A modelling language for the resilience assessment of networked systems of systems

Systems of Systems (SoS) present challenging features and existing tools result often inadequate for their analysis, especially for heteregeneous networked infrastructures. Most accident scenarios in networked systems cannot be addressed by a simplistic black or white (i.e. functioning or failed) approach. Slow deviations from nominal operation conditions may cause degraded behaviours that suddenly end up into unexpected malfunctioning, with large portions of the network affected. In this paper,we present a language for modelling networked SoS. The language makes it possible to represent interdependencies of various natures, e.g. technical, organizational and human. The representation of interdependencies is based on control relationships that exchange physical quantities and related information. The language also makes it possible the identification of accident scenarios, by representing the propagation of failure events throughout the network. The results can be used for assessing the effectiveness of those mechanisms and measures that contribute to the overall resilience, both in qualitative and quantitative terms. The presented modelling methodology is general enough to be applied in combination with already existing system analysis techniques, such as risk assessment, dependability and performance evaluation

Spatial variability patterns of some Vertisol properties at a field scale using standardized data

Spatial variability of Vertisol properties is relevant for identifying those zones with physical degradation. In this sense, one has to face the problem of identifying the origin and distribution of spatial variability patterns. The objectives of the present work were (i) to quantify the spatial structure of different physical properties collected from a Vertisol, (ii) to search for potential correlations between different spatial patterns and (iii) to identify relevant components through multivariate spatial analysis. The study was conducted on a Vertisol (Typic Hapludert) dedicated to sugarcane (Saccharum officinarum L.) production during the last sixty years. We used six soil properties collected from a squared grid (225 points) (penetrometer resistance (PR), total porosity, fragmentation dimension (Df), vertical electrical conductivity (ECv), horizontal electrical conductivity (ECh) and soil water content (WC)). All the original data sets were z-transformed before geostatistical analysis. Three different types of semivariogram models were necessary for fitting individual experimental semivariograms. This suggests the different natures of spatial variability patterns. Soil water content rendered the largest nugget effect (C0 = 0.933) while soil total porosity showed the largest range of spatial correlation (A = 43.92 m). The bivariate geostatistical analysis also rendered significant cross-semivariance between different paired soil properties. However, four different semivariogram models were required in that case. This indicates an underlying co-regionalization between different soil properties, which is of interest for delineating management zones within sugarcane fields. Cross-semivariograms showed larger correlation ranges than individual, univariate, semivariograms (A ≥ 29 m). All the findings were supported by multivariate spatial analysis, which showed the influence of soil tillage operations, harvesting machinery and irrigation water distribution on the status of the investigated area.

Baseline of soil CO2 flux in the Hontomin site (Burgos, Spain)

Baseline of soil CO2 flux in the Hontomin site (Burgos, Spain)

Resilience analysis of networked systems-of-systems based on structural and dynamic interdependencies

Critical infrastructures support everyday activities in modern societies, facilitating the exchange of services and quantities of various nature. Their functioning is the result of the integration of diverse technologies, systems and organizations into a complex network of interconnections. Benefits from networking are accompanied by new threats and risks. In particular, because of the increased interdependency, disturbances and failures may propagate and render unstable the whole infrastructure network. This paper presents a methodology of resilience analysis of networked systems of systems. Resilience generalizes the concept of stability of a system around a state of equilibrium, with respect to a disturbance and its ability of preventing, resisting and recovery. The methodology provides a tool for the analysis of off-equilibrium conditions that may occur in a single system and propagate through the network of dependencies. The analysis is conducted in two stages. The first stage of the analysis is qualitative. It identifies the resilience scenarios, i.e. the sequence of events, triggered by an initial disturbance, which include failures and the system response. The second stage is quantitative. The most critical scenarios can be simulated, for the desired parameter settings, in order to check if they are successfully handled, i.e recovered to nominal conditions, or they end into the network failure. The proposed methodology aims at providing an effective support to resilience-informed design.

Lacunarity of the Spatial Distributions of Soil Types in Europe.

