to carry out a comprehensive experimental programme, and a rigorous scientific approach to critically analyze the experimental results and put them in the theoretical framework of soil mechanics and of critical state theory. The experimental activities involved X-ray diffractometry, electron scanning microscopy (SEM) and one-dimensional compression tests carried out on both wet and dry soil specimens characterized by different initial densities. To examine the effects of loading on the evolution of the micro-structure, both the particle size distribution and the particle shape, before and after the tests, were analyzed through a dynamic image analysis using several size and shape parameters. The experimental results show that grain crushing becomes evident at vertical pressures larger than 1 MPa whereas it seems to be progressively inhibited for pressures larger than 10 MPa. Furthermore, regardless the initial void ratio of the soil specimens, at high stresses the obtained non-linear e −log σ′v relationship converges toward a unique limiting compression curve.

The static and seismic sliding limit equilibrium condition of retaining walls is investigated, and analytical solutions for the angle of the active slip surface, the critical acceleration coefficient and the coefficient of active earth pressure are provided for different surcharge conditions. In particular, walls retaining a horizontal backfill without surcharge, walls supporting an extended uniform surcharge applied at different distances from the wall and walls supporting a limited uniform surcharge or linear uniform surcharge parallel to the wall are considered in the analysis. The solutions have been derived in the framework of the limit equilibrium approach, considering the effect of the wall through its weight, and accounting for the shear resistance at the base of the wall and the inertia force arising in the wall under seismic conditions. For the wall without surcharge the effect of the vertical component of the seismic acceleration as well as the effects of the inclination of the wall internal face and of the soil–wall friction were also investigated. The angle of the slip plane, the critical seismic acceleration coefficient and the coefficient of active earth pressure are given as functions of dimensionless parameters and the boundary conditions for the applicability of each solution are specified. The influence of soil weight, surcharge conditions and inertia forces on the active earth pressure coefficient is analysed.

The paper focuses on the seismic performance of the San Pietro dam (located in Southern Italy) evaluated, with different levels of accuracy, through pseudo-static, simplified-displacement and dynamic 2D finite difference analyses. For critical mechanisms, detected through pseudo-static analyses, simplified displacement analyses were performed assessing the horizontal and vertical components of the expected permanent displacements. Dynamic analyses were carried out accounting for non-linear soil behavior under cyclic loading. The adopted input motions consist of several sets of accelerograms selected, from a worldwide database, assuming as a reference the seismicity of the area where the dam is located. The results of the analyses show a satisfactory behavior of the dam for the selected input motions.

Pseudo-static seismic analysis of retaining walls requires the selection of an equivalent seismic coefficient synthetically representing the effects of the transient seismic actions on the soil-wall system. In this paper, a rational criterion for the selection of the equivalent seismic coefficient is proposed with reference to sliding retaining walls. In the proposed approach earthquake-induced permanent displacements are assumed as a suitable parameter to assess the seismic performance and an alternative definition of the wall safety factor is introduced comparing expected and limit values of permanent displacements. Using a simplified displacement prediction model it is shown that, for a given design earthquake, reliable values of the equivalent seismic coefficient should depend on all the factors affecting the stability condition of the soil-wall system and on a threshold value of permanent displacement related to a given ultimate or serviceability limit state. To achieve a match between the results of the pseudo-static and of the displacement-based analysis, the proposed procedure detects the value of the equivalent seismic coefficient for which the two approaches provide the same factor of safety. Thus, without necessarily carrying out a displacement analysis, a measure of the safety condition of a soil-wall system consistent with the actual seismic performance may be achieved through an equivalent pseudo-static analysis.

The method of preloading associated with prefabricated vertical drains was used to accelerate the consolidation process and anticipate the long-term settlements of the foundation soil of two cylindrical oil tanks founded on an alluvial deposit mainly consisting of silty clays. In-situ investigations, including boreholes and cone penetration tests (CPTs), and laboratory tests were carried out to define the geotechnical profile of the construction site and the soil mechanical properties. Dissipation tests were also carried out during the CPTs and allowed evaluating the horizontal consolidation and permeability coefficients through several procedures. An extensive field monitoring of the site was carried out during the embankment construction, the preloading period and, after the embankment removal, during the hydraulic leakage test of the tanks. Differential settlements and angular distortions of the tank foundation evaluated from the measured settlement profiles were compared with expected profile shapes for tanks overlying homogeneous compressible soil layers and with available empirical relationships. A general fair agreement was observed even if the heterogeneity of the alluvial soil deposit affects the tank response. Observed absolute and differential settlements and distortions are consistent with the allowable limits provided by the literature and with the design prescriptions, thus confirming the effectiveness of the preloading and drainage technique adopted in the project and envisaging a satisfactory performance of the tank under service conditions.