Lacunarity as a means of quantifying textural properties of spatial distributions suggests a classification into three main classes of the most abundant soils that cover 92% of Europe. Soils with a well-defined self-similar structure of the linear class are related to widespread spatial patterns that are nondominant but ubiquitous at continental scale. Fractal techniques have been increasingly and successfully applied to identify and describe spatial patterns in natural sciences. However, objects with the same fractal dimension can show very different optical properties because of their spatial arrangement. This work focuses primary attention on the geometrical structure of the geographical patterns of soils in Europe. We made use of the European Soil Database to estimate lacunarity indexes of the most abundant soils that cover 92% of the surface of Europe and investigated textural properties of their spatial distribution. We observed three main classes corresponding to three different patterns that displayed the graphs of lacunarity functions, that is, linear, convex, and mixed. They correspond respectively to homogeneous or self-similar, heterogeneous or clustered and those in which behavior can change at different ranges of scales. Finally, we discuss the pedological implications of that classification.

Fractal analysis of laplacian pyramidal filters applied to segmentation of soil images

The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter ?. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results.

Differential resultants of super essential systems of linear OD-polynomials

The sparse differential resultant dres(P) of an overdetermined system P of generic nonhomogeneous ordinary differential polynomials, was formally defined recently by Li, Gao and Yuan (2011). In this note, a differential resultant formula dfres(P) is defined and proved to be nonzero for linear "super essential" systems. In the linear case, dres(P) is proved to be equal, up to a nonzero constant, to dfres(P*) for the supper essential subsystem P* of P.

Decoupling of soil nutrient cycles as a function of aridity in global drylands

The biogeochemical cycles of carbon (C), nitrogen (N) and phosphorus (P) are interlinked by primary production, respiration and decomposition in terrestrial ecosystems. It has been suggested that the C, N and P cycles could become uncoupled under rapid climate change because of the different degrees of control exerted on the supply of these elements by biological and geochemical processes. Climatic controls on biogeochemical cycles are particularly relevant in arid, semi-arid and dry sub-humid ecosystems (drylands) because their biological activity is mainly driven by water availability. The increase in aridity predicted for the twenty-first century in many drylands worldwide may therefore threaten the balance between these cycles, differentially affecting the availability of essential nutrients. Here we evaluate how aridity affects the balance between C, N and P in soils collected from 224 dryland sites from all continents except Antarctica. We find a negative effect of aridity on the concentration of soil organic C and total N, but a positive effect on the concentration of inorganic P. Aridity is negatively related to plant cover, which may favour the dominance of physical processes such as rock weathering, a major source of P to ecosystems, over biological processes that provide more C and N, such as litter decomposition. Our findings suggest that any predicted increase in aridity with climate change will probably reduce the concentrations of N and C in global drylands, but increase that of P. These changes would uncouple the C, N and P cycles in drylands and could negatively affect the provision of key services provided by these ecosystems.

Morphological Functions with Parallel Sets for the Pore Space of X-ray CT Images of Soil Columns

During the last few decades, new imaging techniques like X-ray computed tomography have made available rich and detailed information of the spatial arrangement of soil constituents, usually referred to as soil structure. Mathematical morphology provides a plethora of mathematical techniques to analyze and parameterize the geometry of soil structure. They provide a guide to design the process from image analysis to the generation of synthetic models of soil structure in order to investigate key features of flow and transport phenomena in soil. In this work, we explore the ability of morphological functions built over Minkowski functionals with parallel sets of the pore space to characterize and quantify pore space geometry of columns of intact soil. These morphological functions seem to discriminate the effects on soil pore space geometry of contrasting management practices in a Mediterranean vineyard, and they provide the first step toward identifying the statistical significance of the observed differences.

Discrete Multi-Criteria Methods for lands use and conservation planning on La Colacha in Arroyos Menores (Río Cuarto, Province of Córdoba, Argentina)

The study area is La Colacha sub-basins from Arroyos Menores basins, natural areas at West and South of Río Cuarto in Province of Córdoba of Argentina, fertile with loess soils and monsoon temperate climate, but with soil erosions including regressive gullies that degrade them progressively. Cultivated gently since some hundred sixty years, coordinated action planning became necessary to conserve lands while keeping good agro-production. The authors had improved data on soils and on hydrology for the study area, evaluated systems of soil uses and actions to be recommended and applied Decision Support Systems (DSS) tools for that, and were conducted to use discrete multi-criteria models (MCDM) for the more global views about soil conservation and hydraulic management actions and about main types of use of soils. For that they used weighted PROMETHEE, ELECTRE, and AHP methods with a system of criteria grouped as environmental, economic and social, and criteria from their data on effects of criteria. The alternatives resulting offer indication for planning depending somehow on sub basins and on selections of weights, but actions for conservation of soils and water management measures are recommended to conserve the basins conditions, actually sensibly degrading, mainly keeping actual uses of the lands.

Mapping variability of soil water content and flux across 1¿1000 m scales using the actively heated fiber optic method

The Actively Heated Fiber Optic (AHFO) method is shown to be capable of measuring soil water content several times per hour at 0.25 m spacing along cables of multiple kilometers in length. AHFO is based on distributed temperature sensing (DTS) observation of the heating and cooling of a buried fiber-optic cable resulting from an electrical impulse of energy delivered from the steel cable jacket. The results presented were collected from 750 m of cable buried in three 240 m colocated transects at 30, 60, and 90 cm depths in an agricultural field under center pivot irrigation. The calibration curve relating soil water content to the thermal response of the soil to a heat pulse of 10 W m−1 for 1 min duration was developed in the lab. This calibration was found applicable to the 30 and 60 cm depth cables, while the 90 cm depth cable illustrated the challenges presented by soil heterogeneity for this technique. This method was used to map with high resolution the variability of soil water content and fluxes induced by the nonuniformity of water application at the surface.

Nematodes as indicators of the effect of soil fumigants on soil functioning

Debido al futuro incierto de la mayor parte de los fumigantes edáficos usados actualmente en la Unión Europea, que pueden implicar riesgos para la salud humana/animal y el medio ambiente, es necesario desarrollar programas de manejo integrado para el control de plagas de cultivos. Estos programas se incluyen como obligatorios en el Reglamento (EC) No. 1107/2009. De acuerdo con este Reglamento, es obligatoria la evaluación del riesgo asociado al uso de productos fitosanitarios sobre los organismos edáficos no diana y sus funciones, además de llevar a cabo ensayos con diferentes especies indicadoras para obtener datos de toxicidad que puedan ser usados posteriormente en la evaluación de riesgo. Sin embargo, la baja representatividad de algunas de estas especies indicadoras en el área Mediterránea supone una gran limitación. En esta situación, el Panel Científico de Productos Fitosanitarios y sus Residuos de la Autoridad Europea en Seguridad Alimentaria (EFSA), ha señalado la necesidad de modificar los datos ecotoxicológicos requeridos para evaluar los efectos adversos de los productos fitosanitarios de una manera más integrada, incluyendo criterios funcionales y estructurales mediante organismos como bacterias, hongos, protozoos y nematodos. De este modo, la EFSA ha recomendado el uso de los nematodos en la evaluación de la funcionalidad y estructura del suelo. Los nematodos están globalmente distribuidos y son morfológicamente diversos; esto junto con su gran abundancia y diversidad de respuestas a las perturbaciones edáficas, los convierte en indicadores adecuados del estado del suelo. Puesto que los nematodos interaccionan con muchos otros organismos que participan en diferentes eslabones de la red trófica edáfica, jugando papeles importantes en procesos edáficos esenciales en los agroescosistemas, la diversidad de nematodos es, a menudo, usada como indicador biológico de los efectos de las prácticas agrícolas en el estado del suelo. En los últimos años, diferentes índices basados en la comunidad nematológica han facilitado la interpretación de datos complejos sobre la ecología del suelo. Los índices de la red trófica edáfica, basados en la abundancia de grupos funcionales definidos como grupos C-P y grupos tróficos, permiten la evaluación de la funcionalidad de la red trófica edáfica. Por otra parte, la dificultad en la identificación taxonómica de nematodos para explicar su uso limitado como indicadores ecológicos, es ampliamente discutida, y existe cierta controversia en cuanto a la eficacia de los diferentes métodos de identificación de nematodos. Se argumenta que la identificación morfológica es difícil y puede llevar mucho tiempo debido a la falta de expertos especializados, y se afirma que las técnicas moleculares pueden resolver algunas limitaciones de las técnicas morfológicas como la identificación de juveniles. Sin embargo, los métodos de identificación molecular tienen también limitaciones; la mayoría de las bases de datos de secuencias de ADN están fuertemente orientadas hacia los nematodos fitoparásitos, los cuales representan sólo una parte de la comunidad edáfica de nematodos, mientras que hay poca información disponible de nematodos de vida libre a pesar de representar la mayoría de los nematodos edáficos. Este trabajo se centra en el estudio de los efectos de fumigantes edáficos en la funcionalidad del suelo a través del uso de diferentes indicadores basados en la comunidad de nematodos, como los índices de la red trófica, índices de diversidad, abundancia de los taxones más relevantes etc. También se han analizado otros indicadores funcionales relacionados con la supresividad edáfica, el ciclo de nutrientes o la actividad de la microfauna del suelo. En el capítulo 1, la diversidad de nematodos estudiada en una explotación comercial de fresa y sus alrededores durante dos campañas consecutivas en el suroeste español, fue baja en los suelos