This paper describes the application of a methodology for the evaluation of debris-flow risk in alluvial fans by incorporating numerical simulations with Geographical Information Systems to identify potential debris-flow hazard areas. The methodology was applied to a small catchment located in the north-eastern part of Sicily, Italy where an extreme debris flow event occurred in October 2007. The adopted approach integrates a slope stability model that identifies the areas of potential shallow landslides under different meteorological conditions using a two-dimensional finite-element model based on the De Saint Venant equation for the debris-flow propagation. The mechanical properties of the debris were defined using both laboratory and in situ test results. The risk classification of the area under study was derived using total hydrodynamic force per unit width ( impact pressure ) as an indicator for event intensity. Based on the simulation results, a potential risk zone was identified and mapped.

The response of an earth dam to seismic loading is studied through displacement-based analyses and finite element, effective stress dynamic analyses. Displacement-based analyses are carried out using both empirical relationships and the decoupled approach in which the deformable response of the soil is accounted for through ground response analyses, and the resulting accelerograms are used in the sliding block analysis. The FE analyses are carried out using a constitutive model capable to reproduce soil non-linearity, calibrated against laboratory measurements of the stiffness at small strains. The influence of the assumed input motion and bedrock depth on the seismic response of the dam is also studied. The FE analyses permitted evaluation of the overall patterns of the dam behaviour in terms of displacements and of stress, strain and acceleration fields. For any of the seismic scenarios considered in the analyses the performance of the dam was satisfactory in that maximum computed settlements at the crest were considerably smaller than the service freeboard of the dam and limited shear strains were obtained within the dam during earthquake loading. Comparison of FE dynamic analyses with displacement-based analyses allowed predictions from different approaches to be compared. A fair agreement was obtained provided that ground response analysis was accounted for when using the displacement-based approach.

The seismic stability of an earth dam is evaluated via the decoupled displacement analysis using the accelerograms obtained by ground response analysis to compute the earthquake-induced displacements. The response analysis of the dam is carried out under both 1D and 2D conditions, incorporating the non-linear soil behaviour through the equivalent linear method. Ten artificial and five real accelerograms were used as input motions and four different depths were assumed for the bedrock. 1D and 2D response analyses were in a fair agreement with the exception of the top third of the dam where only a 2D modelling of the problem could ensure that the acceleration field is properly described. The acceleration amplification ratio obtained in the 2D analyses was equal to about 2 in all the cases considered, consistently with data from real case histories. The maximum permanent displacements computed by the sliding block analysis were small, being less than 10% of the service freeboard; a satisfactory performance of the dam can then be envisaged for any of the seismic scenarios considered in the analyses.

The effects of earthquake induced pore pressure on seismic and post seismic stability conditions of cohesionless slopes are investigated with reference to the infinite slope scheme. In cohesionless slopes the shear strength reduction caused by pore pressure build-up may lead the slope to a deformation failure or to a flow failure if liquefaction conditions are approached. Two critical values of the seismic induced pore pressure ratio are introduced to evaluate the effect of shear strength reduction on the slope failure mechanism. The results are given in the form of stability charts and a procedure for the evaluation of the seismic stability condition is described. The procedure gives useful information about the failure mechanism that slopes may exhibit and the displacement analysis which should be carried out.

Foundations resting adjacent to the crest of a slope exhibit a smaller bearing capacity respect to the case of horizontal ground. In this paper the static and seismic values of the bearing capacity factor Nγg for shallow strip foundations adjacent to slopes were evaluated using the method of characteristics, extended to the seismic case by means of the pseudo-static approach. Nγg was evaluated for different values of the slope angle and, under seismic conditions, accounting only for the effect of horizontal and vertical inertia forces arising in the foundation soil. The results, for both smooth and rough foundations, are presented and checked against those obtained through finite element analyses.

The paper describes a multi‐block displacement model for the evaluation of seismic permanent displacements of natural slopes with slip surface of general shape. A rigorous limit equilibrium method of stability analysis is considered and an application to an ideal clay slope is presented including the effect of excess pore pressure build‐up on the displacement response.