fumigados con fumigantes químicos ambas campañas y, aunque se observó una recuperación a lo largo de la campaña en la zona tratada, los suelos fumigados mostraron una condición perturbada permanente. La comunidad de nematodos estuvo más asociada al ciclo de nutrientes en la zona sin cultivar que en los suelos cultivados, y se observó poca relación entre la biomasa de las plantas y la estructura de la comunidad de nematodos. Los surcos sin tratar dentro de la zona de cultivo funcionaron como reservorio tanto de nematodos fitoparásitos como beneficiosos; sin embargo estas diferencias entre los surcos y los lomos de cultivo no fueron suficientes para mantener la supresividad edáfica en los surcos. Los suelos tratados fueron menos supresivos que los suelos sin tratar, y se observaron correlaciones positivas entre la supresividad edáfica y la estructura de la red trófica edáfica y la diversidad de nematodos. En el capítulo 2, se evaluaron los efectos de dos pesticidas orgánicos con efecto nematicida y dos nematicidas convencionales sobre las propiedades físico químicas del suelo, la diversidad de nematodos y la biomasa de las plantas en condiciones experimentales en dos tipos de suelo: suelos agrícolas poco diversos y suelos provenientes de una zona de vegetación natural muy diversos. El mayor efecto se observó en el tratamiento con neem, el cual indujo un gran incremento en el número de dauerlarvas en los suelos pobres en nutrientes, mientras que el mismo tratamiento indujo un incremento de poblaciones de nematodos bacterívoros, más estables y menos oportunistas, en los suelos del pinar ricos en materia orgánica. En el capítulo 3, se comparó la eficacia de métodos moleculares (TRFLP, Terminal Restriction Fragment Length Polymorphism) y morfológicos (microscopía de alta resolución) para la identificación de diferentes comunidades denematodos de España e Irlanda. Se compararon estadísticamente las diferencias y similitudes en la diversidad de nematodos, otros indicadores ecológicos y de la red trófica edáfica. Las identificaciones mediante el uso de TRFLP sólo detectó un porcentaje de los taxones presentes en las muestras de suelo identificadas morfológicamente, y los nematodos omnívoros y predadores no fueron detectados molecularmente en nuestro estudio. Los índices calculados en base a los nematodos micróboros mostraron más similitud cuando se identificaron morfológica y molecularmente que los índices basados en grupos tróficos más altos. Nuestros resultados muestran que, al menos con la técnica usada en este estudio, la identificación morfológica de nematodos es una herramienta fiable y más precisa que la identificación molecular, puesto que en general se obtiene una mayor resolución en la identificación de nematodos. En el capítulo 4, se estudiaron también los efectos de los nematicidas químicos sobre la comunidad de nematodos y la biomasa de las plantas en condiciones experimentales de campo, donde se aplicaron en una rotación de cultivo judía-col durante un ciclo de cultivo. Se aplicaron dos tipos de enmiendas orgánicas con el objetivo de mitigar el efecto negativo de los productos fitosanitarios sobre la diversidad edáfica. El efecto de los nematicidas sobre las propiedades del suelo y sobre la comunidad de nematodos fue más agudo que el efecto de las enmiendas. La incorporación de los restos de cosecha al final del ciclo de cultivo de la judía tuvo un gran efecto sobre la comunidad de nematodos, y aunque el número total de nematodos incrementó al final del experimento, se observó una condición perturbada permanente de la red trófica edáfica a lo largo del experimento. ABSTRACT Due to the uncertain future of the soil fumigants most commonly used in the EU, that might involve risks for human/animal health and the environment, there is a need to develop new integrated pest management programs, included as mandatory in the Regulation (EC) No. 1107/2009, to control crop diseases. According to this Regulation, evaluating the risk associated to the use of the plant production products (PPP) on non-target soil fauna and their function, and developing assays with different indicator species to obtain toxicity data to be used in the risk evaluation is mandatory. However, the low representativeness of some of these indicator species in the Mediterranean area is a relevant limitation. In this situation, the Scientific Panel of Plant Protection Products and their Residues of the European Food Safety Authority (EFSA) has pointed out the necessity of modifying the ecotoxicological data set required to evaluate non-target effects of PPP in a more integrated way, including structural and functional endpoints with organism such as bacteria, fungi, protists and nematodes. Thus, EFSA has recommended the use of nematodes in the assessment of the functional and structural features of the soil. Nematodes are globally distributed and morphologically diverse, and due to their high abundance and diversity of responses to soil disturbance, they are suitable indicators of the soil condition. Since nematodes interact with many other organisms as participants in several links of the soil food web, playing important roles in essential soil processes in agroecosystems, nematode diversity is often used as a biological indicator of the effects of agricultural practices on soil condition. In the last years, various indices based on soil nematode assemblages, have facilitated the interpretation of complex soil ecological data. Soil food web indices based on the abundances of functional guilds defined by C-P groups and trophic groups, permit evaluating soil food web functioning. On the other hand, the difficulty of nematode taxonomical identification is commonly argued to explain their limited used as ecological indicators, and there is a certain controversy in terms of the efficacy of various nematode identification methods. It is argued that the morphological identification is difficult and time consuming due to the lack of specialist knowledge, and it is claimed that molecular techniques can solve some limitations of morphological techniques such as the identification of juveniles. Nevertheless, molecular identification methods are limited too, since most of the DNA-based databases are strongly oriented towards plant-parasitic nematodes that represent only a fraction of the soil nematode community, while there is little information available on free-living nematodes, which represent most soil nematodes. This work focuses on the study of the effects of soil fumigants on soil functioning through the use of different indicators based on soil nematode community as soil food web indices, diversity indices, the abundance of more relevant taxa etc. Other functional indicators related to soil suppressiveness, nutrient cycling, or the activity of soil microfauna have been also studied. In chapter 1, nematode diversity assessed in a commercial strawberry farm and its surroundings for two consecutive growing seasons in southern Spain, was low in fumigated soils with chemical pesticides throughout both seasons and, although yearly recovery occurred within the treated fields, fumigated soils showed a permanent perturbed condition. The nematode community was more closely associated to nutrient cycling in the non-cropped than in the cropped soils, and the link between plant biomass and nematode community structure was weak. Non-treated furrows within the treated fields were a reservoir of both beneficial and plant-parasitic nematodes, but such difference between furrows and beds was not enough to maintain more suppressive soil assemblages in the furrows. Treated soils were less suppressive than unmanaged soils, and there was a positive and significant correlation between soil suppressiveness and soil food web structure and diversity. In chapter 2, the effects of two organic pesticides with nematicide effect and two chemical nematicides on soil physicalchemical properties, soil nematode diversity and plant biomass in experimental conditions were assessed in two types of soils: low diversity soils from an agricultural farm, and high diversity soils from a natural vegetation area. The larger effect was observed on the neem treatment, which induced a large boost of dauer juveniles in the nutrient-depleted soil, while the same treatment induced the increase of more stable, less opportunistic, populations of generalist bacterivore nematodes in the pine forest soil, rich in organic matter. In chapter 3, comparison of the efficiency of molecular (TRFLP, Terminal Restriction Fragment Length Polymorphism) and morphological (microscopy at high magnification) identification methods was carried out in different nematode communities from five sites of different land uses in Spain and Ireland. Differences and similarities on nematode diversity and other ecological and soil food web indices assessed by both methods, were statistically compared. Molecular identification with TRFLP only detected a percentage of the taxa present in the soil samples identified morphologically, and omnivores and predators were not detected molecularly in our study. Indices involving microbial feeding nematodes were more similar between identification methods than indices involving higher trophic links. Our results show that, at least with the technique used in this study, identifying nematodes morphologically is a reliable and more precise identification tool than molecular identification, since a higher taxonomic resolution is in general obtained compared to TRFLP. In chapter 4, the effect of chemical nematicides on nematode community descriptors and plant biomass was also studied in field conditions in an experimental area in which dazomet and dimethyl disulfide was applied in a bean-cabbage rotation system for a single season. Organic amendments were incorporated into the soil with the aim of mitigate the negative effect of the pesticides on soil diversity. The effect of the nematicides was much more noticeable than the effect of the amendments on soil properties and nematode community descriptors. The incorporation of bean crop residues into the soil at the end of bean crop cycle affected soil nematode community descriptors to a great extent, and although total number of nematodes increased at the end of the experiment, a permanent perturbed soil food web condition was observed along the experiment.

Values of the deformation modulus of soil at different ways of determining this amount

In accordance with Russian, Kazakh and European building regulations, the deformation modulus of soil should be determined in the laboratory and also apply in situ soil tests on the stages of engineering geology prospecting. In this paper we present data on the determination and adjustment of the deformation characteristics at different stages of construction

Variability of Arundo donax growth in dry-farming as a function of soil properties

Arundo donax L., commonly known as giant reed or arundo, is a perennial rhizomatous grass that has been studied since the decade of 1980 for bioenergy. In the Mediterranean region -characterised by dry and hot summers- arundo is usually grown with the support of irrigation. However, there is evidence that this plant species can tolerate dry-farming conditions once the crop is fully established. In this work the variation observed in plant growth of a 5-year-old arundo crop when the management changed from irrigated to dry-farming, is assessed. The hypothesis underlying this work was that punctual variations of soil properties might be responsible for the differences observed in plant growth

Influence of soil stiffness on the dynamic response of an offshore wind turbine

La industria de la energía eólica marina ha crecido de forma significativa durante los últimos 15 años, y se espera que siga creciendo durante los siguientes. La construcción de torres en aguas cada vez más profundas y el aumento en potencia y tamaño de las turbinas han creado la necesidad de diseñar estructuras de soporte cada vez más fiables y optimizadas, lo que requiere un profundo conocimiento de su comportamiento. Este trabajo se centra en la respuesta dinámica de una turbina marina con cimentación tipo monopilote y sobre la que actúa la fuerza del viento. Se han realizado cálculos con distintas propiedades del suelo para cubrir un rango de rigideces que va desde una arena muy suelta a una muy densa. De este modo se ha analizado la influencia que tiene la rigidez del suelo en el comportamiento de la estructura. Se han llevado a cabo análisis estáticos y dinámicos en un modelo de elementos finitos implementado en Abaqus. El desplazamiento en la cabeza de la torre y la tensión en su base se han obtenido en función de la rigidez del suelo, y con ellos se ha calculado la amplificación dinámica producida cuando la frecuencia natural del sistema suelo‐cimentación torre se aproxima a la frecuencia de la carga. Dos diferentes enfoques a la hora de modelizar el suelo se han comparado: uno utilizando elementos continuos y otro utilizando muelles elásticos no lineales. Por último, un análisis de fiabilidad se ha llevado a cabo con un modelo analítico para calcular la probabilidad de resonancia del sistema, en el que se han considerado las propiedades de rigidez del suelo como variables aleatorias. Offshore wind energy industry has experienced a significant growth over the past 15 years, and it is expected to continue its growth in the coming years. The expansion to increasingly deep waters and the rise in power and size of the turbines have led to a need for more reliable and optimized support designs, which requires an extensive knowledge of the behaviour of these structures. This work focuses on the dynamic response of an offshore wind turbine founded on a monopile and subjected to wind loading. Different soil properties have been considered in order to cover the range of stiffness from a very loose to a very dense sand. In this way, the influence of stiffness on the structure behaviour has been assessed. Static and dynamic analyses have been carried out by means of a finite element model implemented in Abaqus. Head displacement and stress at the tower base have been obtained as functions of soil stiffness, and they have been used to calculate the dynamic amplification that is produced when the natural frequency of the system soil‐foundation‐tower approaches the load frequency. Two different approaches of soil modelling have been compared: soil modelled as a continuum and soil simulated with non linear elastic springs. Finally, a reliability analysis to assess the probability of resonance has been performed with an analytical model, in which soil stiffness properties are considered as stochastic variables.